> ## Documentation Index > Fetch the complete documentation index at: https://docs.sayed.app/llms.txt > Use this file to discover all available pages before exploring further. # Chapter 10: Steel Structures ## 10.1 SCOPE This chapter provides the requirements for the use of structural steel in general building construction including the use of hot rolled steel sections and steel tubes. The provisions are generally applicable to riveted, bolted and welded constructions. Two types of design procedures are covered: Working Stress Design (WSD) method and Load Factor Design (LFD) method. ## 10.2 DEFINITIONS AND NOTATION ### 10.2.1 Definitions For the purpose of this chapter the following definitions shall apply. **BUCKLING LOAD:** The load at which a member or a structure as a whole collapses or buckles in a load test. **EFFECTIVE LATERAL RESTRAINT:** Restraint which provides sufficient resistance against buckling of the compression flange of a loaded strut, beam or girder to either side at the point of its application. **ELASTIC CRITICAL MOMENT:** The elastic moment which will initiate yielding or cause buckling. **FACTOR OF SAFETY:** The factor by which the yield stress of the material of a member is divided to get the permissible stress of that material. **GAUGE:** The transverse spacing between parallel adjacent lines of fasteners. **MAIN MEMBER:** A structural member which is primarily responsible for carrying and distributing the applied load. **PITCH:** The centre to centre distance between individual fasteners in a line. **SECONDARY MEMBER:** A member provided for stability and for restraining the main member from buckling. ### 10.2.2 Notation Symbols used in this chapter shall have the following meaning unless otherwise defined elsewhere in this chapter. * A = cross-sectional area, mm² * Ap = loaded area of concrete, mm² * Ab = nominal body area of a fastener, mm² * Ar = area of an upset rod based upon the major diameter of its threads, mm² * Ac = area of effective concrete flange in composite design, mm² * Ac' = area of concrete, mm² * Af = area of compression flange, mm² * Af = area of flange, mm² * Afe = effective tension flange area, mm² * Afg = gross area of beam flange, mm² * Afn = net flange area of beam, mm² * Ag = gross area, mm² * Ans = net area subject to shear, mm² * App = projected bearing area, mm² * Ar = area of reinforcing bars, mm² * As = area of steel beam in composite design, mm² * As' = area of compressive reinforcing steel, mm² * Asc = cross-sectional area of stud shear connector, mm² * Asy = area of reinforcing steel providing composite action at point of negative moment, mm² * Ast = cross-sectional area of a stiffener or pair of stiffeners, mm² * Asl = area of link stiffener, mm² * Avf = shear area on the failure path, mm² * At = net tension area, mm² * Av = net shear area, mm² * Aw = web area, mm² * Aw = effective area of weld, mm² * Awl = link web area, mm² * Az = area of steel bearing concentrically on a concrete support, mm² * Az2 = total cross-sectional area of a concrete support, mm² * B = factor for bending stress in web-tapered members * B1, B2 = factors used in determining Mn for combined bending and axial forces when first order analysis is employed * Ca = numerical coefficient * Cb = bending coefficient dependent upon moment gradient * Cc = column slenderness ratio separating elastic and inelastic buckling * Ci = slenderness ratio of compression elements * Cm = coefficient applied to bending term in interaction equation for prismatic members and dependent upon column curvature caused by applied moments * Cm' = coefficient applied to bending term in interaction equation for tapered members and dependent upon axial stress at the small end of the member * Cpg = plate girder coefficient * Cp = stiffness factor for primary member in a flat roof * Cs = stiffness factor for secondary member in a flat roof * Cp = ratio of "critical" web stress, according to the linear buckling theory, to the shear yield stress of web material * Cw = warping constant, mm⁶ * C1 = increment used in computing minimum spacing of oversized and slotted holes * C2 = increment used in computing minimum edge distance for oversized and slotted holes * D = outside diameter of tubular member, mm * D = factor depending upon type of transverse stiffeners used * D = dead load due to self weight and permanent elements on the structure * E = modulus of elasticity of steel (200,000 N/mm²) * E = earthquake load (see Sec 2.7) * E' = amplified earthquake load (see Sec 2.7) * Ec = modulus of elasticity of concrete, N/mm² * Em = modified modulus of elasticity, N/mm² * Fa = axial compressive stress permitted in a prismatic member in the absence of moment, N/mm² * Fay = axial compressive stress permitted in a tapered member in the absence of moment, N/mm² * Fb = bending stress permitted in a prismatic member in the absence of axial force, N/mm² * Fby = bending stress permitted in a tapered member in the absence of axial force, N/mm² * FBM = nominal strength of base material to be welded, N/mm² * FEXX = classification strength of weld metal, N/mm² * Fb' = allowable bending stress in compression flange of plate girders as reduced for hybrid girders or because of large web depth to thickness ratio, N/mm² * Fbx, Fby = bending stress permitted in a prismatic member in the absence of axial force about x and y axes respectively, N/mm² * Fcr = critical stress, N/mm² * Fe = elastic buckling stress, N/mm² * Fe' = euler stress for a prismatic member divided by factor of safety, N/mm² * Fex = elastic flexural buckling stress about the major axis, N/mm² * Fey = elastic flexural buckling stress about the minor axis, N/mm² * Fet = elastic torsional buckling stress, N/mm² * Fmy = modified yield stress for composite column, N/mm² * Frn = nominal shear rupture strength, N/mm² * Fr = compressive residual stress in flange, N/mm² * Fp = allowable bearing stress, N/mm² * Fsy = St. Venant torsion resistance bending stress in a tapered member, N/mm² * Ft = allowable axial tensile stress, N/mm² * Fu = specified minimum tensile strength of the type of steel or fastener being used, N/mm² * Fv = allowable shear stress, N/mm² * Fw = nominal strength of weld electrode material, N/mm² * Fwy = flange warping torsion resistance bending stress in a tapered member, N/mm² * Fy = specified minimum yield stress of the type of steel being used, N/mm² * Fyb = specified minimum yield stress of beam, N/mm² * Fyc = specified minimum column yield stress, N/mm² * Fyf = specified minimum yield stress of flange, N/mm² * Fym = yield stress obtained from mill test reports or from physical tests, N/mm² * Fyp = specified minimum yield stress of the longitudinal reinforcing bars, N/mm² * Fys = static yield stress, N/mm² * Fyst = specified minimum yield stress of stiffener, N/mm² * Fyw = specified minimum yield stress of the web, N/mm² * G = shear modulus of elasticity of steel (77220 N/mm²) * H = average storey height above and below a beam to column connection, mm * Hs = length of a stud shear connector after welding, mm * I = moment of inertia, mm⁴ * Id = moment of inertia of steel deck supported on secondary members, mm⁴ per m * Ieff = effective moment of inertia of composite sections for deflection computations, mm⁴ * Ip = moment of inertia of primary members, mm⁴ * Is = moment of inertia of secondary members, mm⁴ * Ist = moment of inertia of steel beam in composite construction, mm⁴ * Ist = moment of inertia of a transverse stiffener, mm⁴ * Itr = moment of inertia of transformed composite section, mm⁴ * Ix, Iy = moment of inertia about the principal axes, mm⁴ * Jc = torsional constant for a section, mm⁴ * K = effective length factor for prismatic member * Ks = slip coefficient * Kt = effective length factor for torsional buckling * Ky = effective length factor for a tapered member * L = unbraced length of tensile members, mm * Lb = unbraced length of member measured between centre of gravity of the bracing members, mm * Lbr = length of bracing member, mm * Lc = distance in line of force from centre of a standard or oversized hole or from the centre of the end of a slotted hole to an edge of a connected part, mm * Lo = live load due to occupancy and moveable equipment * Lp = limiting laterally unbraced length for full plastic bending capacity, uniform moment case (Cb=1.0), mm * Lpd = limiting laterally unbraced length for plastic analysis, mm * Lr = limiting laterally unbraced length for inelastic lateral-torsional buckling, mm * Ls = length of secondary member in flat roof framing, m * Lspace = column spacing perpendicular to direction of girder, mm * M = moment, kNm * Mn = nominal flexural strength of a member or joint, kNm * Mp = plastic bending moment, kNm * Mpc = plastic bending moment modified by axial load ratio, kNm * Mu = required flexural strength of member or joint, kNm * Muy = required flexural strength about the y-axis, kNm * M1 = smaller moment at end of unbraced length of beam - column * M2 = larger moment at one end of three-segment proportion of a tapered member * M2' = larger moment at end of unbraced length of beam - column * Mmax = maximum moment in three adjacent segments of a tapered member * Mcr = elastic buckling moment, kNm * Mlt = required flexural strength in member due to lateral frame translation, kNm * Mn' = nominal flexural strength, kNm * Mn', Mmy = flexural strength for use in alternate interaction equations for combined bending and axial force, kNm * Mnt = required flexural strength in member assuming there is no lateral translation of the frame, kNm * Mp' = plastic bending moment, kNm * Mny' = moment for use in alternate interaction equations for combined bending and axial force, kNm * Mr = limiting buckling moment, Mcr when λ = λr, Cb = 1.0, kNm * Mu = required flexural strength, kNm * My = initial yield bending moment, kNm * N = length of bearing, mm * Np = number of stud shear connectors on a beam in one transverse rib of a metal deck * N1 = number of shear connectors required between point of maximum moment and point of zero moment * N2 = number of shear connectors required between concentrated load and point of zero moment * P = axial load, kN * Pb = force transmitted by a fastener to the critical part, kN * Pf = factored axial load, kN * Pn = normal force, kN * Pn/Vn = ratio of required axial force Pu to nominal shear strength Vn of a link * Pbf = factored beam flange or connection plate force in a restrained connection, kN * Pcr = maximum strength of an axially loaded compression member or beam, kN * Pd = required axial strength of a column resulting from application of dead load, kN * Pe = euler buckling load, kN * Pel = elastic buckling load, kN * Pe' = required axial strength of a column resulting from application of the amplified earthquake load E' * Pl = required axial strength of a column resulting from application of live load L, kN * Pn = nominal axial strength (tension or compression), kN * Ppb = bearing load on concrete, kN * Pu = required axial strength of a column or a link, kN * Pse = required axial strength of a column based on load combination with seismic loads, kN * Py = nominal yield axial strength of a member, Py = 10 FyAg, kN * Qf = full reduction factor for slender compression elements * Qs = ratio of effective profile area of an axially loaded member to its total profile area * Qs' = reduction factor for slender stiffened compression elements * Qsc = nominal strength of one stud shear connector, kN * Qs = axial stress reduction factor where width-thickness ratio of unstiffened elements exceeds noncompact section limits * R = reaction or concentrated load applied to beam or girder, kN * R = earthquake response modification coefficient for structural system given in Table 6.2.24 of Chapter 2, Loads * RN = nominal strength of a member * RPG = plate girder bending strength reduction factor * Rz = hybrid girder factor * Rn = nominal resistance, kN * Rv = web shear strength, kN * S = spacing of secondary members in a flat roof, m * S = elastic section modulus, mm³ * Seff = governing slenderness ratio of tapered member * (Sx)eff = effective section modulus corresponding to partial composite action, mm³ * Sx, Sxc = elastic section modulus about major axis, mm³ * Sx = elastic section modulus referred to tension and compression flanges respectively, mm³ * Sx = elastic section modulus about major axis * Sy = section modulus of steel beam used in composite design referred to the bottom flange, mm³ * Sxc = section modulus of transformed composite section referred to the bottom flange, based upon maximum permitted effective width of concrete flange, mm³ * T = factored applied tension force per bolt, kN * Tb = specified pretension load in a high-strength bolt, kN * Up, Us = ponding stress index for primary and secondary members * V = shear force, kN * Vf = friction force, kN * Vh = total horizontal shear to be resisted by connectors under full composite action, kN * Vhp = total horizontal shear provided by the connectors providing partial composite action, kN * Vn = nominal shear strength, kN * Vu = required shear strength, kN * Vnl = nominal shear strength of an active link, kN * Vind = nominal shear strength of a member modified by the axial load magnitude, kN * X1, X2 = beam buckling factors * Y = ratio of yield stress of web steel to yield stress of stiffener steel * Z = plastic section modulus, mm³ * Zb = plastic section modulus of beam, mm³ * Zc = plastic section modulus of column, mm³ * a = clear distance between transverse stiffeners, mm * a = distance between connectors in a built-up member, mm * a = dimension parallel to the direction of stress, mm * a = shortest distance from edge of pin hole to edge of member measured parallel to direction of force, mm * a' = distance beyond theoretical cut-off point required at ends of welded partial length cover plate to develop stress, mm * aw = ratio of web area to compression flange area * b = actual width of stiffened and unstiffened compression elements, mm * b = dimension normal to the direction of stress, mm * bdf = column flange width, mm * be = effective width of stiffened compression element, mm * be' = reduced effective width for slender compression elements, mm * beff = effective edge distance, mm * bf = flange width, mm * c1, c2, c3 = numerical coefficients * d = depth of beam or girder, mm * dr = diameter of a roller or rocker bearing, mm * db = pin or roller diameter, mm * db = nominal diameter of a fastener, mm * db = overall beam depth, mm * dc = web depth clear of fillets, mm * dco = overall column section depth, mm * dL = depth at the larger end of a tapered member, mm * ds = depth at the smaller end of a tapered member or unbraced segment thereof, mm * dpz = overall panel zone depth between continuity plates, mm * e = EBF link length, mm * fa = axial compression stress on member based on effective area, N/mm² * fc = computed compressive stress in the stiffened element, N/mm² * fa = computed axial stress, N/mm² * fau = computed axial stress at the smaller end of a tapered member or unbraced segment thereof, N/mm² * fb = computed bending stress, N/mm² * fb1 = smallest computed bending stress at one end of a tapered segment, N/mm² * fb2 = largest computed bending stress at one end of a tapered segment, N/mm² * fbl = computed bending stress at the large end of a tapered member or unbraced segment thereof, N/mm² * fbx, fby = computed bending stress in axes x and y respectively, N/mm² * fc' = specified compressive strength of concrete, N/mm² * ft = computed tensile stress, N/mm² * fun = required normal stress, N/mm² * fuw = required shear stress, N/mm² * fvs = computed shear stress, N/mm² * fws = shear between girder web and transverse stiffeners per linear mm of single stiffener or pair of stiffeners, N * g = transverse centre to centre spacing (gauge) of any two consecutive holes, mm * gc = clear distance between flanges of a beam or girder, mm * hc = assumed web depth for stability, mm * hr = nominal rib height for steel deck, mm * ht, hw = factors for web tapered members * im = factor for minimum moment of inertia for a transverse stiffener * k = distance from outer face of flange to web toe of fillet of rolled shape, mm * kc = web plate buckling coefficient * ks = compression element restraint coefficient * kw = shear buckling coefficient for girder webs * l = actual unbraced length of a member, mm * l' = unsupported length of lacing bar, mm * l" = largest laterally unbraced length along either flange at the point of load, mm * lbr = length of bearing, mm * lb = actual unbraced length in plane of bending, mm * lcr = critical unbraced length in plane of bending, mm * m = ratio of web to flange yield stress or critical stress in hybrid beams * n = modular ratio (Ec/Es) * q = allowable horizontal shear to be resisted by a shear connector, kN * r = radius of gyration, mm * rb = radius of gyration about axis of concurrent bending, mm * rn = radius of gyration about axis of concurrent bending at the smaller end of a tapered member or unbraced segment thereof, mm * rl = minimum radius of gyration of individual component in a built-up member, mm * rm = radius of gyration of the steel shape, pipe or tubing in composite columns * rs = radius of gyration at the smaller end of a tapered member, mm * ro = polar radius of gyration about the shear centre, mm * rsx, rsy = radius of gyration about x and y axes at the smaller end of a tapered member respectively, mm * rT = radius of gyration of a section comprising the compression flange plus 3/4 of the compression web area, taken about an axis in the plane of the web, mm * rT0 = radius of gyration at the smaller end of a tapered member or unbraced segment thereof, considering only the compression flange plus 3/4 of the compression web area, taken about an axis in the plane of the web, mm * rx, ry = radius of gyration about the x and y axes respectively, mm * s = longitudinal centre to centre spacing (pitch) of any two consecutive holes, mm * t = compression element thickness, mm * t = thickness of an element part, mm * t = wall thickness of a tubular member, mm * t = thickness of connected part, mm * tc = thickness of the critical part, mm * tfc = flange thickness, mm * tp = thickness of beam flange or moment connection plate at rigid beam to column connection, mm * tpf = thickness of beam flange, mm * tcf = thickness of column flange, mm * tf = flange thickness, mm * tp = thickness of panel zone including doubler plates, mm * tw = web thickness, mm * twc = column web thickness, mm * tpz = thickness of panel zone (doubler plate not necessarily included), mm * w = length of channel shear connectors, mm * wc = unit weight of concrete, kN/m³ * wr = average width of rib or haunch of concrete slab on formed steel deck, mm * wp = width of panel zone between column flanges, mm * xo, yo = coordinates of shear centre with respect to the centroid, mm * z = distance from the smaller end of a tapered member, mm * Δsh = translation deflection of the storey under consideration, mm * η = depth tapering ratio * ηy, ζ = exponents for alternate beam-column interaction equation * λ = slenderness parameter * λc = column slenderness parameter * λc = equivalent slenderness parameter * λeff = effective slenderness ratio * λp = limiting slenderness parameter for compact element * λr = limiting slenderness parameter for noncompact element * ϕ = resistance factor * ϕb = resistance factor for flexure * ϕc = resistance factor for compression * ϕcc = resistance factor for axially loaded composite columns * ϕgf = resistance factor for shear on the failure path * ϕt = resistance factor for tension * ϕv = resistance factor for shear * ϕw = resistance factor for welds * μ = coefficient of friction ## 10.3 MATERIAL ### 10.3.1 Structural Steel Material conforming to one of the following standard specifications is approved for use under the provisions of this Code: * BDS 878: Specification for Weldable Structural Steels. * ASTM A36/A36M: Standard Specification for Structural Steel. * ASTM A53: Standard Specification for Pipe, Steel, Black and Hot-dipped, Zinc-coated Welded and Seamless. * ASTM A242/A242M: Specification for High-strength Low-alloy Structural Steel. * ASTM A441: Standard Specification for High-strength Low-alloy Structural Manganese Vanadium Steel. * ASTM A500: Standard Specification for Cold-formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes. * ASTM A501: Standard Specification for Hot-formed Welded and Seamless Carbon Steel Structural Tubing. * ASTM A514/A514M: Standard Specification for High-yield Strength, Quenched and Tempered Alloy Steel Plate, Suitable for Welding. * ASTM A529/A529M: Standard Specification for Structural Steel with 42 ksi (290 MPa) Minimum Yield Point (1/4 in (13 mm) Maximum Thickness). * ASTM A570/A570M: Standard Specification for Steel, Sheet and Strip, Carbon, Hot-rolled, Structural Quality. * ASTM A572/A572M: Standard Specification for High-strength Low-alloy Columbium-Vanadium Steel of Structural Quality. * ASTM A588/A588M: Standard Specification for High-strength Low-alloy Structural Steel with 50 ksi (345 MPa) Minimum Yield Point to 4 in (100 mm) Thick. * ASTM A606: Standard Specification for Steel, Sheet and Strip, High-strength, Low-alloy, Hot-rolled and Cold-rolled, with Improved Atmospheric Corrosion Resistance. * ASTM A607: Standard Specification for Steel, Sheet and Strip, High-strength, Low-alloy, Columbium or Vanadium, or Both, Hot-rolled and Cold-rolled. * ASTM A618: Standard Specification for Hot-formed Welded and Seamless High-strength Low-alloy Structural Tubing. * ASTM A852: Quenched and Tempered Low-alloy Structural Steel Plate with 70 ksi Minimum Yield Strength to 4 in (100 mm) Thick. Certified mill test reports or certified reports of tests made by the fabricator or a testing laboratory in accordance with ASTM A6 or A568, as applicable, shall constitute sufficient evidence of conformity with one of the above standards. If requested, the fabricator shall provide an affidavit stating that the structural steel furnished meets the requirements of the grade specified. ### 10.3.2 Rivets, Bolts, Washers and Nuts Unidentified steel may be used for unimportant members or details where the precise physical properties and weldability of the steel would not affect the strength of the structure, provided the surface conditions are acceptable according to the criteria specified in ASTM A6. Steel rivets shall conform to ASTM A502: Standard Specification for Steel Structural Rivets. Steel bolts shall conform to one of the following standards: * ASTM A307: Standard Specification for Carbon Steel Bolts and Studs, 60,000 psi Tensile Strength. * ASTM A325: Standard Specification for Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength. * ASTM A449: Standard Specification for Quenched and Tempered Steel Bolts and Studs. * ASTM A490: Standard Specification for Heat-treated Steel Structural Bolts, 150 ksi Minimum Tensile Strength. * ASTM A563: Standard Specification for Carbon and Alloy Steel Nuts. * ASTM F436: Standard Specification for Hardened Steel Washers. A449 bolts are permitted only in connections requiring bolt diameters greater than 38 mm and shall not be used in slip-critical connections. Manufacturer's certification may be accepted as sufficient evidence of conformity with the standards. ### 10.3.3 Anchor Bolts and Threaded Rods Anchor bolt and threaded rod shall conform to one of the following standards: * ASTM A36: Standard Specification for Structural Steel. * ASTM A194/A194M: Standard Specification for Carbon and Alloy Steel Nuts for Bolts for High-pressure and High-temperature Service. * ASTM A354: Standard Specification for Quenched and Tempered Alloy Steel Bolts, Studs and Other Externally Threaded Fasteners. * ASTM A449: Standard Specification for Quenched and Tempered Steel Bolts and Studs. * ASTM A588/A588M: Standard Specification for High-Strength Low alloy Structural Steel with 50 ksi (345 MPa) Minimum Yield Point to 4 in (100 mm) Thick. * ASTM A687: Standard Specification for High-strength Non-headed Steel Bolts and Studs. Threads on bolts and rods shall conform to Unified Standard Series of latest edition of ANSI B18.1 and shall have Class 2A tolerances. A449 material is acceptable for high-strength anchor bolts and threaded rods of any diameter. Manufacturer's certification may be accepted as sufficient evidence of conformity with the standards. ### 10.3.4 Welds Welding electrodes and fluxes shall conform to one of the following specifications of the American Welding Society: * AWS A5.1: Specification for Covered Carbon Steel Arc Welding Electrodes. * AWS A5.5: Specification for Low-alloy Steel Covered Arc Welding Electrodes. * AWS A5.17: Specification for Carbon Steel Electrodes and Fluxes for Submerged-arc Welding. * AWS A5.18: Specification for Carbon Steel Filler Metals for Gas-shielded Arc Welding. * AWS A5.20: Specification for Carbon Steel Electrodes for Flux-cored Arc Welding. * AWS A5.23: Specification for Low-alloy Steel Electrodes and Fluxes for Submerged-arc Welding. * AWS A5.28: Specification for Low-alloy Steel Filler Metals for Gas-shielded Arc Welding. * AWS A5.29: Specification for Low-alloy Steel Electrodes for Flux-cored Arc Welding. Manufacturer's certification may be accepted as sufficient evidence of conformity with the standards. ### 10.3.5 Stud Shear Connectors Steel stud shear connectors shall conform to the requirements of AWS D1.1: Structural Welding Code-Steel. Manufacturer's certification may be accepted as sufficient evidence of conformity with the above standard. ## 10.4 TYPES OF CONSTRUCTION Two basic types of construction and associated design assumptions are permissible both for Working Stress Design method and Load Factor Design method under the conditions stated herein. Each type of construction will govern in a specific manner the size of members and the types and strength of their connections. Both types of construction must comply with the stability requirements of Sec 10.5.2. a) Type FR, fully restrained construction, commonly designated as "rigid-frame" (continuous frame), assumes that beam to column connections have sufficient rigidity to hold the original angles between intersecting members virtually unchanged. b) Type PR, partially restrained construction, assumes that the connections of beams and girders do not have enough rigidity to hold the original angles between intersecting members virtually unchanged. The design of all connections shall be consistent with the assumptions as to the type of construction assumed in the analysis. The use of PR construction depends on the evidence of predictable proportion of full end restraint. Where the connection restraint is ignored, i.e for "simple framing," it is assumed that under gravity loads the ends of the beams and girders are connected for shear only and are free to rotate. For "simple framing" the following requirements shall apply: a) The connections and connected members shall be adequate to carry the gravity loads as simply supported beams. b) The connections and connected members shall be adequate to resist the lateral loads. c) The connections shall have sufficient inelastic rotation capacity to avoid overload of fasteners or welds under combined gravity and lateral loading. When the rotational restraint of the connections is used in the design of the connected members or for the stability of the structure as a whole, the capacity of the connection for such restraint must be established by analytical or empirical means. ## 10.5 FRAMES AND OTHER STRUCTURES ### 10.5.1 General In addition to meeting the requirements of member strength and stiffness, frames and other continuous structures shall be designed to provide the needed deformation capacity and overall frame stability. ### 10.5.2 Frame Stability Stability shall be provided for the whole structure and for each compression element. Considerations shall be given to P-Delta effects resulting from deflected shape of the structure or of individual elements of the lateral load resisting system. #### 10.5.2.1 Braced Frames In frames where lateral stability is provided by diagonal bracing, shear walls or equivalent means, the effective length factor K for compression members shall be taken as unity, unless structural analysis shows that a smaller value may be used. The vertical bracing system for a braced multi-storey frame shall be adequate to prevent buckling and maintain the lateral stability of the structure, including the overturning effects of drift, under the design loads specified in Sec 10.7.2.4 or 10.8.2.4 as the case may be. The vertical bracing system for a multi-storey frame may be considered to function together with shear walls, floor and roof slabs, which are properly secured to the structural frames. The columns, girders, beams and diagonal members, when used as the vertical bracing system, may be considered to comprise a simply connected vertical cantilever truss in the analyses for frame buckling and lateral instability. Axial deformation of all members in the vertical bracing system shall be included in the lateral stability analysis. Girders and beams included in the vertical bracing system of a braced multi-storey frame shall be proportioned for axial force and moment caused by concurrent horizontal and gravity loads. #### 10.5.2.2 Unbraced Frames In frames where lateral stability depends upon the bending stiffness of rigidly connected beams and columns, the effective length factor K of compression members shall be determined by structural analysis and shall not be less than unity. Analysis of unbraced multi-story frames shall include the effects of frame instability and column axial deformation under the design loads specified in Sec 10.7.2.4 or 10.8.2.4 as the case may be. In plastic design the axial force in the columns caused by the combination of gravity and lateral loads specified in Sec 10.8.2.4 shall not exceed 0.75A\g\F\y\. ## 10.6 DESIGN REQUIREMENTS ### 10.6.1 Gross Area The gross area A\g\ of a member at any point is the sum of the products of the thickness and the gross width of each element as measured normal to the axis of the member. ### 10.6.2 Net Area The net area A\n\ of a member is the sum of the products of the thickness and the net width of each element computed as follows: For a chain of holes extending across a part in any diagonal or zigzag line, the net width of the part shall be obtained by deducting from the gross width the sum of the diameters or slot dimensions as provided in Sec 10.9.3.2 of all holes in the chain, and adding, for each gauge space in the chain, the quantity s²/4g. The width of a bolt or rivet hole shall be taken as 1.50 mm greater than the nominal dimension of the hole. For angles, the gauge for holes in opposite adjacent legs shall be taken as the sum of the gauges from the back of the angles less the thickness. The net area of the part is obtained from that chain which gives the least net width. In determining the net area across plug or slot welds, the weld metal shall be ignored. ### 10.6.3 Effective Net Area When the load is transmitted directly to each of the cross-sectional elements by connectors, the effective net area A\e\ is equal to the net area A\n\. When the load is transmitted by bolts or rivets through some but not all of the cross-sectional elements of the member, the effective net area A\e\ shall be computed as: $$ A_e = UA_n $$ (10.6.1) When the load is transmitted by welds through some but not all of the cross-sectional elements of the member, the effective net area A\e\ shall be computed as: $$ A_e = UA_g $$ (10.6.2) where U = reduction coefficient. Unless a larger coefficient can be justified by tests or other rational means the following values of U shall be used: * W, M or S shapes with flange widths not less than 2/3 the depth, and structural tees cut from these shapes, with connection to the flanges. Bolted or riveted connections shall have at least three fasteners per line in the direction of stress. U = 0.90 * W, M or S shapes not meeting the above conditions, structural tees cut from all shapes including built-up cross-sections. Bolted or riveted connections shall have at least three fasteners per line in the direction of stress. U = 0.85 * All members with bolted or riveted connections having only two fasteners per line in the direction of stress. U = 0.75 When load is transmitted by transverse welds to some but not all of the cross-sectional elements of W, M or S shapes and structural tees cut from these shapes, A\e\ shall be taken as the area of the directly connected elements. When the load is transmitted to a plate by longitudinal welds along both edges at the end of the plate, the length of the welds shall not be less than the width of the plate. The effective net area A\e\ shall be computed by Eq (10.6.2). Unless a larger coefficient can be justified by tests or other rational means the following values of U shall be used: i) When l > 2w: U = 1.00 ii) When 2w > l > 1.5w: U = 0.87 iii) When 1.5w > l > w: U = 0.75 where l = weld length, mm w = plate width (distance between welds), mm ### 10.6.4 Rotational Resistance at Points of Support At the points of support, beams, girders and trusses shall be restrained against rotation about their longitudinal axis. Bolted and riveted splice and gusset plates and other connection fittings subject to tensile force shall be designed in accordance with the provisions of Sec 10.7.4.1, where the effective net area shall be taken as the actual net area, except that, for the purpose of design calculations, it shall not be taken more than 85% of the gross area. **Note:** The hot rolled shapes described as W, M or S are specified in ASTM A6/A6M: Standard Specification for General Requirements for Rolled Steel Plates, Shapes, Sheet Piling, and Bars for Structural Use. ### 10.6.5 Limiting Slenderness Ratios For compression members, the slenderness ratio Kl/r shall not exceed 200. If this limit is exceeded, the allowable stress shall not be more than the value obtained from Eq (10.7.2). For tension members the slenderness ratio L/r should preferably not exceed 300. The above limitation shall not be applicable to rods in tension. Members which have been designed to perform as tension members in a structural system, but experience some compression loading, need not satisfy the compression slenderness limit. ### 10.6.6 Simple Spans Beams, girders and trusses designed as simply supported spans shall have an effective length equal to the distance between centres of gravity of the members to which they deliver their end reactions. ### 10.6.7 End Restraint When full or partial end restraint due to continuous, semi-continuous or cantilever action is considered in the design of beams, girders and trusses as well as the sections of the members to which they connect, these shall be designed to carry the shears and moments introduced due to the restraint, in addition to all other forces. The stresses developed shall not exceed at any point the unit stresses prescribed in Sec 10.7.4 through 10.7.6, except that some nonelastic but self-limiting deformations of a part of the connections is permitted when this is essential to avoid overstressing of fasteners. ## 10.7 WORKING STRESS DESIGN METHOD ### 10.7.1 General This section provides the specifications for the design and construction of steel buildings using Working Stress Design method. ### 10.7.2 Basis of Design #### 10.7.2.1 Allowable Stress All structural members, connections and connectors shall be designed so that the stresses due to the service loads and their combinations stipulated in Sec 10.7.2.4 do not exceed the allowable stresses specified in Sec 10.7.4 through 10.7.11 and Sec 10.9. The allowable stresses specified in these sections do not apply to peak stresses in regions of connections (see Sec 10.6.7) for which requirements of Sec 10.7.11 are to be satisfied. #### 10.7.2.2 Stress Increase The maximum permissible increase in the allowable stress shall be 33% when produced by wind or seismic loading, acting alone or in combination with the service dead and live loads as given in Sec 10.7.2.4 provided the required section shall not be less than that required for the service dead and live loads computed without the 33% stress increase. #### 10.7.2.3 Structural Analysis The stresses in members, connections and connectors shall be determined by elastic analysis for the service loads and their combinations specified in Chapter 2, Loads. #### 10.7.2.4 Loads and Load Combinations The design loads shall be the minimum service loads and their combinations as stipulated in Chapter 2, Loads. #### 10.7.2.5 Design for Serviceability The whole structure and the individual members, connections and connectors shall be checked for serviceability according to the requirements of Sec 10.10. ### 10.7.3 Local Buckling #### 10.7.3.1 Classification of Steel Sections Steel sections are classified as compact, noncompact and slender sections. For a section to be compact, its flanges shall be continuously connected to the web or webs and the width-thickness ratio of its compression elements shall not exceed the applicable limiting width-thickness ratios given in Table 6.10.1. Steel section that do not qualify as compact are classified as noncompact when the width-thickness ratios of one or more compression element do not exceed the values shown for noncompact in Table 6.10.1. If the width-thickness ratio of any compression element exceeds the value, the section is classified as a slender section. a) For unstiffened elements which are supported along only one edge, parallel to the direction of the compression force, the width shall be taken in accordance with (i) through (iv) below. **Table 6.10.1: Limiting Width-Thickness Ratios for Compression Elements** | Description of Element | Width-Thickness Ratio | Limiting Width-Thickness Ratios | | | :--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | :-------------------: | :-----------------------------: | :---------------------------: | | | | Compact | Noncompact\(3)\ | | Flanges of I-shaped rolled beams and channels in flexure\(1)\ | b/t | 170/√Fy | 250/√Fy | | Flanges of I-shaped welded beams in flexure | b/t | 170/√Fy | 250/√(Fyf kc)\(5)\ | | Outstanding legs of pairs of angles in continuous contact; angles or plates projecting from rolled beams or columns, stiffeners on plate girders | b/t | NA | 250/√Fy | | Angles or plates projecting from girders, built-up columns or other compression members; compression flanges of plate girders | b/t | NA | 250/√(Fyf kc) | | Stems of tees | d/t | NA | 333/√Fy | | Unstiffened elements simply supported along one edge, such as legs of single angle strutslegs of double-angle struts with separators and cross or star-shaped cross-sections | b/t | NA | 200/√Fy | | Flanges of square and rectangular box and hollow structural sections of uniform thickness subject to bending or compression\<(2)\<; flange cover plates and diaphragm plates between lines of fasteners or welds | b/t | 500/√Fy | 625/√Fy | | Unsupported width of cover plates perforated with a succession of access holes\<(4)\< | b/t | NA | 832/√Fy | | All other uniformly compressed stiffened elements, i.e. supported along two edges | b/t, h/tw | NA | 665/√Fy | | | d/t | 1680/√Fy | - | | Webs in flexural compression\<(1)\< | h/tw | - | 1995/√Fb | | | | | for fa/Fy \< 0.16 | | Webs in combined flexural and axial compression | d/tw | | 1680/√Fy \[1-3.74(fa/Fy)] | | | | | for fa/Fy > 0.16 | | | | | 675/√Fy | | | h/tw | | 1995/√Fb | | Circular hollow sections | | | | |     In axial compression | D/t | 22752/Fy | - | |     In flexure | | 22752/Fy | - | | | | | | | **Notes:** (1) For hybrid beams, use the yield strength of the flange, Fyf instead of Fy | | | | | (2) Assumes net area of plate at widest hole | | | | | (3) For design of slender sections that exceed the noncompact limits see Sec 10.7.5.7. | | | | | (4) See also Sec 10.7.6.5(a) | | | | | (5) kc = 4.05/(h/t)^0.46 if h/t > 70, otherwise kc = 1.0 | | | | For stiffened elements, i.e. supported along two edges parallel to the direction of the compression force, the width shall be taken as follows: i) Clear distance h between flanges for web of rolled, built-up or formed sections. ii) Full nominal depth d for webs of rolled, built-up or formed sections. iii) Distance between adjacent lines of fasteners or lines of welds (b) for flange or diaphragm plates in built-up sections. iv) Clear distance between webs less the inside corner radius on each side for flanges of rectangular hollow structural sections. If the corner radius is not known, the flat width may be taken as the total section width minus three times the thickness. For tapered flanges of rolled sections, the thickness is the nominal value half-way between the free edge and the corresponding face of the web. ### 10.7.4 Design of Tension Members This section specifies the requirements for design of prismatic members subjected to axial tension due to static forces acting through the centroidal axis. #### 10.7.4.1 Allowable Stress The allowable tensile stress of a member, except eyebars, shall not be greater than Ft = 0.6Fy on the gross area Ft = 0.5Fu on the effective net area #### 10.7.4.2 Built-up Members The longitudinal spacing of connectors between elements in continuous contact consisting of a plate and a shape or two plates shall not exceed the following : a) 24 times the thickness of the thinner plate, nor 300 mm for painted members or unpainted members not subject to corrosion. b) 14 times the thickness of the thinner plate, nor 175 mm for unpainted members of weathering steel subject to atmospheric corrosion. In a tension member the longitudinal spacing of fasteners and intermittent welds connecting two or more shapes in contact shall not exceed 600 mm. Tension members composed of two or more shapes or plates separated by intermittent fillers shall be connected to one another at these fillers at intervals such that the slenderness ratio of either component between the fasteners does not exceed 300. Either perforated cover plates or tie plates without lacing are permitted on the open sides of built-up tension members. The length of tie plates shall not be less than ⅔ of the distance between the lines of welds or fasteners connecting them to the components of the member. The thickness of such tie plates shall not be less than 1/6 of the distance between these lines. The longitudinal spacing of intermittent welds or fasteners at the plates shall not exceed 150 mm. The spacing of the plates shall be such that the slenderness ratio of any component in the length between the plates shall not be greater than 300. #### 10.7.4.3 Pin Connected Members #### c) Eyebars Eyebars shall be of uniform thickness, without reinforcement at the pin holes, and have circular heads whose periphery is connected with the pin hole. The radius of the transition between the circular head and the eyebar body shall be at least equal to the diameter of the head. For calculation purposes, the width of the body of an eyebar shall not be greater than 8 times its thickness. The thickness may be less than 12 mm provided external nuts are used to tighten pin plates and filler plates into snug contact. For calculation purposes, the distance from the hole edge to plate edge perpendicular to the direction of the applied load shall not be less than ½ nor greater than ¾ times the width of the eyebar body. The pin diameter shall be at least ⅞ times the eyebar width. The pin hole diameter shall not be more than 0.08 mm greater than the diameter of the pin. For steel having a yield stress greater than 480 N/mm² the hole diameter shall not be greater than 5 times the plate thickness and the width of the eyebar shall be reduced accordingly. ### 10.7.5 DESIGN OF COLUMNS AND OTHER COMPRESSION MEMBERS These provisions cover the design of compact and noncompact sections subjected to axial compression through the centroidal axis. The provisions also cover the design of members with slender elements, tapered members and members subjected to combined axial compression and flexure. #### 10.7.5.1 Effective Length and Slenderness Ratio The effective length factor K shall be determined in accordance with Sec 10.5.2. In determining the slenderness ratio of an axially loaded compression member, the length shall be taken as its effective length Kl and r as the corresponding radius of gyration. For limiting slenderness ratio see Sec 10.6.5. #### 10.7.5.2 Allowable Stress On the gross section of axially loaded compression members whose cross-sections satisfy the requirements of Table 6.10.1, when Kl/r, the largest effective slenderness ratio of any unbraced segment is less than Cc, the allowable stress is: $$ F_a = \left[1 - \frac{(Kl/r)^2}{2C_c^2}\right] F_y / \left[\frac{5}{3} + \frac{3(Kl/r)}{8C_c} - \frac{(Kl/r)^3}{8C_c^3}\right] \tag{10.7.1} $$ where $$ C_c = \sqrt{\frac{2\pi^2 E}{F_y}} $$ On the gross section of axially loaded compression members, when Kl/r exceeds Cc, the allowable stress is: $$ F_a = \frac{12\pi^2 E}{23(Kl/r)^2} \tag{10.7.2} $$ #### 10.7.5.3 Flexural-Torsional Buckling Singly symmetric and unsymmetric columns, such as angles or tee-shaped columns, and doubly symmetric columns such as cruciform or built-up columns with very thin walls, may require consideration of flexural-torsional and torsional buckling. #### 10.7.5.4 Built-up Members All parts of built-up compression members and the transverse spacing of their lines of fasteners shall satisfy the requirements of Sec 10.6.5. Spacing and edge distance requirements for weathering steel members shall satisfy the requirements of Sec 10.9.3.10. At the ends of built-up compression members bearing on base plates or milled surfaces, all components in contact with one another shall be connected by rivets or bolts spaced longitudinally not more than 4 diameters apart for a distance equal to 1½ times the maximum width of the member, or by continuous welds having a length not less than the maximum width of the member. The maximum longitudinal spacing of bolts, rivets or intermittent welds connecting two rolled shapes in contact shall not be greater than 600 mm. In addition, for painted members and unpainted members not subject to corrosion where the outside component consists of a plate, the maximum longitudinal spacing shall not exceed: a) $333/\sqrt{F_y}$ times the thickness of the outside plate nor 300 mm when fasteners are not staggered along adjacent gauge lines. b) $500/\sqrt{F_y}$ times the thickness of the outside plate nor 450 mm when fasteners are staggered along adjacent gauge lines. Compression members composed of two or more rolled shapes separated by intermittent fillers shall be connected at these fillers at intervals such that the slenderness ratio Kl/r of either shape, between the fasteners, does not exceed ¾ times the governing slenderness ratio of the built-up member. The least radius of gyration r shall be used in computing the slenderness ratio of each component part. At least two intermediate connectors shall be used along the length of the built-up member. All connections, including those at the ends, shall be welded or shall utilize high strength bolts tightened to the requirements of Table 6.10.12. Open sides of compression members built up from plates or shapes shall be provided with lacing or tie plates at each end and at intermediate points if the lacing is interrupted. Tie plates shall be as near the ends as practicable. In main members carrying calculated stress, the end tie plates shall have a length of not less than the distance between the lines of fasteners or welds connecting them to the components of the member. Intermediate tie plates shall have a length not less than half of this distance. The thickness of the plates shall not be less than ⅜ of the distance between the lines of fasteners or welds connecting them to the components of the member. In bolted and riveted construction, the spacing in the direction of stress in tie plates shall not be more than 6 diameters and the tie plates shall be connected to each component by at least 3 fasteners. In welded construction, the welding on each line connecting a tie plate shall aggregate not less than ⅜ of the length of the plate. Lacing, including flat bars, angles, channels or other shapes employed as lacing, shall be so spaced that the ratio l/r of the flange included between their connections shall not exceed ¾ times the governing ratio for the member as a whole. Lacing shall be proportioned to resist a shearing stress normal to the axis of the member equal to 2% of the total compressive stress in the member. The ratio l/r for lacing bars arranged in single systems shall not exceed 140. For double lacing this ratio shall not exceed 200. Double lacing bars shall be joined at their intersections. For lacing bars in compression the unsupported length of the lacing bar shall be taken as the distance between fasteners or welds connecting it to the components of the built-up member for single lacing, and 70% of that distance for double lacing. The inclination of lacing bars to the axis of the member shall preferably be not less than 60° for single lacing and 45° for double lacing. When the distance between the lines of fasteners or welds in the flanges is more than 375 mm, the lacing shall preferably be double or be made of angles. The function of the tie plates and lacing may be performed by continuous cover plates perforated with access holes. The unsupported width of such plates at access holes, as defined in Sec 10.7.3, is assumed available to resist axial stresses, provided that: a) The width to thickness ratio conforms to the limitations of Sec 10.7.3; b) The ratio of length (in direction of stress) to width of holes shall not exceed 2; c) The clear distance between holes in the direction of stress shall be not less than the transverse distance between nearest lines of connecting fasteners or welds; and d) The periphery of the holes at all points shall have a minimum radius of 40 mm. #### 10.7.5.5 Pin Connected Compression Member Pin connections of pin connected compression members shall conform to the requirements of Sec 10.7.4.3. #### 10.7.5.6 Column Web Shear Column connections shall be investigated for concentrated force introduction in accordance with Sec 10.7.11.1. #### 10.7.5.7 Slender Compression Elements #### a) Unstiffened Compression Elements The allowable stress of unstiffened compression elements whose width-thickness ratio exceeds the applicable noncompact value as specified in Sec 10.7.3.1 shall be subject to a reduction factor Qs. The value of Qs shall be determined by Eq (10.7.3) through (10.7.8), as applicable, where b is the width of the unstiffened element as defined in Sec 10.7.3.1. When such elements comprise the compression flange of a flexural member, the maximum allowable bending stress shall not exceed 0.60 FyQs nor the applicable value as provided in Sec 10.7.6.3(c). The allowable stress of axially loaded compression members shall be modified by the appropriate reduction factor Qs as provided in (c) below. For Single Angles: When $200/\sqrt{F_y} < b/t < 407/\sqrt{F_y}$ $$ Q_s = 1.340 - 0.0017(b/t)\sqrt{F_y} \tag{10.7.3} $$ When $b/t \geq 407/\sqrt{F_y}$ $$ Q_s = \frac{106867}{F_y(b/t)^2} \tag{10.7.4} $$ For angles or plates projecting from columns or other compression members, and for projecting elements of compression flanges of beams and girders: When $250/\sqrt{F_y/k_c} < b/t < 512/\sqrt{F_y/k_c}$ $$ Q_s = 1.293 - 0.0012(b/t)\sqrt{F_y/k_c} \tag{10.7.5} $$ When $b/t > 512/\sqrt{F_y/k_c}$ $$ Q_s = \frac{180640 k_c}{F_y(b/t)^2} \tag{10.7.6} $$ where $$ k_c = \frac{4.05}{(h/t)^{0.46}} \text{ if } h/t > 70, \text{ otherwise } k_c = 1.0 $$ For stems of tees: When $333/\sqrt{F_y} < b/t < 462/\sqrt{F_y}$ $$ Q_s = 1.908 - 0.0027(b/t)\sqrt{F_y} \tag{10.7.7} $$ When $b/t \geq 462/\sqrt{F_y}$ $$ Q_s = \frac{137890}{F_y(b/t)^2} \tag{10.7.8} $$ Unstiffened elements of tees whose proportions exceed the limits of Sec 10.7.3.1 shall conform to the limits given in Table 6.10.2. **Table 6.10.2: Limiting Proportions for Channels and Tees** | Shape | Ratio of Full Flange Width to Profile Depth | Ratio of Flange Thickness to Web or Stem Thickness | | :----------------- | :-----------------------------------------: | :------------------------------------------------: | | Built-up or rolled | ≤0.25 | ≤3.0 | | Channels | ≤0.50 | ≤2.0 | | Built-up tees | ≥0.50 | ≥1.25 | | Rolled tees | ≥0.50 | ≥1.10 | #### b) Stiffened Compression Elements When the width-thickness ratio of uniformly compressed stiffened elements (except perforated cover plates) exceeds the noncompact limit stipulated in Sec 10.7.3.1 reduced effective width be shall be used in computing the design properties of the section containing the element, except that the ratio be/t need not be taken as less than the applicable value permitted in Sec 10.7.3.1. i) For the flanges of square and rectangular sections of uniform thickness: $$ b_e = \frac{665}{\sqrt{f}} \left[1 - \frac{132}{(b/t)\sqrt{f}}\right] \leq b \tag{10.7.9} $$ ii) For other uniformly compressed elements: $$ b_e = \frac{665}{\sqrt{f}} \left[1 - \frac{116}{(b/t)\sqrt{f}}\right] \leq b \tag{10.7.10} $$ Where be = reduced width, mm f = computed compressive stress (axial plus bending stresses) in the stiffened elements, based on the design properties as specified herein, N/mm². If unstiffened elements are included in the total cross section, f for the stiffened element must be such that the maximum compressive stress in the unstiffened element does not exceed FyQs or FyQa, as applicable. When the allowable stresses are increased due to wind or seismic loading in accordance with the provisions of Sec 10.7.2.2 the effective width be shall be determined on the basis of 0.75 times the stress caused by wind or seismic loading acting alone or in combination with the design dead and live loading. iii) For axially loaded circular sections: Members with diameter to thickness ratios D/t greater than 22752/Fy, but having a diameter to thickness ratio of less than 89630/Fy, shall not exceed the smaller value determined by Sec 10.7.5.2 nor $$ F_a = \frac{4564}{D/t} + 0.40F_y \tag{10.7.11} $$ #### c) Design Properties Properties of sections shall be determined using the full cross-section, except as follows: In computing the moment of inertia and section modulus of flexural members, the effective width of uniformly compressed stiffened elements, as determined in (b) above, shall be used in determining effective cross-sectional properties. For stiffened elements of the cross-section $$ Q_a = \frac{\text{effective area}}{\text{actual area}} \tag{10.7.12} $$ For unstiffened elements of the cross-section, Qs is to be determined according to (a) above. For axially loaded compression members the gross cross-sectional area and the radius of gyration r shall be computed on the basis of the actual cross-section. The allowable stress for axially loaded compression members containing unstiffened or stiffened elements shall not exceed $$ F_a = \frac{\left[1 - \frac{(Kl/r)^2}{2C_c^2}\right] F_y}{\frac{5}{3} + \frac{3(Kl/r)}{8C_c} - \frac{(Kl/r)^3}{8C_c^3}} \tag{10.7.13} $$ when Kl/r is less than $C_c'$, where $$ C_c' = \sqrt{\frac{2\pi^2 E}{QF_y}} \tag{10.7.14} $$ and Q is to be determined as follows: i) Cross-sections composed entirely of unstiffened elements, Q = Qs ii) Cross-sections composed entirely of stiffened elements, Q = Qa iii) Cross-sections composed of both stiffened and unstiffened elements, Q = QsQa When Kl/r exceeds $C_c'$: $$ F_a = \frac{12\pi^2 E}{23(Kl/r)^2} \tag{10.7.15} $$ #### d) Combined Axial and Flexural Stress In applying the provisions of Sec 10.7.8 to members subject to combined axial and flexural stress and containing stiffened elements whose width-thickness ratio exceeds the applicable noncompact limit given in Sec 10.7.3.1, the stresses Fy, fy and fjy shall be calculated on the basis of the section properties as provided in (c) above, as applicable. The allowable bending stress Fb for members containing unstiffened elements whose width-thickness ratio exceeds the noncompact limit given in Sec 10.7.3.1 shall be the smaller of 0.60FyQs or the value provided in Sec 10.7.6.3(c). The term fy/0.60Fy in Eq (10.7.59) and (10.7.48) shall be replaced by fy/0.60FyQs. ### 10.7.6 DESIGN OF BEAMS AND OTHER FLEXURAL MEMBERS This section covers the design of singly or doubly symmetric beams including hybrid beams and girders loaded in the plane of symmetry. It also applies to channels loaded in a plane passing through the shear centre parallel to the web or restrained against twisting at load points and points of support. #### 10.7.6.1 Proportioning of Beams and Girders Rolled or welded shapes, plate girders and cover plated beams shall be proportioned by the moment of inertia of the gross section. No reduction shall be made for shop or field bolt or rivet holes in either flange provided that $$ 0.5F_t A_{fn} \geq 0.6F_y A_{fg} \tag{10.7.16} $$ where Afg and Afn are calculated in accordance with the provisions of Sec 10.6.1 and 10.6.2. When $$ 0.5F_t A_{fn} < 0.6F_y A_{fg} \tag{10.7.17} $$ the member flexural properties shall be based on an effective tension flange area Afe, where $$ A_{fe} = 0.833\frac{F_u}{F_y} A_{fn} \tag{10.7.18} $$ Hybrid girders may be proportioned by the moment of inertia of their gross section, subject to the applicable provisions in Sec 10.7.7.1, provided they are not required to resist an axial force greater than 0.15Fy times the area of the gross section, where Fy is the yield stress of the flange material. For hybrid girders, the flanges at any given section shall have the same cross-sectional area and be of the same grade of steel. Flanges of welded beams or girders may be varied in thickness or width by splicing a series of plates or by the use of cover plates. The total cross-sectional area of cover plates of bolted or riveted girders shall not exceed 70% of the total flange area. High strength bolts, rivets or welds connecting flange to web, or cover plate to flange shall be designed to resist the total horizontal shear resulting from the bending forces on the girder. The longitudinal distribution of these bolts, rivets or intermittent welds shall be in proportion to the intensity of the shear. However, the longitudinal spacing of the connector shall not exceed the maximum spacing permitted for tension or compression members in Sec 10.7.4.2 or 10.7.5.4 respectively. Bolts, rivets or welds connecting flange to web shall also be designed to transmit to the web any loads applied directly to the flange, unless provision is made to transmit such loads by direct bearing. Partial length cover plates shall be extended beyond the theoretical cut-off point and the extended portion shall be attached to the beam or girder by high strength bolts in a slip critical connection or by rivets or fillet welds. The connection shall be adequate to develop the cover plate's portion of the flexural stresses in the beam or girder at the theoretical cut-off point within the applicable allowable stresses specified in Sec 10.9.2.4 and 10.9.3.4 to develop the cover plates portion of the flexural stresses in the beam or girder at the theoretical cutoff point. In addition, for welded cover plates, the welds connecting the cover plate termination to the beam or girder in the length a' defined below, shall be adequate at the allowable stresses, to develop the cover plate's portion of the flexural stresses in the beam or girder at the distance a' from the end of the cover plate. The length a', measured from the end of the cover plate, shall be: a) A distance equal to the width of the cover plate when there is a continuous weld equal to or larger than ⅔ of the plate thickness across the end of the plate and continuous welds along both edges of the cover plate in the length a'. b) A distance equal to 1½ times the width of the cover plate when there is a continuous weld smaller than ⅔ of the plate thickness across the end of the plate in the length a'. c) A distance equal to 2 times the width of the cover plate when there is no weld across the end of the plate, but continuous welds along both edges of the cover plate in the length a'. #### 10.7.6.2 Proportioning of Crane Girders In addition to satisfying the provisions of Sec 10.7.6.1 the flanges of beams or girders supporting cranes or other moving loads shall be proportioned to resist the horizontal forces produced by such loads, as specified in Sec 2.3.8 of Chapter 2, Loads. #### 10.7.6.3 Allowable Stresses - Strong Axis Bending of I-shaped Members and Channels #### a) Members with Compact Sections For compact symmetrical sections loaded in the plane of their minor axis, the allowable stress is $$ F_b = 0.66F_y \tag{10.7.19} $$ provided the flanges are connected continuously to the web or webs and the laterally unsupported length of the compression flanges Lb shall not exceed the value of Lc as given by the smaller of the following: $$ \frac{200b_f}{\sqrt{F_y}} \text{ or } \frac{138000}{(d/A_f)\sqrt{F_y}} \tag{10.7.20} $$ Members (including composite members and excluding hybrid members and members with yield points greater than 445 N/mm²) which meet the requirements for compact sections and are continuous over supports or rigidly framed to columns may be proportioned for ⅑ of the negative moments produced by gravity loading when such moments are maximum at points of support, provided that, for such members, the maximum positive moment is increased by ⅑ of the average negative moments. This reduction shall not apply to moments produced by loading on cantilevers. If the negative moment is resisted by a column rigidly framed to the beam or girder, the ⅑ reduction is permitted in proportioning the column for the combined axial and bending loading, provided that the stress fa due to any concurrent axial load on the member does not exceed 0.15Fy. #### b) Members with Noncompact Sections For members satisfying the requirement of (a) above except that their flanges are noncompact (excluding built-up members and members with yield points greater than 445 N/mm²), the allowable stress is $$ F_b = F_y \left[0.79 - 0.00038\frac{b_f}{t_f}\sqrt{F_y}\right] \tag{10.7.21} $$ For built-up members satisfying the requirements of (a) above except that their flanges are noncompact and their webs are compact or noncompact, (excluding hybrid girders and members with yield points greater than 445 N/mm²) the allowable stress is $$ F_b = F_y \left[0.79 - 0.00038\frac{b_f}{t_f}\sqrt{\frac{F_y}{k_c}}\right] \tag{10.7.22} $$ where $$ k_c = \frac{4.05}{(h/t_w)^{0.46}} \text{ if } h/t_w > 70, \text{ otherwise } k_c = 1.0 $$ For members with a noncompact section but not included above, and loaded through the shear centre and braced laterally in the region of compression stress at intervals not exceeding $\frac{200b_f}{\sqrt{F_y}}$ the allowable stress is $$ F_b = 0.60F_y \tag{10.7.23} $$ #### c) Members with Compact or Noncompact Sections with Unbraced Length Greater Than Lc For flexural members with compact or noncompact sections and with unbraced lengths greater than Lc as defined in (a) above the allowable bending stress in tension is determined from Eq (10.7.23). For such members with an axis of symmetry in, and loaded in the plane of their web, the allowable bending stress in compression is determined as the larger value from Eq (10.7.24) or (10.7.25) and (10.7.26) except that Eq (10.7.26) is applicable only to sections with a compression flange that is solid and approximately rectangular in cross-section and that has an area not less than the tension flange. Higher values of the allowable compressive stress are permitted if justified by a more precise analysis. Stresses shall not exceed those permitted by Sec 10.7.7 if applicable. For channels bent about their major axes, the allowable compressive stress is determined from Eq (10.7.26). When $$ \sqrt{\frac{703 \times 10^3 C_b}{F_y}} \leq \frac{l}{r_T} \leq \sqrt{\frac{3516 \times 10^3 C_b}{F_y}} $$ $$ F_b = \left[\frac{2}{3} - \frac{F_y(l/r_T)^2}{10550 \times 10^3 C_b}\right] F_y \leq 0.60F_y \tag{10.7.24} $$ When $$ \frac{l}{r_T} > \sqrt{\frac{3516 \times 10^3 C_b}{F_y}} $$ $$ F_b = \frac{1172 \times 10^3 C_b}{(l/r_T)^2} \leq 0.60F_y \tag{10.7.25} $$ For any value of l/rT: $$ F_b = \frac{83 \times 10^3 C_b}{(ld/A_f)} \leq 0.60F_y \tag{10.7.26} $$ where $l$ = distance between cross-sections braced against twist or lateral displacement of the compression flange, mm. For cantilevers braced against twist only at the support, $l$ may conservatively be taken as the actual length. $C_b$ = $1.75+1.05(M_1/M_2)+0.3(M_1/M_2)^2$, but not more than 2.3, where $M_1$ is the smaller and $M_2$ the larger bending moment at the ends of the unbraced length, taken about the strong axis of the member, and where $M_1/M_2$, the ratio of end moments, is positive when $M_1$ and $M_2$ have the same sign (reverse curvature bending) and negative when they are of opposite signs (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, the value of $C_b$ shall be taken as unity. When computing $C_b$, to be used in Eq (10.7.58), $C_b$ may be computed by the equation given above for frames subject to joint translation. $C_b$ shall be taken as unity for frames braced against joint translation. $C_b$ may conservatively be taken as unity for cantilever beams. For hybrid plate girders, $F_y$ in Eq (10.7.26) shall not apply to hybrid girders. The provisions of this section do not apply to T-sections if the stem is in compression anywhere along the unbraced length. #### 10.7.6.4 Allowable Stress : Weak Axis Bending of I-Shaped Members, Solid Bars and Rectangular Plates Lateral bracing is not required for members loaded through the shear centre about their weak axis, nor for members of equal strength about both axes. a) Members with Compact Sections : For doubly symmetrical I- and H-shaped members with compact flanges continuously connected to the web and bent about their weak axes (except members with yield points greater than 445 N/mm²), solid round and square bars, and solid rectangular sections bent about their weaker axes, the allowable stress is $$ F_b = 0.75 F_y $$ (10.7.27) b) Members with Noncompact Sections : For members not meeting the requirements for compact sections and not covered in Sec 10.7.6.5, bent about their minor axis, the allowable stress is $$ F_b = 0.60 F_y $$ (10.7.28) Doubly symmetrical I- and H-shape members bent about their weak axes (except members with yield points greater than 445 N/mm²) with noncompact flanges continuously connected to the web may be designed on the basis of an allowable stress of $$ F_b = F_y \left[ 1.075 - 0.00095 \left( \frac{b_f}{t_f} \right) \sqrt{F_y} \right] $$ (10.7.29) #### 10.7.6.5 Allowable Stress : Bending of Box Members, Circular and Rectangular Tubes a) Members with Compact Sections : For members bent about their strong or weak axes, members with compact sections and flanges continuously connected to the webs, the allowable stress is $$ F_b = 0.66 F_y $$ (10.7.30) To be classified as a compact section, a box-shaped member shall have, in addition to the requirements of Sec 10.7.3, a depth not greater than 6 times the width, a flange thickness not greater than 2 times the web thickness and a laterally unsupported length $L_b$ less than or equal to $L_c$ given by Eq (10.7.31). $$ L_c = \left( 13445 + 8274 \frac{M_1}{M_2} \right) \frac{b}{F_y} $$ (10.7.31) However, $L_b$ need not be less than 8274 (b/Fy), where $M_1$ is the smaller and $M_2$ the larger bending moment at the ends of the unbraced length, taken about the strong axis of the member, and where $M_1/M_2$, the ratio of moments is positive when $M_1$ and $M_2$ have the same sign (reverse curvature bending) and negative when they are of opposite signs (single curvature bending). b) Members with Noncompact Sections : For box-type and tubular flexural members that meet the noncompact section requirements, the allowable stress is #### 10.7.6.6 Allowable Shear Stresses For $h/t_w ≤ 1000/ \sqrt{F_y}$, on the overall depth times the web thickness, the allowable shear stress is : $$ F_s = 0.40F_y $$ (10.7.33) For $h/t_w > 1000/ \sqrt{F_y}$, the allowable shear stress on an area obtained by multiplying the clear distance between the flanges by the web thickness is $$ F_s = 0.346C_v F_y ≤ 0.40F_y $$ (10.7.34) where $$ C_v = \frac{310260k_v}{F_y(h/t_w)^2} \text{ when } C_v \text{ is less than } 0.8 $$ $$ = \frac{500}{h/t_w} \sqrt{\frac{k_v}{F_y}} \text{ when } C_v \text{ is more than } 0.8 $$ $$ k_v = 4.00 + \frac{5.34}{(a/h)^2} \text{ when } a/h \text{ is less than } 1.0 $$ $$ = 5.34 + \frac{4.00}{(a/h)^2} \text{ when } a/h \text{ is more than } 1.0 $$ For shear rupture on coped beam end connections see Sec 10.9.4.1. Maximum h/tₘ limits are given in Sec 10.7.7. An alternative design method for plate girders utilizing tension field action is given in Sec 10.7.7. #### 10.7.6.7 Transverse Stiffeners Intermediate stiffeners are required when the ratio h/tₘ is greater than 260 and the maximum web shear stress fₛ is greater than that permitted by Eq (10.7.34). The spacing of intermediate stiffeners, when required, shall be such that the web shear stress will not exceed the value for Fₛ given by Eq (10.7.34) or (10.7.53), as applicable, and $$ \frac{a}{h} ≤ \left[ \frac{260}{h/t_w} \right]^2 $$ (10.7.35) The spacing of intermediate stiffeners shall, however, not be more than 3h. #### 10.7.6.8 Built-up Members Where two or more rolled beams or channels are used side by side to form a flexural member, they shall be connected together at intervals of not more than 1500 mm. Through-bolts and separators are permitted, provided that, in beams having a depth of 300 mm or more, not less than 2 bolts shall be used at each separator location. When concentrated loads are carried from one beam to the other, or distributed between the beams, diaphragms having sufficient stiffness to distribute the load shall be riveted, bolted or welded between the beams. #### 10.7.6.9 Web-tapered Members a) General Requirements : The design of tapered members shall meet the following special requirements along with the requirements of Sec 10.7.6.3 through 10.7.6.8. i) It shall possess at least one axis of symmetry which shall be perpendicular to the plane of bending if moments are present. ii) The flanges shall be of equal and constant area. iii) The depth shall vary linearly as $$ d = d_o \left( 1 + \gamma \frac{z}{L} \right) $$ (10.7.36) where $$ \gamma = (d_L - d_o)/d_o ≤ \text{ the smaller of } 0.268 \text{ (} L/d_o \text{) or } 6.0 $$ b) Allowable Tensile Stress : The allowable tensile stress of tapered tension members shall be determined in accordance with Sec 10.7.4.1. c) Allowable Compressive Stress : On the gross section of axially loaded tapered compression members, the allowable compressive stress in N/mm² shall not exceed the following: When the effective slenderness ratio S is less than Cₑ : $$ F_{cr} = \frac{\left(1.0 - \frac{S^2}{2C_c^2}\right) F_y}{\frac{5}{3} - \frac{3S}{8C_c} - \frac{S^3}{8C_c^3}} $$ (10.7.37) When the effective slenderness ratio S exceeds Cₑ : $$ F_{cr} = \frac{12 π^2 E}{23S^2} $$ (10.7.38) where * $S$ = $Kl/r_{eg}$ for weak axis bending and $K_y l/r_{eg}$ for strong axis bending * $K_y$ = effective length factor for a tapered member as determined by an analysis following reliable references d) Allowable Flexural Stress : Tension and compression stresses on extreme fibres of tapered flexural members, in N/mm², shall not exceed the following values : $$ F_{by} = \frac{2}{3} \left[ 1.0 - \frac{F_y}{6B_e} \sqrt{F_{sy}^2 + F_{wy}^2} \right] F_y ≤ 0.60F_y $$ (10.7.39) unless $F_{by} ≤ F_y / 3$ in which case $$ F_{by} = B_y \sqrt{F_{sy}^2 + F_{wy}^2} $$ (10.7.40) In the above equations, $$ F_{sy} = \frac{2.1 \times 10^6}{h_s L_{d_s}/A_f} $$ (10.7.41) $$ F_{wy} = \frac{756 \times 10^6}{(h_w L_f/r_w)^2} $$ (10.7.42) where $$ h_w = \text{factor equal to } 1.0 + 0.023 \gamma \sqrt{L_{d_s}/A_f} $$ and B is determined as follows : i) When the maximum moment $M_2$ in three adjacent segments of approximately equal unbraced length is located within the central segment and $M_1$ is the larger moment at one end of the three-segment portion of a member: $$ B = 1.0 + 0.37 \left(1.0 + \frac{M_1}{M_2}\right) + 0.50\gamma \left(1.0 + \frac{M_1}{M_2}\right) ≥ 1.0 $$ (10.7.43) ii) When the largest computed bending stress fb2 occurs at the larger of two adjacent segments of approximately equal unbraced lengths and fb1 is the computed bending stress at the smaller end of the two-segment portion of a member : $$ B = 1.0 + 0.58 \left(1 + \frac{f_{b1}}{f_{b2}}\right) - 0.707\left(1 + \frac{f_{b1}}{f_{b2}}\right) ≥ 1 $$ (10.7.44) iii) When the largest computed bending stress fb2 occurs at the smaller end of two adjacent segments of approximately equal unbraced length and fb1 is the computed bending stress at the larger end of the two-segment portion of a member : $$ B = 1.0 + 0.55 \left(1.0 + \frac{f_{b1}}{f_{b2}}\right) + 2.20\gamma \left(1.0 + \frac{f_{b1}}{f_{b2}}\right) ≥ 1.0 $$ (10.7.45) In the foregoing, $γ = (d_L - d_o)/d_o$ is calculated for the unbraced length containing the maximum computed bending stress. iv) When the computed bending stress at the smaller end of a tapered member or segment thereof is equal to zero: $$ B = \frac{1.75}{1.0 + 0.25\sqrt{\gamma}} $$ (10.7.46) where $γ = (d_L - d_o)/d_o$, calculated for the unbraced length adjacent to the point of zero bending stress. e) Allowable Shear : The allowable shear stress of tapered flexural members shall be in accordance with Sec 10.7.6.6. f) Combined Flexure and Axial Force : Tapered members and unbraced segments thereof subject to both axial compression and bending stresses shall be proportioned to satisfy the following requirement: $$ \left(\frac{f_{ao}}{F_{ay}}\right) + \frac{C'_{m}}{1 - \frac{f_{a0}}{F'_{ey}}} \left(\frac{f_b}{F_{by}}\right) ≤ 1.0 $$ (10.7.47) and $$ \frac{f_a}{0.60F_y} + \frac{f_b}{F_{by}} ≤ 1.0 $$ (10.7.48) When $\frac{f_{ao}}{F_{ay}} ≤ 0.15$, Eq (10.7.49) is permitted in lieu of Eq (10.7.47) and (10.7.48). $$ \left(\frac{f_{ao}}{F_{ay}}\right) + \left(\frac{f_b}{F_{by}}\right) ≤ 1.0 $$ (10.7.49) ### 10.7.7 Design of Plate Girders Plate girders shall be distinguished from beams on the basis of the web slenderness ratio h/tₘ. When this value is greater than $1995/ \sqrt{F_b}$, the provisions of this section shall apply for allowable bending stress, otherwise Sec 10.7.6 shall be applicable. For allowable shear stress and transverse stiffener design, the provisions of Sec 10.7.6.6 and 10.7.6.7 shall apply, unless tension field action is utilized, in which case Sec 10.7.7.3 and 10.7.7.4 shall be applicable. #### 10.7.7.1 Web Slenderness Limitations When no transverse stiffeners are provided or when transverse stiffeners are spaced more than 1½ times the distance between flanges $$ \frac{h}{t_w} ≤ \frac{96550}{\sqrt{F_{yf}(F_{yf} + 114)}} $$ (10.7.50) When transverse stiffeners are provided, spaced not more than 1½ times the distance between flanges $$ \frac{h}{t_w} ≤ \frac{5250}{\sqrt{F_yf}} $$ (10.7.51) #### 10.7.7.2 Allowable Bending Stress When the web depth to thickness ratio exceeds $1995/ \sqrt{F_b}$, the maximum bending stress in the compression flange shall not exceed $$ F'_b ≤ F_b R_{PG} R_e $$ (10.7.52) where $F_b$ = applicable bending stress given in Sec 10.7.6, N/mm² and $$ R_{PG} = 1 - 0.0005 \frac{A_w}{A_f} \left(\frac{h}{t} \frac{1995}{\sqrt{F_b}}\right) ≤ 1.0 $$ $$ R_e = \frac{12 + \left(\frac{A_w}{A_f}\right)(3α - α^2)}{12 + 2\left(\frac{A_w}{A_f}\right)} ≤ 1.0 $$ $α = 0.6 F_{yw}/F_b ≤ 1.0$ For nonhybrid girders, $R_e$ shall be taken as 1.0. #### 10.7.7.3 Allowable Shear Stress with Tension Field Action Except as herein provided, the largest average web shear, fᵥ, N/mm² computed for any condition of complete or partial loading, shall not exceed the value given by Eq (10.7.34). Alternatively, for girders other than hybrid girders, if intermediate stiffeners are provided and spaced to satisfy the provisions of Sec 10.7.7.4 and if Cₛ ≤ 1, the allowable shear including tension field action given by Eq (10.7.53) is permitted in lieu of the value given by Eq (10.7.34). $$ F_b = 0.346F_y \left[ C_v + \frac{1 - C_v}{1.15\sqrt{1 + (a/h)^2}} \right] ≤ 0.40F_y $$ (10.7.53) #### 10.7.7.4 Transverse Stiffeners Transverse stiffeners shall meet the requirements of Sec 10.7.6.7. In girders designed on the basis of tension field action, the spacing between stiffeners at end panels, at panels containing large holes, and at panels adjacent to panels containing large holes shall be such that fᵥ does not exceed the value given by Eq (10.7.34). Bolts and rivets connecting stiffeners to the girder web shall be spaced not more than 300 mm on centres. If intermittent fillet welds are used, the clear distance between welds shall not be more than 16 times the web thickness nor more than 250 mm. The moment of inertia, Iₛₜ of a pair of intermediate stiffeners, or a single intermediate stiffener, with reference to an axis in the web centre line of the web shall be limited as follows $$ I_{st} ≥ \left(\frac{h}{50}\right)^4 $$ (10.7.54) The gross area (total area, when stiffeners are furnished in pairs), in mm², of intermediate stiffeners spaced as required for Eq (10.7.53) shall be not less than $$ A_{st} = \frac{1 - C_v}{2} \left[\frac{a}{h} - (a/h)^2\right] \sqrt{1 + (a/h)^2} \text{YDH} $$ (10.7.55) where * $D$ = 1.0 for stiffeners furnished in pairs * $D$ = 1.8 for single angle stiffeners * $D$ = 2.4 for single plate stiffeners When the greatest shear stress fᵥ in a panel is less than that permitted by Eq (10.7.53) the reduction of this gross area requirement is permitted in like proportion. Intermediate stiffeners required by Eq (10.7.53) shall be connected for a total shear transfer, N per linear mm of single stiffener or pair of stiffeners, not less than $$ f_{ws} = h_e \left(\frac{F_y}{647}\right)^3 $$ (10.7.56) where Fy = yield stress of web steel. This shear transfer may be reduced in the same proportion that the largest computed shear stress fₛ in the adjacent panels is less than that permitted by Eq (10.7.53). However, rivets and welds in intermediate stiffeners which are required to transmit the web an applied concentrated load or reaction shall be proportioned for not less than the applied load or reaction. Intermediate stiffeners may be stopped short of the tension flange, provided bearing is not needed to transmit a concentrated load or reaction. The weld by which intermediate stiffeners are attached to the web shall be terminated not less than four times nor more than six times the web thickness from the nearest toe of the web to flange weld. When single stiffeners are used, they shall be attached to the compression flange, if it consists of a rectangular plate, to resist any uplift tendency due to torsion in the plate. When lateral bracing is attached to a stiffener, or a pair of stiffeners, in turn, these, in turn, shall be connected to the compression flange to transmit 1% of the total flange stress, unless the flange is composed only of angles. ### 10.7.8 Combined Stresses The design of members subject to combined stresses shall be in accordance with this section. This section deals with doubly and singly symmetrical members only. For determination of Fₐ see 10.7.5 and for determination of Fbx and Fby see Sec 10.7.6. #### 10.7.8.1 Axial Compression and Bending Members subjected to both axial compression and bending stresses shall be proportioned to satisfy the following requirements : $$ \frac{f_a}{F_a} + \frac{C_{m} f_{bx}}{1 - \frac{f_a}{F'_{ex}}} + \frac{C_{my} f_{by}}{1 - \frac{f_a}{F'_{ey}}} ≤ 1.0 $$ (10.7.58) $$ \frac{f_a}{0.60F_y} + \frac{f_{bx}}{F_{bx}} + \frac{f_{by}}{F_{by}} ≤ 1.0 $$ (10.7.59) When fa/Fₐ ≤ 0.15, Eq (10.7.60) is permitted in lieu of Eq (10.7.58) and (10.7.59). $$ \frac{f_a}{F_a} + \frac{f_{bx}}{F_{bx}} + \frac{f_{by}}{F_{by}} ≤ 1.0 $$ (10.7.60) In Eq (10.7.58), (10.7.59) and (10.7.60) the subscripts x and y, combined with subscripts b, m and e, indicate the axis of bending about which a particular stress or design property applies, and $$ F'_e = \frac{12 \pi^2 E}{23(Kl_b/r_b)^2} $$ \= Euler stress divided by a factor of safety, N/mm². (In the expression for Fₑ', lₒ is the actual unbraced length in the plane of bending and rᵦ is the corresponding radius of gyration. K is the effective length factor in the plane of bending.) As in the case of Fₐ, Fbx and 0.60Fₘ, Fₐ, may be increased ¼ in accordance with Sec 10.7.2.2. a) For compression members in frames subject to joint translation (sideway), Cm = 0.85. b) For rotationally restrained compression members in frames braced against joint translation and not subject to transverse loading between their supports in the plane of bending, $$ C_m = 0.6 - 0.4(M_1/M_2) $$ where M₁/M₂ is the ratio of the smaller to larger moments at the ends of that portion of the member unbraced in the plane of bending under consideration. M₁/M₂ is positive when M₁ and M₂ have the same sign (reverse curvature, negative when bent in single curvature. c) For compression members in frames braced against joint translation in the plane of loading and subjected to transverse loading between their supports, the value of Cm may be determined by an analysis. However, in lieu of such analysis, the following values are permitted : i) For members whose ends are restrained against rotation in the plane of bending Cm = 0.85 ii) For members whose ends are unrestrained against rotation in the plane of bending Cm = 1.0. #### 10.7.8.2 Axial Tension and Bending Members subject to both axial tension and bending stresses shall be proportioned at all points along their length to satisfy the following equation : $$ \frac{f_a}{F_t} + \frac{f_{bx}}{F_{bx}} + \frac{f_{by}}{F_{by}} ≤ 1.0 $$ (10.7.61) where fb is the computed bending tensile stress, fs is the computed axial tensile stress, Fb is the allowable bending stress and Ft is the governing allowable tensile stress defined in Sec 10.7.4.1. However, the computed bending compressive stress arising from an independent load source relative to the axial tension, taken alone, shall not exceed the applicable value required in Sec 10.7.6. ### 10.7.9 Design of Trusses #### 10.7.9.1 General Trusses are composed of individual members connected by welds, rivets or bolts. #### 10.7.9.2 Purlins The spacing of purlins shall be determined on the basis of the maximum safe span of the roof covering. If roof covering is supported through battens and common rafters, the purlins shall preferably be located at the panel points of the truss, by varying the spacing and size of battens and common rafters. #### 10.7.9.3 Design of Members a) Compression Members : All members under compressive forces shall be designed to satisfy the requirements of Sec 10.7.5. b) Tension Members : All members under tensile forces shall be designed to satisfy the requirements of Sec 10.7.4. #### 10.7.9.4 Joints and Connections Joints and connections in trusses shall satisfy the requirements of Sec 10.9. #### 10.7.9.5 Deflection and Camber a) Deflection : Deflection due to service live load plus impact load, if any, shall be limited so as not to impair serviceability. b) Camber : Trusses shall be provided with camber in accordance with Sec 10.10.1. #### 10.7.9.6 Bracing : Trusses shall be adequately braced against instability. ### 10.7.10 Composite Construction This section covers the design and construction of steel beams supporting a reinforced concrete slab so interconnected that the beams and the slab act together to resist bending. Simple and continuous composite beams with shear connectors and concrete-encased beams, constructed with or without temporary shores, are included. #### 10.7.10.1 General Requirements Composite members may either be totally encased members which depend upon natural bond for interaction with the concrete or those with shear connectors (mechanical anchorage to the slab) with the steel member not necessarily encased. A beam totally encased in concrete cast integrally with the slab may be assumed to be connected to the concrete by natural bond, without additional anchorage, provided that : a) Concrete cover over beam sides and soffit is at least 50 mm. b) The top of the beam is at least 40 mm below the top and 50 mm above bottom of the slab. c) Concrete encasement contains adequate mesh or other reinforcing steel throughout the whole depth and across the soffit of the beam to prevent spalling of the concrete. Shear connectors must be provided for composite action if the steel member is not totally encased in concrete. The portion of the effective width of the concrete slab on each side of the beam centre line shall not exceed : a) One-eighth of the beam span, centre to centre of supports; b) One-half the distance to the centre line of the adjacent beam; or c) The distance from the beam centre line to the edge of the slab. #### 10.7.10.2 Design Assumptions a) Encased beams shall be proportioned to support, unassisted, all dead loads applied prior to the hardening of the concrete (unless these loads are supported temporarily on shoring) and, acting in conjunction with the slab, to support all dead and live loads applied after hardening of the concrete, without exceeding a computed bending stress of 0.66fy, where Fy is the yield stress of the steel beam. The bending stress produced by loads after the concrete has hardened shall be computed on the basis of the sections and sectional properties of the composite section. Concrete tension stresses shall be neglected. Alternatively, the steel beam alone may be proportioned to resist, unassisted, the positive moment produced by all loads, live and dead, using a bending stress equal to 0.76 Fy in which case temporary shoring is not required. b) When shear connectors are used in accordance with Sec 10.7.10.4, the composite section shall be proportioned to support all of the loads without exceeding the allowable stresses prescribed in 10.7.6.3(a), even when the steel section is not shored during construction. In limited areas (Sec 10.7.6.3), the stress in the composite section shall be exempt from compact flange criteria (Sec 10.7.3) and there is no limit on the unsupported length of the compression flange. Reinforcement parallel to the beam within the effective width of the slab, when anchored in accordance with the requirements of Chapter 8, may be included in computing the properties of composite sections, provided that shear connectors are furnished in accordance with the requirements of Sec 10.7.10.4. The section properties of the composite section shall be computed in accordance with the elastic theory. Concrete tension stresses shall be neglected. For stress and deflection computations, the compression area of concrete shall be treated as an equivalent area of steel by dividing it by the modular ratio when determining section properties. In cases where it is not feasible or necessary to provide adequate connectors to satisfy the horizontal shear requirements for full composite action, the effective section modulus shall be determined as $$ S_{eff} = S_s + \sqrt{\frac{V'_h}{V_h}}(S_{tr} - S_s) $$ (10.7.62) where $V_h$ and $V_h'$ are as defined in Sec 10.7.10.4. For composite beams constructed without temporary shoring, stresses in the steel section shall not exceed 0.90$F_y$. Stresses shall be computed assuming that the steel section alone resists all loads applied before the concrete has reached 75% of its required strength and the effective composite section resists all loads applied after that time. The actual section modulus of the transformed composite section shall be used in calculating the concrete flexural compression stress and for construction without temporary shores; this stress shall be based upon loading applied after the concrete has reached 75% of its required strength. The stress in the concrete shall not exceed 0.45$f'_c$ #### 10.7.10.3 End Shear The web and the end connections of the steel beam shall be designed to carry the total reaction. #### 10.7.10.4 Shear Connectors Except in the case of encased beams, as defined in Sec 10.7.10.2(a), the entire horizontal shear at the junction of the steel beam and the concrete slab shall be assumed to be transferred by shear connectors welded to the top flange of the beam and embedded in the concrete. For full composite action with concrete subject to flexural compression, the total horizontal shear to be resisted between the point of maximum positive moment and points of zero moment shall be taken as the smaller value using Eq (10.7.63) and (10.7.64). $$ V_h = 0.85 f'_c A_c / 2 $$ (10.7.63) and $$ V_h = F_y A_s / 2 $$ (10.7.64) In continuous composite beams where longitudinal reinforcing steel is considered to act compositely with the steel beam in the negative moment regions, the total horizontal shear to be resisted by shear connectors between an interior support and each adjacent point of contraflexure shall be taken as $$ V_h = F_{yr} A_{sr} / 2 $$ (10.7.65) For full composite action, the number of connectors resisting the horizontal shear, $V_h$, on each side of the point of maximum moment, shall not be less than that determined by the relationship $V_h/q$, where $q$, the allowable shear load for one connector, is given in Table 6.10.3 for flat soffit concrete slabs made with ASTM C33 aggregates. For partial composite action with concrete subjected to flexural compression, the horizontal shear $V'_h$ to be used in computing $S_{eff}$ shall be taken as the product of $q$ and the number of connectors furnished between the point of maximum moment and the nearest point of zero moment. The value of $V'_h$ shall not be less than, $\frac{1}{4}$ the smaller value of Eq (10.7.63), using the maximum permitted effective width of the concrete flange, and Eq (10.7.64). The effective moment of inertia for deflection computations shall be determined by : $$ I_{eff} = I_s + \sqrt{\frac{V'_h}{V_h}}(I_{tr} - I_s) $$ (10.7.66) The connectors required on each side of the point of maximum moment in an area of positive bending may be uniformly distributed between that point and adjacent points of zero moment, except that $N_2$, the number of shear connectors required between any concentrated load in that area and the nearest point of zero moment, shall be not less than that determined by Eq (10.7.67). **Table 6.10.3** **Allowable Horizontal Shear Load for One Connector (q), kN⁽¹⁾** | Connector⁽²⁾ | 20 | 25 | ≥ 27.5 | | :-------------------------------- | :- | :- | :----- | | 12 dia × 50 hooked or headed stud | 22 | 24 | 26 | | 16 dia × 65 hooked or headed stud | 35 | 38 | 40 | | 20 dia × 75 hooked or headed stud | 51 | 55 | 59 | | 22 dia × 90 hooked or headed stud | 70 | 75 | 80 | Specified Compressive Strength of Concrete ($f'_c$), N/mm² — columns above correspond to 20, 25, and ≥ 27.5. Notes: (1) Applicable only to concrete made with ASTM C33 aggregates. (2) The allowable horizontal loads tabulated are also permitted for studs longer than shown. $$ N_2 = \frac{N_1\left[\dfrac{M\beta - 1}{M_{\max}}\right]}{\beta - 1} $$ (10.7.67) where $$ \beta = \frac{S_{tr}}{S_s} \text{ or } \frac{S_{eff}}{S_s} \text{ as applicable} $$ For a continuous beam, connectors required in the region of negative bending may be uniformly distributed between the point of maximum moment and each point of zero moment. Shear connectors shall have at least 25 mm of lateral concrete cover, except for connectors installed in the ribs of formed steel decks. Unless located directly over the web, the diameter of studs shall not be greater than $2\frac{1}{2}$ times the thickness of the flange to which they are welded. The minimum centre to centre spacing of stud connectors shall be 6 diameters along the longitudinal axis of the supporting composite beam and 4 diameters transverse to the longitudinal axis of the supporting composite beam. The maximum centre to centre spacing of stud connectors shall not exceed 8 times the total slab thickness. #### 10.7.10.5 Composite Beams or Girders with Formed Steel Deck Composite construction of concrete slabs on formed steel deck with nominal rib height not greater than 75 mm connected to steel beams or girders shall be designed by the applicable portions of Sec 10.7.10.1 through 10.7.10.4 with the following modifications. a) General : i) The average width of concrete rib or haunch wᵣ, shall be not less than 50 mm, but shall not be taken in calculations as more than the minimum clear width near the top of the steel deck. For additional provisions see c(i) and c(iii) below. ii) The concrete slab shall be connected to the steel beam or girder with welded stud shear connectors 20 mm or less in diameter. Studs may be welded through the deck or directly to the steel member. iii) Stud shear connectors shall extend not less than 40 mm above the top of the steel deck after installation. iv) The slab thickness above the steel deck shall not be less than 50 mm. b) Deck Ribs Oriented Perpendicular to Beam or Girder i) Concrete below the top of the steel deck shall be neglected when determining section properties and in calculating Aᶜ for Eq (10.7.63). ii) The spacing of stud shear connectors along the length of a supporting beam or girder shall not exceed 900 mm. iii) The allowable horizontal shear load per stud connector q shall be the value stipulated in Sec 10.7.10.4 (Table 6.10.3) multiplied by the following reduction factor : $$ \left(\frac{0.85}{\sqrt{N_r}} \right) \left(\frac{H_s}{h_r} \right) \left(\frac{H_s}{h_r} - 1.0\right) ≤ 1.0 $$ (10.7.68) where * $N_r$ shall not exceed 3 in computations, although more than 3 studs may be installed. * $H_s$ shall not exceed the value $(h_r + 75)$ in computations, although the actual length may be greater. c) Deck Ribs Oriented Parallel to Beam or Girder i) Concrete below the top of the steel deck shall be included when determining section properties and in calculating Aᶜ for Eq (10.7.63). ii) Steel deck ribs over supporting beams or girders may be split longitudinally and separated to form a concrete haunch. iii) When the nominal depth of steel deck is 40 mm or greater, the average width wᵣ, of the supported haunch or rib shall be not less than 50 mm for the first stud in transverse row plus 4 stud diameters for each additional stud. iv) The allowable horizontal shear load per stud connector q shall be the value stipulated in Sec 10.7.10.4 (Table 6.10.3) except when the ratio wᵣ/hᵣ is less than 1.5, the allowable load shall be multiplied by the following reduction factor : $$ 0.6\left(\frac{w_r}{h_r}\right)\left(\frac{H_s}{h_r} - 1.0\right) ≤ 1.0 $$ (10.7.69) where * Nᵣ shall not exceed 3 in computations. * Hₛ shall not exceed the value (hᵣ + 75) in computations, although the actual length may be greater. ### 10.7.11 Special Design Considerations This section provides the design considerations related to special situations such as concentrated loads, ponding and torsion. #### 10.7.11.1 Webs and Flanges Under Concentrated Loads a) Design Basis : Members with concentrated loads applied normal to one flange and symmetric to the web shall have a flange and web proportioned to satisfy the local flange bending, web yielding strength, web crippling and column web buckling criteria of (b) through (e) below. Members with concentrated loads applied to both flanges shall have a web proportioned to satisfy the web yielding, web crippling and column web buckling criteria of (c), (d) and (f) below. Where pairs of stiffeners are provided on opposite sides of the web, at concentrated loads, and extend at least half the depth of the member, provision of (b) and (c) below need not apply. For column webs subjected to high shears, see (g) below, and for bearing stiffeners, see (h) below. b) Local Flange Bending : A pair of stiffeners shall be provided opposite the tension flange or flange plate of the beam or girder framing into the member when $$ t_f < 12.65 \sqrt{\frac{P_{bf}}{F_{yc}}} $$ (10.7.70) where $P_{bf}$ = the computed force delivered by the flange or moment connection plate multiplied by $\frac{3}{4}$, when the computed force is due to live and dead load only, or by $\frac{2}{3}$, when the computed force is due to live and dead load in conjunction with wind or earthquake forces, kN. When the length of loading measured across the member flange is less than 0.15b, Eq (10.7.70) need not be checked. c) Local Web Yielding : Bearing stiffeners shall be provided in beams and welded plate girders if the compressive stress at the web toe of the fillets resulting from concentrated loads exceeds 0.66Fy. i) When the force to be resisted is a concentrated load producing tension or compression applied at a distance from the member end that is greater than the depth of the member, $$ \frac{1000R}{t_w(N + 5k)} ≤ 0.66F_y $$ (10.7.71) ii) When the force to be resisted is a concentrated load at or near the end of the member, $$ \frac{1000R}{t_w(N + 2.5k)} ≤ 0.66F_y $$ (10.7.72) d) Web Crippling : Bearing stiffeners shall be provided in the webs of members under concentrated loads, when the compressive force exceeds the following limits : i) When the concentrated load is applied at a distance not less then d/2 from the end of the member : $$ R = 0.1771t_c^2 \left[ 1 + 3\left(\frac{N}{d}\right)\left(\frac{t_w}{t_f}\right)^{1.5} \right] \sqrt{\frac{F_{yw}}{f_{f/w}}} $$ (10.7.73) ii) When the concentrated load is applied less than a distance d/2 from the end of the member : $$ R = 0.0891t_c^2 \left[ 1 + 3\left(\frac{N}{d}\right)\left(\frac{t_w}{t_f}\right)^{1.5} \right] \sqrt{\frac{F_{yw}}{f_{f/w}}} $$ (10.7.74) If stiffeners are provided and extend at least one-half the web depth, Eq (10.7.73) and (10.7.74) need not be checked. #### 10.7.11.2 Ponding The roof system shall be investigated by structural analysis to assure adequate strength and stability under ponding conditions, unless the roof surface is provided with sufficient slope toward points of free drainage or adequate individual drains to prevent the accumulation of rainwater. The roof system shall be considered stable and not requiring further investigation if : $$ C_p + 0.9C_s ≤ 0.25 $$ (10.7.79) and $$ I_d ≥ 3955(S)^4 $$ (10.7.80) where $$ C_p = \frac{506L_s I_s^4}{I_p} $$ $$ C_s = \frac{5065L_s^4}{I_s} $$ For trusses and steel joists, the moment of inertia Iₛ shall be decreased 15% when used in the above equation. A steel deck shall be considered a secondary member when it is directly supported by the primary members. Total bending stress due to dead loads, gravity live loads (if any) and ponding shall not exceed 0.80Fy, for primary and secondary members. Stresses due to wind or seismic forces need not be included in a ponding analysis. #### 10.7.11.3 Torsion The effects of torsion shall be considered in the design of members and the normal and shearing stresses due to torsion shall be added to those from all other loads, with the resultants not exceeding the allowable values. ## 10.8 LOAD FACTOR DESIGN METHOD ### 10.8.1 General This section provides the specifications for design and construction of steel buildings using Load Factor Design method. ### 10.8.2 Basis of Design #### 10.8.2.1 Required Strength for Factored Loads The required strength of structural members and connections shall be determined by structural analysis for the combinations of appropriate factored loads stipulated in Sec 10.8.2.4. Design by either elastic or plastic analysis is permitted except that plastic analysis is permitted only for steels with yield stress not exceeding 450 N/mm² and shall comply with provision of Sec 10.8.3.2, 10.5.2, 10.8.6.1(b), 10.8.6.1(a), 10.8.8.1 and 10.8.11. Except for hybrid girders and members of A514 steel, beams and girders which are continuous over support or are rigidly framed to columns by means of rivets, high strength bolts or welds may be proportioned for $\frac{1}{12}$ of the maximum negative moments at the support provided that the maximum positive moment at mid-span shall be increased by $\frac{1}{12}$ of the average negative moments. This reduction is not allowed for cantilever moments. If the negative moment is resisted by a column rigidly framed to the beam or girder, the $\frac{1}{12}$ reduction may be used in proportioning the column for the combined axial and bending loading, provided that the stress fₐ due to any concurrent axial load on the member, does not exceed 0.15 Fₐ. #### 10.8.2.2 Limit States The members shall be of such size and strength that no applicable limit state is exceeded when the structure is designed for appropriate factored loads and their combinations stipulated in Sec 10.8.2.4. Strength limit states are related to safety and maximum load carrying capacity whereas serviceability limit states are related to performance under normal service conditions. The term "resistance" includes both strength limit states and serviceability limit states. #### 10.8.2.3 Design for Strength The design strength of each structural component or assemblage must equal or exceed the required strength based on the factored design loads. The design strength φ Rₙ is calculated for each applicable limit state as the nominal strength Rₙ multiplied by a resistance factor φ. The required strength is determined for each applicable load combination according to Sec 10.8.2.4. #### 10.8.2.4 Loads and Load Combinations The design loads shall be the minimum factored loads and their combinations as stipulated in Chapter 2, Loads. #### 10.8.2.5 Design for Serviceability The overall structure and individual members, connections and connectors shall be checked for serviceability according to the requirements of Sec 10.10. ### 10.8.3 Local Buckling #### 10.8.3.1 Classification of Steel Sections Steel sections are classified as compact, noncompact and slender element sections. For a section to qualify as compact, its flanges must be continuously connected to the web or webs and the width-thickness ratio of its compression elements shall not exceed the applicable limiting width-thickness ratios given in Table 6.10.4. If the width-thickness ratio of one or more compression elements exceeds the values for compact section given in Table 6.10.4, the section shall be treated as noncompact provided the width-thickness ratio does not exceed the value for noncompact section given in the same table. If the width-thickness ratio of any compression element exceeds the noncompact values given in Table 6.10.4, the section is classified as a slender element section. a) For unstiffened elements which are supported along only one edge, parallel to the direction of the compression force, the width shall be taken as follows: i) For flanges of I-shaped members and tees, the width b is half the full nominal width. ii) For legs of angles and flanges of channels and zees, the width b is the full nominal dimension. iii) For plates, the width b is the distance from the free edge to the first row of fasteners or line of welds. iv) For stems of tees, d is taken as the full nominal depth. b) For stiffened elements, i.e., supported along two edges parallel to the direction of the compression force, the width shall be taken as follows: i) For webs of rolled or formed sections, h is the clear distance between flanges less the fillet or corner radius at each flange; hc is twice the distance from the neutral axis to the inside face of the compression flange less the fillet or corner radius. ii) For webs of built-up sections, h is the distance between adjacent lines of fasteners or the clear distance between flanges when welds are used, and hc is twice the distance from the neutral axis to the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used. iii) For flange or diaphragm plates in built-up sections, the width b is the distance between adjacent lines of fasteners or the clear distance between flanges when welds are used. iv) For flanges of rectangular hollow structural sections, the width b is the clear distance between webs less the inside corner radius on each side. If the corner radius is not known, the flat width may be taken as the total section width minus three times the thickness. c) For tapered flanges of rolled sections, the thickness is the nominal value halfway between the free edge and the corresponding face of the web. #### 10.8.3.2 Section for Plastic Analysis Plastic analysis is permitted when flanges subjected to compression involving hinge rotation and all webs and flange slenderness ratios less than the limiting value for compact section from Table 6.10.4. For circular hollow sections refer to note (4) of Table 6.10.4. Plastic analysis is subject to the limitations as outlined in Sec 10.8.2.1. ### 10.8.4 Design of Tension Members This section specifies the requirements for design of prismatic members subjected to axial tension due to static forces acting through the centroidal axis. #### 10.8.4.1 Design Tensile Strength The design tensile strength of a member φₜ Pₙ shall be the lesser of the value obtained using the limit states of yielding in the gross section and fracture in the net section. a) For yielding in the gross section : $$ φ_t = 0.90 $$ $$ P_n = 0.001 F_y A_g $$ (10.8.1) b) For fracture in the net section : $$ φ_t = 0.75 $$ $$ P_n = 0.001 F_u A_e $$ (10.8.2) When members without holes are fully connected by welds, the effective net section used in Eq (10.8.2) shall be comprised using the entire area of the member or the effective area of the welds as defined in Sec 10.9.2. When holes are present in a welded member between end connections or at the welded connection in the case of plug or slot welds, the net section through the holes shall be used in Eq (10.8.2). #### 10.8.4.2 Built-up Members The longitudinal spacing of connectors between elements in continuous contact consisting of a plate and a shape or two plates shall not exceed a) 24 times the thickness of the thinner plate or 300 mm for painted members or unpainted members not subject to corrosion. b) 14 times the thickness of the thinner plate or 175 mm for unpainted members of weathering steel subject to atmospheric corrosion. The longitudinal spacing of connectors between components should preferably limit the slenderness ratio in any component between the connectors to 300 or less. Either perforated cover plates or tie plates without lacing may be used on the open sides of built-up tension members. Tie plates shall have a length not less than $\frac{2}{3}$ the distance between the lines of welds or fasteners connecting them to the components of the member. The thickness of such tie plates shall not be less than $\frac{1}{4}$ of the distance between these lines. The longitudinal spacing of intermittent welds or fasteners at the plates shall not exceed 150 mm. The spacing of tie plates shall be such that the slenderness ratio of any component in the length between tie plates shall not exceed 300 mm. #### 10.8.4.3 Eyebars and Pin-connected Members The design strength of eyebars shall be determined as in Sec 10.8.4.1(a) with Aₛ taken as the cross-sectional area of the body. Eyebars shall be of uniform thickness, without reinforcement at the pin holes, and have circular heads whose periphery is concentric with the pin hole. The radius of transition between the circular head and the eyebar body shall be not less than the head diameter. The width of the body of the eyebars shall not exceed eight times its thickness. The thickness can be less than 12 mm only if external nuts are provided to tighten pin plates and filler plates into snug contact. The width b from the hole edge to the plate edge perpendicular to the direction of applied load shall be greater than $\frac{2}{3}$ and, for the purpose of calculation, not more $\frac{3}{4}$ times the eyebar body width. The pin diameter shall not be less than $\frac{7}{8}$ times the eyebar body width. The pin hole diameter shall not be more than 1 mm greater than the pin diameter. For steels having a yield stress greater than 480 N/mm², the hole diameter shall not exceed five times the plate thickness and the width of the eyebar body shall be reduced accordingly. In pin-connected members in which the pin is expected to provide for relative rotation while under full load, the diameter of pin hole shall not be more than 1 mm greater than the diameter of the pin. The width of the plate beyond the pin hole shall be not less than pin hole shall be not less than $\frac{2}{3}$ of the net area required for strength across the pin hole. In pin-connected plates others than eyebars, the design strength shall be determined according to Eq (10.8.2) and the bearing strength of the projected area of the pin shall be determined according to Sec 10.9.8.2. The ### 10.8.5 Design of Columns and Other Compression Members This section covers the design of prismatic members subjected to axial compression through the centroidal axis. #### 10.8.5.1 Effective Lengths and Slenderness Limitations a) Effective Length : The effective length factor K shall be determined in accordance with Sec 10.5.2. b) Plastic Analysis : Plastic analysis, as limited in Sec 10.8.2.1 is permitted if the column slenderness parameter λc defined by Eq (10.8.9) does not exceed 1.5K. #### 10.8.5.2 Design Compressive Strength The design strength of compression members whose elements have a width-thickness ratio less than the noncompact values of Table 6.10.4 is φc Pₙ, where $$ φ_c = 0.85 $$ $$ P_n = 0.001 A_g F_{cr} $$ (10.8.6) For $λ_c ≤ 1.5$ $$ F_{cr} = \left( 0.658^{λ_c^2} \right) F_y $$ (10.8.7) For $λ_c > 1.5$ $$ F_{cr} = \left[ \frac{0.877}{λ_c^2} \right] F_y $$ (10.8.8) where $$ λ_c = \frac{Kl}{r π} \sqrt{\frac{F_y}{E}} $$ (10.8.9) For slender sections, as classified in Sec 10.8.3.1, the design shall conform to the requirements of Sec 10.8.5.6. #### 10.8.5.3 Flexural Torsional Buckling Singly symmetric and unsymmetric columns, such as angle or tee-shaped columns, and doubly symmetric columns such as cruciform or built-up columns with very thin walls, may require consideration of the limit states of flexural-torsional and torsional buckling. The strength of compression members determined by the limit state of torsional and flexural-torsional buckling is φcPₙ , where $$ φ_c = 0.85 $$ $$ P_n = 0.001A_g F_{cr} $$ (10.8.10) $Q$ = 1.0 for elements meeting the width-thickness ratios, for noncompact values from Table 6.10.4. \= $Q_sQ_a$ for elements not meeting the width-thickness ratios for noncompact values from Table 6.10.4 and determined in accordance with the provisions of Sec 10.8.5.6. The nominal critical stress Fcr is determined as follows: a) For $λ_e \sqrt{Q} ≤ 1.5$ : $$ F_{cr} = \left( Q\,0.658^{Qλ_e^2} \right) F_y $$ (10.8.11) b) For $λ_e \sqrt{Q} > 1.5$ : $$ F_{cr} = \left[ \frac{0.877}{λ_e^2} \right] F_y $$ (10.8.12) where $$ λ_e = \sqrt{\frac{F_y}{F_e}} $$ (10.8.13) The critical torsional or flexural-torsional elastic buckling stress Fₑ is determined as follows: a) For doubly symmetric shapes the critical torsional elastic buckling stress is $$ F_e = \frac{π^2 EC_w}{(K_s L)^2} + GJ \frac{1}{I_x + I_y} $$ (10.8.14) b) For singly symmetric shapes, where y is the axis of symmetry, the critical flexural-torsional elastic buckling stress is $$ F_e = \frac{F_{cy} + F_cz}{2H} \left[ 1 - \sqrt{1 - \frac{4F_{cy}F_{cz}H}{(F_{cy} + F_{cz})^2}} \right] $$ (10.8.15) c) For unsymmetric shapes, the critical flexural-torsional elastic buckling stress Fₑ is the smallest root of the cubic equation $(F_c - F_ex)(F_c - F_ey)(F_c - F_ez) - F_c^2(F_c - F_ey)(x_o/r_o)^2 - F_c^2(F_c - F_ex)(y_o/r_o)^2 = 0$ (10.8.16) In Eq (10.8.14), (10.8.15), (10.8.16) above, $$ r_o^2 = x_o^2 + y_o^2 + \frac{I_x + I_y}{A} $$ (10.8.17) $$ H = 1 - \left( \frac{x_o^2 + y_o^2}{r_o^2} \right) $$ (10.8.18) $$ F_{cx} = \frac{π^2 E}{(K_x L/r_x)^2} $$ (10.8.19) $$ F_{cy} = \frac{π^2 E}{(K_y L/r_y)^2} $$ (10.8.20) $$ F_{cz} = \frac{π^2 EC_w}{(K_s L)^2} + GJ \frac{1}{A r_o^2} $$ (10.8.21) #### 10.8.5.4 Built-up Members At the ends of built-up compression members bearing on base plates or milled surfaces, all components in contact with one another shall be connected by a weld having a length not less than the maximum width of the member. For intermediate connections required by sections below, spacing between the connectors or bolts, or both, shall be spaced longitudinally no more than four diameters apart for a distance equal to 1½ times the maximum width of the member. Along the length of built-up compression members between the end connections required above, longitudinal spacing for intermediate welds, bolts or rivets shall be such that the web shear stress along the length of the web will not exceed the value permitted. However, where a component of a built-up compression member consists of an outside plate, except as provided in the next sentence, the maximum spacing shall not exceed the thickness of the thinner outside plate nor 300 mm, when intermittent welds are provided along the edges of the components or when fasteners are provided on all gauge lines at each section. When fasteners are staggered, the maximum spacing on each gauge line shall not exceed the thickness of the thinner outside plate times $\frac{500}{\sqrt{F_y}}$, nor 450 mm . For unpainted built-up members made of weathering steel which will be exposed to atmospheric corrosion, the fasteners connecting a plate and a shape or two-plate components in contact with one another shall not exceed 14 times the thickness of the thinnest part nor 175 mm and the maximum end distance shall not exceed eight times the thickness of the thinnest part nor 125 mm. Compression members composed of two or more shapes shall be connected to one another at intervals such that the slenderness ratio L/r of either shape, between the fasteners, does not exceed the governing slenderness ratio of the built-up members. The least radius of gyration r shall be used in computing the slenderness ratio of each component part. The design strength of built-up members composed of two or more shapes shall be determined in accordance with Sec 10.8.5.2 or 10.8.5.3 subject to the following modification. If the bulking mode involves relative deformation that produces shear forces in the connectors between individual shapes, K/r is replaced by $(K/r)_m$ determined as follows: a) For Snug-tight Bolted Connectors : $$ \left( \frac{Kl}{r} \right)_m = \sqrt{\left( \frac{Kl}{r} \right)_o^2 + \left( \frac{a}{r_i} \right)^2} $$ (10.8.22) b) For Welded Connectors and for Fully Tightened Bolted Connectors as required for Slip-critical Joints: with $\frac{a}{r_i} > 50$ : $$ \left( \frac{Kl}{r} \right)_m = \sqrt{\left( \frac{Kl}{r} \right)_o^2 + \left( \frac{a}{r_i} - 50 \right)^2} $$ (10.8.23) with $\frac{a}{r_i} ≤ 50$ : $$ \left( \frac{Kl}{r} \right)_m = \left( \frac{Kl}{r} \right)_o $$ (10.8.24) where $(Kl/r)_o$ = column slenderness of built-up members acting as a unit $a/r_i$ = larger column slenderness of individual components $(Kl/r)_m$ = modified column slenderness of built-up members $a$ = distance between connectors, mm $r_i$ = minimum radius of gyration of individual component Open sides of compression members built up from plates or shapes shall be provided with continuous cover plates perforated with a succession of access holes. The unsupported width of such plates at access holes, as defined in Sec 10.8.3.1 is assumed to contribute to the design strength provided that: i) The width-thickness ratio conforms to the limitations of Sec 10.8.3.1. ii) The ratio of length (in direction of stress) to width of hole shall not exceed 2. iii) The clear distance between holes in the direction of stress shall not be less than the transverse distance between nearest line of connecting fasteners or welds. iv) The periphery of the holes at all points shall have a minimum radius of 40 mm. The function of perforated cover plates may be performed by lacing with tie plates at each end and at intermediate points if the lacing is interrupted. Tie plates shall be as near the ends as practicable. In main members providing design strength, the end tie plates shall have a length of not less than the distance between the lines of fasteners or welds connecting them to the components of the member. Intermediate tie plates shall have a length of not less than $\frac{1}{2}$ of this distance. The thickness of tie plates shall be not less than $\frac{1}{50}$ of the distance between lines of welds or fasteners connecting them to the segments of the members. In welded construction, the welding on each line connecting a tie plate shall in aggregate be not less than $\frac{1}{3}$ the length of the plate. In bolted and riveted construction, the spacing in the direction of stress in tie plates shall be not more than 6 diameters and the tie plates shall be connected to each segment by at least three fasteners. Lacing, including flat bars, angles, channels or other shapes employed as lacing, shall be so spaced that the L/r ratio of the flange included between their connections shall not exceed the governing slenderness ratio for the member as a whole. Lacing shall be proportioned to provide a shearing strength normal to the axis of the member equal to 2% of the compressive design strength of the member. The L/r ratio for lacing bars arranged in single systems shall not exceed 140. For double lacing this ratio shall not exceed 200. Double lacing bars shall be joined at their intersections. For lacing bars in compression, L may be taken as the unsupported length of the lacing bar between welds or fasteners connecting it to the components of the built-up member for single lacing, and 70% of that distance for double lacing. The inclination of lacing bars to the axis of the member shall preferably be not less than 60° for single lacing and 45° for double lacing. When the distance between the lines of welds or fasteners in the flanges is more than 375 mm, the lacing shall preferably be double or be made of angles. #### 10.8.5.5 Pin-Connected Compression Members Pin-connections of pin-connected compression members shall conform to the requirements of Sec 10.8.4.3 except Eq (10.8.3) and (10.8.4) do not apply. #### 10.8.5.6 Slender Compression Elements Axially loaded members containing elements subjected to compression which have a width-thickness ratio in excess of the noncompact values as stipulated in Sec 10.8.3.1 shall be designed in accordance with this section. Flexural members with slender compression elements shall be designed in accordance with Sec 10.8.6.1(f). Rolled flexural members with proportions not covered by Sec 10.8.6.1(f) shall be designed in accordance with this section. a) Unstiffened Compression Elements : The design strength of unstiffened compression elements whose width-thickness ratio exceeds the applicable value for noncompact sections as stipulated in Sec 10.8.3.1 shall be subject to a reduction factor $Q_s$. The value of $Q_s$ shall be determined by Eq (10.8.25) through (10.8.30) as applicable. When such elements comprise the compression flange of a flexural member, the maximum required bending stress shall not exceed $\phi_b F_y Q_s$, where $\phi_b = 0.90$. The design strength of axially loaded compression members shall be modified by the appropriate reduction factor $Q_s$, as provided in (c) below. For single angles : When $\frac{200}{\sqrt{F_y}} < b/t < \frac{407}{\sqrt{F_y}}$ $$ Q_s = 1.340 - 0.0017(b/t)_i \sqrt{F_y} $$ (10.8.25) When $b/t ≥ \frac{407}{\sqrt{F_y}}$ $$ Q_s = \frac{106867}{F_y (b/t)^2} $$ (10.8.26) For angles of plates projecting from columns or other compression members, and for projecting elements of compression flanges of girders : When $\frac{250}{\sqrt{F_y}} < b/t < \frac{462}{\sqrt{F_y}}$ $$ Q_s = 1.415 - 0.00166(b/t)_i \sqrt{F_y} $$ (10.8.27) When $b/t ≥ \frac{462}{\sqrt{F_y}}$ $$ Q_s = \frac{137890}{F_y (b/t)^2} $$ (10.8.28) For stems of tees : When $\frac{333}{\sqrt{F_y}} < b/t < \frac{462}{\sqrt{F_y}}$ $$ Q_s = 1.908 - 0.0027(b/t)_i \sqrt{F_y} $$ (10.8.29) When $b/t ≥ \frac{462}{\sqrt{F_y}}$ $$ Q_s = \frac{137890}{F_y (b/t)^2} $$ (10.8.30) Unstiffened elements of tees whose proportions exceed the limits of Sec 10.8.3.1 shall conform to the limits given in Table 6.10.2. b) Stiffened Compression Elements : When the width-thickness ratio of uniformly compressed stiffened elements (except perforated cover plates) exceeds the noncompact limit stipulated in Sec 10.8.3.1 a reduced effective width, bₑ, shall be used in computing the design properties of the section containing the element. i) For flanges of square and rectangular sections of uniform thickness : $$ b_e = \frac{856t}{\sqrt{f}} \left[ 1 - \frac{170}{(b/t)\sqrt{f}} \right] ≤ b $$ (10.8.31) ii) For other uniformly compressed elements : $$ b_e = \frac{856t}{\sqrt{f}} \left[ 1 - \frac{150}{(b/t)\sqrt{f}} \right] ≤ b $$ (10.8.32) where $b_e$ = reduced width, mm $f$ = computed elastic compressive stress in the stiffened elements, based on the design properties as specified in (c) below, N/mm². If unstiffened elements are included in the total cross-section, $f$ for the stiffened element must be such that the maximum compressive stress in the unstiffened element does not exceed $\phi_c F_{cr}$ as defined in (c) below, with $Q = Q_s$ and $\phi_c = 0.85$, or $\phi_b F_y Q_s$ with $\phi_b = 0.90$, as applicable. iii) For axially loaded circular sections : Members with diameter to thickness ratios $D/t$ greater than $22752/F_y$, but having a diameter to thickness ratio of less than $89630/F_y$ ; $$ Q = \frac{7584}{F_y(D/t)} + \frac{2}{3} $$ (10.8.33) c) Design Properties : Properties of sections shall be determined using the full cross-section, except as follows : In computing the moment of inertia and elastic section modulus of flexural members, the effective width of uniformly compressed stiffened elements, as determined in (b) above, shall be used in determining effective cross-sectional properties. For unstiffened elements of the cross-section, $Q_s$ is determined from (a) above. For stiffened elements of the cross-section $$ Q_a = \frac{\text{effective area}}{\text{actual area}} $$ (10.8.34) where the effective area is equal to the summation of the effective areas of cross-section. For axially loaded compression members the gross cross-sectional area and the radius of gyration $r$ shall be computed on the basis of the actual cross-section. However, when $\lambda_c\sqrt{Q} ≤ 1.5$, the critical stress $F_{cr}$ shall be determined by $$ F_{cr} = Q\left(0.658^{Q\lambda_c^2}\right)F_y $$ (10.8.35) where Q is given by the following : i) Cross-sections composed entirely of unstiffened elements, $Q = Q_s$ ii) Cross-sections composed entirely of stiffened elements, $Q = Q_a$ iii) Cross-sections composed of both stiffened and unstiffened elements, $Q = Q_s Q_a$ When $\lambda_c\sqrt{Q} > 1.5$, the critical stress $F_{cr}$ shall be determined by $$ F_{cr} = \left[\frac{0.877}{\lambda_c^2}\right]F_y $$ (10.8.36) ### 10.8.6 Design of Beams and Other Flexural Members This section specifies the requirements for the design of singly or doubly symmetric beams including hybrid beams and girders loaded in the plane of symmetry, and channels loaded in a plane passing through the shear centre parallel to the web or restrained against twisting at load points and points of support. #### 10.8.6.1 Design for Flexure a) Unbraced Length for Plastic Analysis: Plastic analysis, as limited in Sec 10.8.2.1, is permitted when the laterally unbraced length Lp of the compression flange at plastic hinge locations associated with the failure mechanism, for a compact section bent about the major axis, does not exceed Lpd, determined as follows : i) For doubly symmetric and singly symmetric I-shaped members with the compression flange larger than the tension flange (including hybrid members) loaded in the plane of the web $$ L_{pd} = \frac{25000 + 15000(M_1/M_p)}{F_y} $$ (10.8.37) ii) For solid rectangular bars and symmetric box beams $$ L_{pd} = \frac{34500 + 20700(M_1/M_p)}{F_y} F_y ≥ 20700σ_y/F_y $$ (10.8.38) There is no limit on Lb for members with circular or square cross-sections nor for any beam bent about its minor axis. In the region of the last hinge to form, and in regions not adjacent to a plastic hinge, the flexural design strength shall be determined as in (b) below. b) Flexural Design Strength: The flexural design strength, determined by the limit state of lateral-torsional buckling, is φbMₙ, where the nominal strength Mₙ shall be determined in accordance with the following sections, and φb = 0.90. c) Compact Section Members with Lb ≤ Lr For laterally unsupported compact section members bent about the major axis: $$ M_n = C_b M_p - \left( M_p - M_r \right) \left( \frac{L_b - L_p}{L_r - L_p} \right) ≤ M_p $$ (10.8.39) where * $C_b$ = 1.75+1.05(M₁/M₂)+0.3(M₁/M₂)² ≤ 2.3 where M₁ is the smaller and M₂ the larger end moment in the unbraced segment of the member; M₁/M₂ is positive when M₁ and M₂ have the same sign (reverse curvature bending) and negative when bent in single curvature. * $C_b$ = 1.0 for unbraced cantilevers and for members where the moment within a significant portion of the unbraced segment is greater than or equal to the larger of the segment end moments. * $L_p$ = distance between points braced against lateral displacement of the compression flange, or between points braced to prevent twist of the cross-section. * $L_r$ = distance between points braced against lateral displacement of the compression flange, between points braced to prevent twist of the cross-section. For I-shaped members including hybrid sections and channels bent about the major axis: $$ L_p = \frac{790 r_y}{\sqrt{F_{yf}}} $$ (10.8.40) For solid rectangular bars and symmetric box sections: $$ L_p = \frac{25.86 \times 10^{-3} r_y}{M_p} \sqrt{JA} $$ (10.8.41) The limiting laterally unbraced length Lr and the corresponding buckling moment Mr shall be determined as follows: i) For I-shaped members, doubly symmetric and singly symmetric with the compression flange larger than the tension flange, and channels loaded in the plane of the web: $$ L_r = \frac{r_y X_1}{F_{yw} - F_r} \sqrt{1 + \sqrt{1 + X_2(F_{yw} - F_r)^2}} $$ (10.8.42) $$ M_r = 10^{-6}(F_{yw} - F_r)S_x $$ (10.8.43) where $$ X_1 = \frac{π}{S_x}\sqrt{\frac{EGJA}{2}} $$ (10.8.44) $$ X_2 = 4\frac{C_w}{I_y}\left(\frac{S_x}{GJ}\right)^2 $$ (10.8.45) $F_r$ = compressive residual stress in flange; 70 N/mm² for rolled shapes, 114 N/mm² for welded shapes. ii) For singly symmetric, I-shaped members with the compression flange larger than the tension flange, use $S_{xc}$ in place of $S_x$ in Eq (10.8.43) through (10.8.45). iii) For symmetric box sections bent about the major axis and loaded in the plane of symmetry, M, and Lr shall be determined from Eq (10.8.43) and (10.8.46) respectively. iv) For solid rectangular bars bent about major axis: $$ L_r = \frac{0.393 r_y \sqrt{JA}}{M_r} $$ (10.8.46) $$ M_r = 10^{-6} F_y S_x $$ (10.8.47) d) Compact Section Members With Lₚ > Lr For laterally unsupported members with compact section members bent about the major axis: $$ M_n = M_{cr} ≤ C_b M_r $$ (10.8.48) Where Mcr is the critical elastic moment, determined as follows: i) For I-shaped members, doubly symmetric and singly symmetric with compression flange larger than the tension flange (including hybrid members) and channels loaded in the plane of the web: $$ M_{cr} = 10^{-6} C_b \frac{π}{L_b} \sqrt{EI_y GJ + \left( \frac{πE}{L_b} \right)^2 I_y C_w} $$ (10.8.49) $$ = 10^{-6} \frac{C_b S_x X_1 \sqrt{2}}{L_b/r_y} \sqrt{1 + \frac{X_1^2 X_2}{2 (L_b/r_y)^2}} $$ ii) For solid rectangular bars and symmetric box sections: $$ M_{cr} = \frac{0.393 C_b \sqrt{JA}}{L_b/r_y} $$ (10.8.50) e) Tees and Double-angle Beams: The nominal strength of tees and double-angle beams loaded in the plane of symmetry and bent about the major axis, with flange and web slenderness ratios less than the corresponding noncompact values given in Table 6.10.4. $$ M_n = M_{cr} = 10^{-6} \frac{C_b π \sqrt{EI_y GJ}}{L_b} \left[ B ± \sqrt{1 + B^2} \right] ≤ M_y $$ (10.8.51) where $$ B = ± 2.3\left( \frac{d}{L_b} \right) \sqrt{\frac{I_y}{J}} $$ (10.8.52) The plus sign for B applies when the stem is in tension and the minus sign applies when the stem is in compression. f) Nominal Flexural Strength of Other Sections : There is no lateral-torsional buckling limit state for circular or square shapes nor for any shape bent about its minor axis. The nominal strength $M_n$ of other types of cross-sections including noncompact sections or sections with slender elements, shall be determined as follows for each limit state: For $λ ≤ λ_p$ $$ M_n = M_p $$ (10.8.53) For $λ_p < λ ≤ λ_r$: For the limit state of lateral-torsional buckling: $$ M_n = C_b \left[ M_p - \left(M_p - M_r\right)\left(\frac{λ - λ_p}{λ_r - λ_p}\right) \right] ≤ M_p $$ (10.8.54) For the limit states of flange and web local buckling: $$ M_n = M_p - \left(M_p - M_r\right)\left(\frac{λ - λ_p}{λ_r - λ_p}\right) $$ (10.8.55) For $λ > λ_r$: For the limit state of lateral-torsional buckling and for flange local buckling: $$ M_n = M_{cr} = 10^{-6} S F_{cr} $$ (10.8.56) #### 10.8.6.2 Design for Shear This section applies to the web (or webs in the case of multiple web members) of singly or doubly symmetric beams, including hybrid beams, subjected to shear in the plane of symmetry, and channels subjected to shear in the web. Where failure might occur by shear along a plane through fasteners, refer to Sec 10.9.4. For members subjected to high shear from concentrated loads, refer to Sec 10.8.11.1(g). a) Web Area Determination : The web area Aᵥ shall be taken as the overall depth d times the web thickness tᵥ. b) Design Shear Strength : The design shear strength of webs is φᵥVₙ, where φᵥ = 0.90 and the nominal shear strength Vₙ is determined as follows : For $\frac{h}{t_w} ≤ 490 \sqrt{k/F_{yw}}$ $$ V_n = 0.0006 F_{yw} A_w $$ (10.8.57) For $490 \sqrt{k/F_{yw}} < \frac{h}{t_w} ≤ 615 \sqrt{k/F_{yw}}$ $$ V_n = 0.0006 F_{yw} A_w \frac{490 \sqrt{k/F_{yw}}}{h/t_w} $$ (10.8.58) For $\frac{h}{t_w} > 615 \sqrt{k/F_{yw}}$ $$ V_n = A_w \frac{182k}{(h/t_w)^2} $$ (10.8.59) The web plate buckling coefficient k is given by $$ k = 5 + \frac{5}{(a/h)^2} $$ (10.8.60) Except that k shall be taken as 5 if a/h exceeds 3.0 or $[260/(h/t_w)]^2$. When stiffeners are not required, k = 5. Maximum h/tw limits are given below : For $\frac{a}{h} ≤ 1.5$ $$ \left(\frac{h}{t_w}\right)_{\max} = \frac{5250}{\sqrt{F_{yf}}} $$ (10.8.61) For $\frac{a}{h} > 1.5$ $$ \left(\frac{h}{t_w}\right)_{\max} = \frac{96525}{\sqrt{F_{yf}(F_{yf} + 114)}} $$ (10.8.62) In unstiffened girders h/tw must be less than 260. #### 10.8.6.3 Transverse Stiffeners Transverse stiffeners are not required when $h/t_w ≤ 1100/\sqrt{F_{yw}}$, or when the required shear $V_u$, as determined by structural analysis for the factored loads, is less than or equal to $\phi_v V_n$ for k = 5 given in Sec 10.8.6.2. Transverse stiffeners used to develop the web design shear strength as provided in Sec 10.8.6.2 shall have a moment of inertia about an axis in the web centre for stiffener pairs or about the face in contact with the web plate for single stiffeners, which shall not be less than $(a t_w^3 j)$. where $$ j = \frac{2.5}{(a/h)^2} - 2 ≥ 0.5 $$ (10.8.63) Intermediate stiffeners may be stopped short of the tension flange, provided bearing is not needed to transmit a concentrated load or reaction. The weld by which intermediate stiffeners are attached to the web shall be terminated not less than 4 times nor more than 6 times the web thickness from the nearest toe of the web to flange weld. When single stiffeners are used, they shall be attached to the compression flange, if it consists of a rectangular plate, to resist any uplift tendency due to torsion in the plate. When lateral bracing is attached to a stiffener, or a pair of stiffeners, these, in turn, shall be connected to the compression flange to transmit one per cent of the total flange stress, unless the flange is composed only of angles. Bolts connecting stiffeners to the girder web shall be spaced not more than 300 mm on centres. If intermittent fillet welds are used, the clear distance between welds shall not be more than 16 times the web thickness nor more than 250 mm. #### 10.8.6.4 Web-Tapered Member Design of tapered members shall satisfy the following modified requirements along with the requirements stipulated in Sec 10.8.6.1 through 10.8.6.3. a) General Requirements i) It shall possess at least one axis of symmetry which shall be perpendicular to the plane of bending if moments are present. ii) The flanges shall be of equal and constant area. iii) The depth shall vary linearly as $$ d = d_o \left( 1 + \gamma \frac{z}{L} \right) $$ (10.8.64) where $$ \gamma = (d_L - d_o)/d_o ≤ \text{ the smaller of } 0.268 \text{ (} L/d_o \text{) or } 6.0 $$ b) Design Tensile Strength : The design tensile strength of tapered members shall be determined in accordance with the requirements of Sec 10.8.4.1. c) Design Compressive Strength : The design compressive strength of tapered members shall be determined in accordance with the requirements of Sec 10.8.5.2 using an effective slenderness parameter $λ_{eff}$ computed as follows: $$ λ_{eff} = \frac{S}{π} \sqrt{\frac{QF_y}{E}} $$ (10.8.65) where * $S$ = $KL/r_{eg}$ for weak axis bending and $K_y L/r_{eg}$ for strong axis bending * $Q$ = reduction factor * 1.0, if all elements meet the limiting noncompact width-thickness ratios of Sec 10.8.3.1 * $Q_sQ_a$ , determined in accordance with Sec 10.8.5.6., if any stiffened and/or unstiffened elements exceeded the noncompact limits given in Sec 10.8.3.1. The smallest area of the tapered member shall be used for Aₛ in Eq (10.8.6). d) Design Flexural Strength: The design flexural strength of tapered flexural members for the limit state of lateral torsional buckling is φbMₙ, where φb = 0.90 and the nominal strength is $$ M_n = 1.67 \times 10^{-3} S^2_c F_y $$ (10.8.66) $$ F_{by} = \frac{2}{3} \left[ 1.0 - \frac{F_y}{6B_e} \sqrt{F_{sy}^2 + F_{wy}^2} \right] F_y ≤ 0.60F_y $$ (10.8.67) unless $F_{by} ≤ F_y / 3$, in which case $$ F_{by} = B_i \sqrt{F_{sy}^2 + F_{wy}^2} $$ (10.8.68) In the above equations, $$ F_{sy} = \frac{82735}{(h_s L_{d_s}/A_f)} $$ (10.8.69) $$ F_{wy} = \frac{1172 \times 10^3}{(h_w L_f/r_{To})^2} $$ (10.8.70) where * $h_s$ = factor equal to 1.0+0.023$γ \sqrt{L_{d_s}/A_f}$ * $h_w$ = factor equal to 1.0+0.00385$γ \sqrt{L/r_{To}}$ * $r_{To}$ = radius of gyration of a section at the smaller end, considering only the compression flange plus ⅓ of the compression web area, taken about an axis in the plane of the web, mm . B is determined as follows: i) When the maximum moment M₂ in three adjacent segments of approximately equal unbraced length is located within the central segment and M₁ is the larger moment at one end of the three-segment portion of a member: $$ B = 1.0 + 0.37\left(1.0 + \frac{M_1}{M_2}\right) + 0.50\gamma\left(1.0 + \frac{M_1}{M_2}\right) \geq 1.0 $$ (10.8.71) ii) When the largest computed bending stress fb2 occurs at the larger end of two adjacent segments of approximately equal unbraced length and fb1 is the computed bending stress at the smaller end of two-segment portion of a member: $$ B = 1.0 + 0.58\left(1 + \frac{f_{b1}}{f_{b2}}\right) - 0.707\left(1 + \frac{f_{b1}}{f_{b2}}\right) \geq 1.0 $$ (10.8.72) iii) When the largest computed bending stress fb2 occurs at the smaller end of two adjacent segments of approximately equal unbraced length and fb1 is the computed bending stress at the larger end of the two-segment portion of a member : $$ B = 1.0 + 0.55\left(1.0 + \frac{f_{b1}}{f_{b2}}\right) + 2.20\gamma\left(1.0 + \frac{f_{b1}}{f_{b2}}\right) \geq 1.0 $$ (10.8.73) In the foregoing, $γ = (d_L - d_o)/d_o$ is calculated for the unbraced length that contains the maximum computed bending stress. iv) When the computed bending stress at the smaller end of a tapered member or segment thereof is equal to zero: $$ B = \frac{1.75}{1.0 + 0.25\sqrt{\gamma}} $$ (10.8.74) where $γ = (d_L - d_o)/d_o$, calculated for the unbraced length adjacent to the point of zero bending stress. e) Design Shear Strength: The design shear strength of tapered flexural members shall be determined in accordance with Sec 10.8.6.2. f) Combined Flexure and Axial Force : For tapered members with a single web taper subjected to compression and bending about the major axis, Eq (10.8.103) through 10.8.106 apply, with the following modifications: Pₐ and Pₘₓ shall be determined for the properties of the smaller end, using appropriate effective length factors. Mₐₓ, Mₘₓ, and Mₘₓ shall be determined for the properties of the larger end, Mₓ = 1.67 × 10⁻³ S²\_c F\_y, and Cₘₓ is replaced by C'ₘₓ, determined as follows: i) When the member is subjected to end moments which cause single curvature bending and approximately equal computed moments at the ends: $$ C'_{m} = 1.0 + 0.1\left(\frac{P_a}{φ_b P_{cx}}\right) + 0.3\left(\frac{P_a}{φ_b P_{cx}}\right)^2 $$ (10.8.75) ii) When the computed bending moment at the smaller end of the unbraced length is equal to zero: $$ C'_{m} = 1.0 + 0.9\left(\frac{P_a}{φ_b P_{cx}}\right) + 0.6\left(\frac{P_a}{φ_b P_{cx}}\right)^2 $$ (10.8.76) When the effective slenderness parameter λeff ≥ 1.0 and combined stress is checked incrementally along the length, the actual area and the actual section modulus at the section under investigation may be used. ### 10.8.7 Design of Plate Girders Plate girders shall be distinguished from beams on the basis of the web slenderness ratio hc/tₘ. When this value is greater than 2550 / $\sqrt{F_{yf}}$, the provisions of this section shall apply for design flexural strength, otherwise the requirements of Sec 10.8.6.1(f) shall be applicable. #### 10.8.7.1 Limitations Doubly and singly symmetrical single web nonhybrid and hybrid plate girders loaded in the plane of the web shall be designed according to the provisions of this section provided that the following limitations are satisfied. a) For $\frac{a}{h} ≤ 1.5$ $$ \left(\frac{h}{t_w}\right)_{\max} = \frac{5250}{\sqrt{F_{yf}}} $$ (10.8.77) b) For $\frac{a}{h} > 1.5$ $$ \left(\frac{h}{t_w}\right)_{\max} = \frac{96525}{\sqrt{F_{yf}(F_{yf} + 114)}} $$ (10.8.78) In unstiffened girders h/tₘ must be less than 260. For girders covered by this section, the shear strength may be determined by the provisions of Sec 10.8.6.2 if tension field action is not utilized, otherwise the requirements stipulated in Sec 10.8.7.3 shall be applicable. #### 10.8.7.2 Design Flexural Strength The design flexural strength of plate girders with slender webs $\left(h_c/t_w > 2550 / \sqrt{F_{yf}}\right)$ shall be φbMₙ, where φb = 0.90 and Mₙ is the lower value obtained according to the limit states of tension flange yield and compression flange buckling. For tension flange yield $$ M_n = 10^{-6} S_{st} R_{PG} R_c F_{yd} $$ (10.8.79) For compression flange buckling $$ M_n = 10^{-6} S_w R_{PG} R_c F_{cr} $$ (10.8.80) where $$ R_{PG} = 1 - 0.0005 a_c \left( \frac{h_c}{t_w} \frac{5250}{\sqrt{F_{cr}}} \right) ≤ 1.0 $$ (10.8.81) $$ R_c = 1.0 - 0.1\left(1 + 3.a_r\right)(0.81 - m) ≤ 1.0 \text{ (for nonhybrid girder, } R_c = 1). $$ The critical stress Fcr to be used is dependent upon the slenderness parameters λ, λₚ, λᵣ, and C\_PG as follows : a) For $λ ≤ λ_p$ $$ F_{cr} = F_{yf} $$ (10.8.82) b) For $λ_p < λ ≤ λ_r$ $$ F_{cr} = C_b F_{yf} \left[ 1 - \frac{1}{2}\left( \frac{λ - λ_p}{λ_r - λ_p} \right) \right] ≤ F_{yf} $$ (10.8.83) c) For $λ > λ_r$ $$ F_{cr} = M_{cr} = 10^{-6} S_{cr} $$ (10.8.84) In the foregoing , the slenderness parameter shall be determined for both the limit state of lateral torsional buckling and the limit state of flange local buckling; the slenderness parameter which results in the lowest value of Fcr, governs. For the limit state of lateral torsional buckling. $$ λ = \frac{L_b}{r_T} $$ (10.8.85) $$ λ_p = \frac{790}{\sqrt{F_{yf}}} $$ (10.8.86) $$ λ_r = \frac{1985}{\sqrt{F_{yf}}} $$ (10.8.87) $$ C_{PG} = 1.97 \times 10^6 C_b $$ (10.8.88) where $$ C_b = 1.75 + 1.05(M_1/M_2) + 0.3(M_1/M_2)^2 ≤ 2.3 $$ $r_T$ = Radius of gyration of compression flange plus one-sixth the web, mm. For the limit state of flange local buckling $$ λ = \frac{b_f}{2t_f} $$ (10.8.89) $$ λ_p = \frac{170}{\sqrt{F_{yf}}} $$ (10.8.90) $$ λ_r = \frac{395}{\sqrt{F_{yf}}} $$ (10.8.91) $$ C_{PG} = 77200 $$ (10.8.92) $C_b$ = 1 The limit state of flexural web local buckling is not applicable. #### 10.8.7.3 Design Shear Strength with Tension Field Action The design shear strength shall be φᵥVₙ, where φᵥ = 0.90 and Vₙ is determined as follows : $$ V_n = 0.0006F_{yw}A_w $$ (10.8.93) b) For $h/t_w > 492 \sqrt{k/F_{yw}}$ $$ V_n = 0.0006 A_w F_{yw} \left[ C_v + \frac{1-C_v}{1.15\sqrt{1+(a/h)^2}} \right] \tag{10.8.94} $$ where $C_v$ = ratio of critical web stress, according to linear buckling theory, to the shear yield stress of web material. Except for end panels in nonhybrid plate girders, for all panels in hybrid and web tapered plate girders and when $a/h$ exceeds 3.0 or $[260/(h/t_w)]^2$, in these cases, tension field action is not permitted and $$ V_n = 0.0006 A_w F_{yw} C_v \tag{10.8.95} $$ The web plate buckling coefficient $k$ is given as $$ k = 5 + \frac{5}{(a/h)^2} \tag{10.8.96} $$ except that $k$ shall be taken as 5.0 if $a/h$ exceeds 3.0 or $[260/(h/t_w)]^2$. The shear coefficient $C_v$ is determined as follows: For $492 \sqrt{k/F_{yw}} \leq \frac{h}{t_w} \leq 615 \sqrt{k/F_{yw}}$ $$ C_v = \frac{492 \sqrt{k/F_{yw}}}{h/t_w} \tag{10.8.97} $$ For $\frac{h}{t_w} > 615 \sqrt{\frac{k}{F_{yw}}}$ $$ C_v = \frac{303365k}{(h/t_w)^2 F_{yw}} \tag{10.8.98} $$ #### 10.8.7.4 Transverse Stiffeners Transverse stiffeners are not required in plate girders when $h/t_y < 1100/\sqrt{F_{yw}}$ or when the required shear $V_u$, as determined by structural analysis for the factored loads, is less than or equal to $0.0006 A_w F_y C_v$, where $C_v$ is determined for $k = 5$ and $\phi = 0.90$. Stiffeners may be required in certain portions of a plate girder to develop the required shear or to satisfy the limitations given Sec 10.8.7.1. The moment of inertia $I_{st}$ of a transverse stiffener about an axis in the web centre for stiffener pairs or about the face in contact with the web plate for single stiffeners shall not be less than $at_w^3 j$, where $$ j = \frac{2.5}{(a/h)^2} - 2 \geq 0.5 \tag{10.8.99} $$ and the stiffener area $A_{st}$ when designing for tension field action shall not be less than $$ \frac{F_{yw}}{F_{ysr}} \left[ 0.15Dh t_w (1-C_v) \frac{V_u}{\phi_v V_n} - 18t_w^2 \right] \geq 0 \tag{10.8.100} $$ where * $D$ = 1.0 for stiffeners in pairs * $D$ = 1.8 for single angle stiffeners * $D$ = 2.4 for single plate stiffeners $C_v$ and $V_n$ are defined in Sec 10.8.7.3, and $V_u$ is the required shear at the location of the stiffener. #### 10.8.7.5 Flexure Shear Interaction Plate girders with webs that depend on tension field action shall satisfy flexure shear interaction criteria. When stiffeners are required and $$ \frac{0.6V_u}{M_u} \leq \frac{V_u}{M_u} \leq \frac{V_n}{0.75M_n} \tag{10.8.101} $$ the following interaction equation shall be satisfied: $$ \frac{M_u}{M_n} + 0.625 \frac{V_u}{V_n} \leq 1.375 \phi \tag{10.8.102} $$ where $M_n$ is the nominal flexural strength of plate girders from Sec 10.8.7.2, $\phi = 0.90$ and $V_n$ is the nominal shear strength from Sec 10.8.7.3, except that $M_n$ may not exceed $\phi M_n$ ($\phi = 0.90$) and $V_n$ may not exceed $\phi V_n$ ($\phi = 0.90$). ### 10.8.8 Members Under Torsion and Combined Forces This section covers the design of prismatic members subjected to axial force and flexure about one or both axes of symmetry, with or without torsion, and torsion only. #### 10.8.8.1 Symmetric Members Subjected to Bending and Axial Force #### a) Doubly and Singly Symmetric Members in Flexure and Tension The interaction of flexure and tension in symmetric shapes shall be limited by Eq (10.8.103) and (10.8.104). For $\frac{P_u}{\phi P_n} \geq 0.2$ $$ \frac{P_u}{\phi P_n} + \frac{8}{9} \left( \frac{M_{ux}}{\phi_b M_{nx}} + \frac{M_{uy}}{\phi_b M_{ny}} \right) \leq 1.0 \tag{10.8.103} $$ For $\frac{P_u}{\phi P_n} < 0.2$ $$ \frac{P_u}{2\phi P_n} + \left[ \frac{M_{ux}}{\phi_b M_{nx}} + \frac{M_{uy}}{\phi_b M_{ny}} \right] \leq 1.0 \tag{10.8.104} $$ where * $\phi = \phi_t$ = resistance factor for tension, 0.90 * $\phi_b$ = resistance factor for flexure, 0.90. Second order effects may be considered in the determination of $M_u$ for use in Eq (10.8.103) and (10.8.104). #### b) Doubly and Singly Symmetric Members in Flexure and Compression The interaction of flexure and compression in symmetric shapes shall be limited by Eq (10.8.103) and (10.8.104), by substituting $\phi$ with $\phi_c$, where $\phi_c$ = resistance factor for compression = 0.85. ##### i) Determination of $M_u$ In elastic design, $M_u$ shall be determined from a second order elastic analysis using factored loads. In plastic design, $M_u$ shall be determined from a plastic analysis. In structures designed on the basis of elastic first order analysis the following procedure for the determination of $M_u$ shall be used. $$ M_u = B_1 M_{ux} + B_2 M_{uy} \tag{10.8.105} $$ where $$ B_1 = \frac{\phi_c}{1 - (P_u/P_{ex})} \tag{10.8.106} $$ $P_{ex} = 10^3 A_g F_y / \lambda_c^2$, where $\lambda_c$ is given by Eq (10.8.9) with $K \leq 1.0$ in the plane of bending. $C_{mx}$ = a coefficient whose value shall be taken as follows: **A. For restrained compression members in frames braced against joint translation and not subjected to transverse loading between their supports in the plane of bending:** $$ C_{mx} = 0.6 - 0.4(M_1/M_2) \tag{10.8.107} $$ where $M_1/M_2$ is the ratio of the smaller to larger moments at the ends of that portion of the member unbraced in the plane of bending under consideration. $M_1/M_2$ is positive when the member is bent in reverse curvature, negative when bent in single curvature. **B. For compression members in frames braced against joint translation in the plane of loading and subjected to transverse loading between their supports, the value of $C_{mx}$ can be determined by rational analysis. In lieu of such analysis, the following values shall be used:** * for members whose ends are restrained $C_{mx} = 0.85$ * for members whose ends are unrestrained $C_{mx} = 1.0$ $$ B_2 = \frac{\phi_c}{1 - (P_u/P_{ey})} \tag{10.8.108} $$ $$ C_{my} = 0.85 \tag{10.8.109} $$ In which * $H$ = sum of all storey horizontal forces producing $\Delta_i$, kN. * $P_{ey} = 10^3 A_g F_y / \lambda_c^2$, where $\lambda_c$ is the slenderness parameter given by Eq (10.8.9), in which the effective length factor $K$ in the plane of bending shall be determined in accordance with Sec 10.5.2.2 but shall not be less than unity. * $L$ = storey height, mm. ##### ii) Determination of $M_n$ In the use of Eq (10.8.103) and (10.8.104), $M_n$ shall be determined in accordance with Sec 10.8.6.1. The actual value of $C_b$ from Sec 10.8.6.1(c) shall be used, provided that the maximum moment $M_{max}$ occurs at the end of the member or at the end of an unbraced segment of a member. When the maximum moment occurs between the ends, $M_n$ shall be determined with $C_b = 1.0$. When Eq (10.8.105) is used for determining $M_u$ the maximum moment for a braced member bent about the strong axis and braced only at its ends will occur at an end whenever the calculated value of $B_1$ is equal to or less than unity. #### 10.8.8.2 Unsymmetric Members and Members Under Torsion and Combined Torsion, Flexure and/or Axial Force The design strength $\phi F_n$ of the member shall equal or exceed the required strength expressed in terms of the normal stress $f_n$ or the shear stress $f_v$, determined by elastic analysis for the factored loads. a) For the limit state of yielding under normal stress: $$ F_n \leq 0.6 F_y \tag{10.8.110} $$ $\phi = 0.90$ b) For the limit state of yielding under shear stress: $$ F_n \leq 0.6 F_y \tag{10.8.111} $$ $\phi = 0.90$ c) For the limit state of buckling: $$ f_n + f_v \leq \phi_c F_{cr} \tag{10.8.112} $$ as applicable where $\phi_c = 0.85$ and $F_{cr}$ shall be determined from Eq (10.8.11) or (10.8.12) as applicable. Some constrained local yielding is permitted in areas adjacent to areas which remain elastic. #### 10.8.8.3 Alternative Interaction Equations for Members under Combined Stress For biaxially loaded I-shaped members used in braced frames only, the following interaction equations may be used in lieu of Eq (10.8.103) and (10.8.104). $$ \frac{P_u}{\phi_c P_n} + \frac{M_{ux}}{\phi_b M_{px}} + \frac{M_{uy}}{\phi_b M_{py}} \leq 1.0 \tag{10.8.113} $$ $$ \frac{P_u}{\phi_c P_n} \gamma + \frac{M_{ux}}{\phi_b M_{nx}} + \frac{M_{uy}}{\phi_b M_{ny}} \leq 1.0 \tag{10.8.114} $$ For $0.5 < b/d \leq 1.0$: $$ \gamma = 1.6 - \frac{P_u}{P_y} \frac{2 \ln(P_y/P_u)} \tag{10.8.115} $$ For $b/d \geq 0.3$: $$ \gamma = 0.44 + \frac{F_u}{d} \frac{10}{(b/d)} \tag{10.8.116} $$ For $b/d < 0.3$: $\gamma = 1.0$ In the above, $$ M_{px} = 1.2 M_{px} [1 - (P_u/P_y)]^2 \leq M_{yx} \tag{10.8.117} $$ $$ M_{py} = 1.2 M_{py} [1 - (P_u/P_y)^2] \leq M_{yy} \tag{10.8.118} $$ $$ M_{nx} = \frac{P_u}{P_y} M_{px} \tag{10.8.119} $$ $$ M_{ny} = M_{ny} \left( 1 - \frac{P_u}{P_y} \right) \leq \frac{P_u}{P_y} \tag{10.8.120} $$ ### 10.8.9 Design of Trusses #### 10.8.9.1 General Trusses are composed of individual members connected by welds, rivets or bolts. #### 10.8.9.2 Purlins Requirements of this section shall be in accordance with the requirements of Sec 10.7.9.2. #### 10.8.9.3 Design of Members a) Compression Members: All members under compressive forces shall be designed to satisfy the requirements of Sec 10.8.5. b) Tension Members: All members under tensile forces shall be designed to satisfy the requirements of Sec 10.8.4. #### 10.8.9.4 Joints and Connections Design of joints and connections in trusses shall satisfy the requirements of Sec 10.9. #### 10.8.9.5 Deflection and Camber a) Deflection: Deflection due to service live load plus impact, if any, shall be limited so as not to impair serviceability. b) Camber: Trusses shall be provided with camber in accordance with Sec 10.10.1. #### 10.8.9.6 Bracing Trusses shall be adequately braced against instability. ### 10.8.10 Design of Composite Members This section specifies the requirements for composite columns made of rolled or built-up structural steel shapes, pipe or tubing and structural concrete acting together and for steel beams supporting a reinforced concrete slab so interconnected that the beams and the slab act together to resist bending. Simple and continuous composite beams with shear connectors and concrete encased beams, constructed with or without temporary shores, are included. #### 10.8.10.1 Design Assumptions a) Force Determination: In determining forces in members and connections of a structure that includes composite columns and beams, consideration must be given to the effective sections at the time each increment of load is applied. b) Elastic Analysis: For an elastic analysis of continuous composite beams without haunched ends, it is acceptable to assume that the stiffness of a beam is uniform throughout the beam length and may be computed using the moment of inertia of the composite transformed section in the positive moment region. c) Plastic Analysis: When plastic analysis is used, the strength of flexural composite members shall be determined from plastic stress distributions as specified in Sec 10.8.10.3. d) Plastic Stress Distribution for Positive Moment: If the slab in the positive moment region is connected to the steel beam with shear connectors, a concrete stress of $0.85 f_c'$ may be assumed uniformly distributed throughout the effective compression zone. Concrete tensile strength shall be neglected. A uniformly distributed steel stress of $F_y$ shall be assumed throughout the tension zone and throughout the compression zone in the structural steel section. The net tensile force in the steel section shall be equal to the compressive force in the concrete slab. e) Plastic Stress Distribution for Negative Moment: If the slab in the negative moment region is connected to the steel beam with shear connectors, a tensile stress of $F_{yr}$ shall be assumed in all adequately developed longitudinal reinforcing bars within the effective width of the concrete slab. Concrete tensile strength shall be neglected. A uniformly distributed steel stress of $F_y$ shall be assumed throughout the tension zone and throughout the compression zone in the structural steel section. The net compressive force in the steel section shall be equal to the total tensile force in the reinforcing steel. f) Elastic Stress Distribution: When a determination of elastic stress distribution is required, strains in steel and concrete shall be assumed to be directly proportional to the distance from the neutral axis. The stress shall equal strain times $E$ or $E_c$. Concrete tensile strength shall be neglected. Maximum stress in the steel shall not exceed $F_y$. Maximum compressive stress in the concrete shall not exceed $0.85 f_c'$. In composite hybrid beams, the maximum stress in the steel flange shall not exceed $F_{yf}$ but the strain in the web may exceed the yield strain and the stress shall be taken as $F_y$ at such locations. g) Fully Composite Beam: Shear connectors are to be provided in sufficient numbers to develop the maximum flexural strength of the composite beam. For elastic stress distribution it may be assumed that no slip occurs. h) Partially Composite Beam: The shear strength of shear connectors governs the flexural strength of the partially composite beam. Elastic computations such as those for deflections and vibrations should include the effect of slip. i) Concrete Encased Beam: A beam totally encased in concrete cast integrally with the slab may be assumed to be interconnected to the concrete by natural bond, without additional anchorage, provided that: (1) concrete cover over beam sides and soffit is at least 50 mm; (2) the top of the beam is at least 40 mm below the top and 50 mm above the bottom of the slab; and (3) concrete encasement contains adequate mesh or other reinforcing steel to prevent spalling of concrete. j) Composite Column: A steel column fabricated from rolled or built-up steel shapes and encased in structural concrete or fabricated from steel pipe or tubing filled with structural concrete. #### 10.8.10.2 Compression Members #### a) Limitations To qualify as a composite column, the following limitations shall be met. i) The cross-sectional area of the steel shape, pipe or tubing shall comprise at least 4% of the total composite cross-section. ii) Concrete encasement of a steel core shall be reinforced with longitudinal load carrying bars, longitudinal bars to restrain concrete and lateral ties. Longitudinal load carrying bars shall be continuous at framed levels; longitudinal restraining bars may be interrupted at framed levels. The spacing of ties shall be not greater than $\frac{1}{4}$ of the least dimension of the composite cross-section. The cross-sectional area of the transverse and longitudinal reinforcement shall be at least 0.0178 mm² per mm of bar spacing. The encasement shall provide at least 40 mm of clear cover outside of both transverse and longitudinal reinforcement. iii) Concrete shall have a specified compressive strength $f_c'$ of not less than 20 N/mm² nor more than 55 N/mm². iv) The specified minimum yield stress of structural steel and reinforcing bars used in calculating the strength of a composite column shall not exceed 380 N/mm². v) The minimum wall thickness of structural steel pipe or tubing filled with concrete shall be equal to $b \sqrt{F_y/3E}$ for each face of width $b$ in rectangular sections and $D \sqrt{F_y/8E}$ for circular sections of outside diameter $D$. #### b) Design Strength The design strength of axially loaded composite columns is $\phi_c P_n$, where $\phi_c = 0.85$ and the nominal axial compressive strength $P_n$ shall be determined from Eq (10.8.6) through (10.8.9) with the following modifications: i) $A_s$ = gross area of steel shape, pipe or tubing, mm² (replaces $A_g$) $r_m$ = radius of gyration of the steel shape, pipe or tubing except that for steel shapes it shall not be less than 0.3 times the overall thickness of composite cross-section in the plane of buckling, mm (replaces $r$) ii) Replace $F_y$ with modified yield stress $F_{ym}$ from Eq (10.8.121) and replace $E$ with modified modulus of elasticity $E_m$ from Eq (10.8.122). $$ F_{ym} = F_y + c_1 F_{yr} (A_r/A_s) + c_2 f_c' (A_c/A_s) \tag{10.8.121} $$ $$ E_m = E + c_3 E_c (A_c/A_s) \tag{10.8.122} $$ where $c_1, c_2, c_3$ = numerical coefficients. For concrete-filled pipe and tubing $c_1 = 1.00$, $c_2 = 0.85$, and $c_3 = 0.40$. For concrete encased shapes $c_1 = 0.70$, $c_2 = 0.60$ and $c_3 = 0.20$. #### c) Columns with Multiple Steel Shapes If the composite cross-section includes two or more steel shapes, the shapes must be interconnected with lacing, tie plates or batten plates to prevent buckling of individual shapes before hardening of concrete. #### d) Load Transfer The portion of the design strength of axially loaded composite columns resisted by concrete shall be developed by direct bearing at connections. When the supporting concrete area is wider than the loaded area on one or more sides and otherwise restrained against lateral expansion on the remaining sides, the maximum design strength of concrete shall be $1.7 \phi_c f_c' A_p$, where $\phi_c = 0.60$ is the resistance factor in bearing on concrete and $A_p$ is the loaded area. #### 10.8.10.3 Flexural Members #### a) Effective Width The portion of the effective width of the concrete slab on each side of the beam centre line shall not exceed: i) One-eighth of beam span, centre to centre of supports; ii) One-half the distance to the centre line of the adjacent beam; or iii) The distance from the beam centre line to the edge of the slab. #### b) Strength of Beams with Shear Connectors The positive design flexural strength $\phi_b M_n$ shall be determined as follows: i) For $h_e/t_y \leq 1680/\sqrt{F_y}$ $\phi_b = 0.85$; $M_n$ shall be determined from plastic stress distribution on the composite section. ii) For $h_e/t_y > 1680/\sqrt{F_y}$ $\phi_b = 0.90$; $M_n$ shall be determined from the superposition of elastic stresses, considering the effects of shoring. The negative design flexural strength $\phi_b M_n$ shall be determined for the steel section alone, in accordance with the requirements of Sec 10.8.6. Alternatively, the negative design flexural strength $\phi_b M_n$ may be computed with $\phi_b = 0.85$ and $M_n$ determined from the plastic stress distribution on the composite section, provided that: i) Steel beam is an adequately braced compact section, as defined in Sec 10.8.3.1. ii) Shear connectors connect the slab to the steel beam in the negative moment region. iii) Reinforcing steel parallel to the steel beam, within the effective width of the slab, is properly developed. #### c) Strength of Concrete Encased Beams The design flexural strength $\phi_b M_n$ shall be computed with $\phi_b = 0.90$ and $M_n$ determined from the superposition of elastic stresses, considering the effects of shoring. Alternatively, the design flexural strength $\phi_b M_n$ may be computed with $\phi_b = 0.90$ and $M_n$ determined from the plastic stress distribution on the steel section alone. #### d) Strength During Construction When temporary shores are not used during construction, the steel section alone shall have adequate strength to support all loads applied prior to the concrete attaining 75% of its specified strength $f_c'$. The design flexural strength of the steel section shall be determined in accordance with the requirements of Sec 10.8.6.1. #### e) Formed Steel Deck i) The design flexural strength $\phi_b M_n$ of composite construction consisting of concrete slabs on formed steel deck connected to steel beams shall be determined by the applicable portions of (b) above with the following modifications. This section is applicable to decks with nominal rib height not greater than 75 mm. The average width of concrete rib or haunch $w_r$ shall be not less than 50 mm, but shall not be taken in calculations as more than the minimum clear width near the top of the steel deck. See (iii) below for additional restrictions. The concrete slab shall be connected to the steel beam with welded stud shear connectors, conforming to AWS D1.1, 20 mm or less in diameter. Studs shall be welded either through the deck or directly to the steel beam. Stud shear connectors, after installation, shall extend not less than 40 mm above the top of the steel deck. The slab thickness above the steel deck shall be not less than 50 mm. ii) Deck Ribs Oriented Perpendicular to Steel Beam: Concrete below the top of the steel deck shall be neglected in determining section properties and in calculating $A_c$ for deck ribs oriented perpendicular to the steel beams. The spacing of stud shear connectors along the length of a supporting beam shall not exceed 800 mm. The nominal strength of a stud shear connector shall be the value stipulated in Sec 10.8.10.5 multiplied by the following reduction factor: $$ \frac{0.85(w_r/h_r)[(H_s/h_r) - 1.0]}{N_s} \leq 1.0 \tag{10.8.123} $$ To resist uplift, steel deck shall be anchored to all supporting members at a spacing not to exceed 400 mm. Such anchorage may be provided by stud connectors, a combination of stud connectors and arc spot welds or other devices specified by the designer. iii) Deck Ribs Oriented Parallel to Steel Beam: Concrete below the top of steel deck may be included in determining section properties and shall be included in calculating $A_c$ for Sec 10.8.10.5. Steel deck ribs over supporting beams may be split longitudinally and separated to form a concrete haunch. When the nominal depth of steel deck is 40 mm or greater, the average width $w_r$ of the supported haunch or rib shall be not less than 50 mm for the first stud in the transverse row plus 4 stud diameters for each additional stud. The nominal strength of a stud shear connector shall be the value stipulated in Sec 10.8.10.5 except that when $w_r/h_r$ is less than 1.5, the value from Sec 10.8.10.5 shall be multiplied by the following reduction factor: $$ 0.6(w_r/h_r)[H_s/h_r - 1.0] \leq 1.0 \tag{10.8.124} $$ #### f) Design Shear Strength The design shear strength of composite beam shall be determined by the shear strength of the steel web, in accordance with the requirements of Sec 10.8.6.2. #### 10.8.10.4 Combined Compression and Flexure The interaction of axial compression and flexure in the plane of symmetry on composite members shall be limited by Eq (10.8.103) through (10.8.109) with the following modifications: $M_n$ = nominal flexural strength determined from plastic stress distribution on the composite cross-section except as provided below, kKNm $P_e$ = $A_s F_{ym} / \lambda_c^2$, elastic buckling load, kN. $\phi_b$ = resistance factor for flexure from Sec 10.8.10.3. $\phi_c$ = 0.85. $\lambda_c$ = column slenderness parameter defined by Eq (10.8.9) as modified in Sec 10.8.10.2(b). When the axial term in Eq (10.8.103) and (10.8.104) is less than 0.3, the nominal flexural strength $M_n$ shall be determined by straight line transition between the nominal flexural strength determined from the plastic distribution on the composite cross-sections at $(P_u/\phi_c P_n) = 0.3$ and the flexural strength at $P_u = 0$ as determined from Sec 10.8.10.3. If shear connectors are required at $P_u = 0$, they shall be provided whenever $(P_u/\phi_c P_n)$ is less than 0.3. #### 10.8.10.5 Shear Connectors This section covers the design of stud and channel shear connectors. #### a) Material Shear connectors shall be headed steel studs not less than four stud diameters in length after installation, or hot rolled steel channels. The stud connectors shall conform to the requirements of Sec 10.3.5. The channel connectors shall conform to the requirements of Sec 10.3.1. Shear connectors shall be embedded in concrete slabs made with ASTM C33 aggregate. #### b) Horizontal Shear Force Except for concrete encased beams as defined in Sec 10.8.10.1, the entire horizontal shear at the interface between the steel beam and the concrete slab shall be assumed to be transferred by shear connectors. For composite action with concrete subject to flexural compression, the total horizontal shear force, kN, between the point of maximum positive moment and the point of zero moment shall be taken as the smallest of: i) $0.85 \times 10^{-3} f_c' A_c$ ii) $10^{-3} A_s F_y$ iii) $\sum Q_n$ where $\sum Q_n$ = sum of nominal strengths of shear connectors between the point of maximum positive moment and the point of zero moment, kN. In continuous composite beams where longitudinal reinforcing steel in the negative moment regions is considered to act compositely with the steel beam, the total horizontal shear force between the point of maximum negative moment and the point of zero moment shall be taken as the smaller of $10^{-3} A_r F_{yr}$ and $\sum Q_n$; where $A_r$ = area of adequately developed longitudinal reinforcing steel within the effective width of the concrete slab, mm². $F_{yr}$ = minimum specified yield stress of the reinforcing steel, N/mm². #### c) Strength of Stud Shear Connectors The nominal strength of one stud shear connector embedded in a solid concrete slab is $$ Q_n = 0.5 \times 10^{-3} A_{sc} \sqrt{f_c' E_c} \leq 10^{-3} A_{sc} F_u \tag{10.8.125} $$ For a stud shear connector embedded in a slab on a formed steel deck, see Sec 10.8.10.3 for reduction factors given by Eq (10.8.123) and (10.8.124) as applicable. The reduction factors should be applied only to $0.5 \times 10^{-3} A_{sc} \sqrt{f_c' E_c}$ term in Eq (10.8.125). #### d) Strength of Channel Shear Connectors The nominal strength of one channel shear connector embedded in a solid concrete slab is $$ Q_n = 0.3 \times 10^{-3} (t_f + 0.5 t_w) L_c \sqrt{f_c' E_c} \tag{10.8.126} $$ #### e) Required Number of Shear Connectors The number of shear connectors required between the section of maximum bending moment, positive or negative, and the adjacent section of zero moment shall be equal to the horizontal shear force as determined from (b) above divided by the nominal strength of one shear connector as determined from (c) or (d) above. #### f) Shear Connector Placement and Spacing Shear connectors on each side of the point of maximum bending moment, positive or negative, shall be distributed uniformly between that point and the adjacent points of zero moment. However, the number of shear connectors placed between any concentrated load and the nearest point of zero moment shall be sufficient to develop the maximum moment required at the concentrated load point. Except for connectors installed in the ribs of formed steel deck, shear connectors shall have at least 25 mm of lateral concrete cover. Unless located over the web, the diameter of studs shall not be greater than 2.5 times the thickness of the flange to which they are welded. The minimum centre to centre spacing of stud connectors shall be 6 diameters along the longitudinal axis of the supporting composite beam and 4 diameters transverse to the longitudinal axis of the supporting composite beam, except that within the ribs of formed steel decks the centre to centre spacing may be as small as 4 diameters in any direction. The maximum centre to centre spacing of shear connectors shall not exceed 8 times the total slab thickness. ### 10.8.11 Special Design Considerations This section provides the design consideration related to special situations such as concentrated loads, ponding and torsion. #### 10.8.11.1 Webs and Flanges with Concentrated Forces #### a) Design Basis Members with concentrated loads applied normal to one flange and symmetric to the web shall have a flange and web design strength sufficient to satisfy the local flange bending, web yielding, web crippling and sidesway web buckling criteria of (b) through (e) below. Members with concentrated loads applied to both flanges shall have a web design strength sufficient to satisfy the web yielding, web crippling and column web buckling criteria of (c), (d) and (f) below. Where pairs of stiffeners are provided on opposite sides of the web at concentrated loads and extend at least half the depth of the member, (b) and (c) below need not be checked. For column webs subjected to high shears, the provisions of (g) below shall apply. For bearing stiffeners, the provisions of (h) below shall apply. b) Local Flange Bending : The flange design strength in bending due to a tensile load shall be $\phi R_n$, kN. where $$ \phi = 0.90 $$ $$ R_n = 0.00625 t_f^2 F_{yf} \tag{10.8.127} $$ If the length of loading measured across the member flange is less than 0.15*b*, where *b* is the member flange width, Eq (10.8.127) need not be checked. c) Local Web Yielding : The design strength of the web at the toe of the fillet under concentrated loads shall be $\phi R_n$, where $\phi = 1.0$ and $R_n$ is determined as follows : i) When the force to be resisted is a concentrated load producing tension or compression, applied at a distance from the member end that is greater than the depth of the member, $$ R_n = \left( \frac{5k + N}{1000} \right) F_{yw} t_w \tag{10.8.128} $$ ii) When the force to be resisted is a concentrated load applied at or near the end of member, $$ R_n = \left( \frac{2.5k + N}{1000} \right) F_{yw} t_w \tag{10.8.129} $$ In the above, *k* = distance from outer face of flange to web toe of fillet, mm. d) Web Crippling: For unstiffened portions of webs of members under concentrated loads, the design compressive strength shall be $\phi R_n$, where $\phi = 0.75$ and nominal strength $R_n$ is determined as follows : i) When the concentrated load is applied at a distance not less than *d*/2 from the end of the member : $$ R_n = 0.354 t_w^2 \left[ 1 + 3 \left( \frac{N}{d} \right) \left( \frac{t_w}{t_f} \right)^{1.5} \right] \sqrt{F_{yw} t_f / t_w} \tag{10.8.130} $$ ii) When the concentrated load is applied less than a distance *d*/2 from the end of the member : $$ R_n = 0.179 t_w^2 \left[ 1 + 3 \left( \frac{N}{d} \right) \left( \frac{t_w}{t_f} \right)^{1.5} \right] \sqrt{F_{yw} t_f / t_w} \tag{10.8.131} $$ If stiffeners are provided and extend at least one-half the web depth, Eq (10.8.130) and (10.8.131) need not be checked. e) Sidesway Web Buckling : For webs of members with flanges not restrained against relative movement by stiffeners or lateral bracing and subject to concentrated compressive loads, the design compressive strength shall be $\phi R_n$, where $\phi = 0.85$ and the nominal strength $R_n$ is determined as follows : i) If the loaded flange is restrained against rotation and $(d_c/t_w)/(l/b_f)$ is less than 2.3 : $$ R_n = \frac{83 t_w^3}{h} \left[ 1 + 0.4 \left( \frac{d_c/t_w}{l/b_f} \right)^3 \right] \tag{10.8.132} $$ ii) If the loaded flange is not restrained against rotation and $(d_c/t_w)/(l/b_f)$ is less than 1.7 : $$ R_n = \frac{83 t_w^3}{h} \left[ 0.4 \left( \frac{d_c/t_w}{l/b_f} \right)^3 \right] \tag{10.8.133} $$ where $d_c = d - 2k$ = web depth clear of fillets, mm. Eq (10.8.132) and (10.8.133) need not be checked provided $(d_c/t_w)/(l/b_f)$ exceeds 2.3 or 1.7 respectively, or for webs subject to distributed load. If a concentrated load is located at a point where the web flexural stress due to factored loads is below yielding, 165 shall be used in lieu of 83 in Eq (10.8.132) and (10.8.133). f) Compression Buckling of the Web : For unstiffened portions of webs of members under concentrated loads to both flanges, the design compressive strength shall be $\phi R_n$, where $$ \phi = 0.90 $$ $$ R_n = \frac{10.76 t_w^3 \sqrt{F_{yw}}}{d_c} \tag{10.8.134} $$ $R_n$ may be exceeded provided that a transverse stiffener or pair of stiffeners is attached to the web to satisfy Sec 10.8.6.3. g) Compression Members with Web Panels Subjected to High Shears : For compression members subjected to high shear stress in the web, the design web shear strength shall be $\phi R_v$, where $\phi = 0.90$ and $R_v$ is determined as follows : i) For $P_u \leq 0.75 P_n$: $$ R_v = 0.0007 F_y d_c t_w \tag{10.8.135} $$ ii) For $P_u > 0.75 P_n$: $$ R_v = 0.0007 F_y d_c t_w \left[ 1.9 - 1.2 (P_u/P_n) \right] \tag{10.8.136} $$ h) Stiffener Requirements for Concentrated Loads : When required, stiffeners shall be placed in pairs at unframed ends of beams and girders. They shall be placed in pairs at points of concentrated load on the interior of beams, girders or column if the load exceeds the nominal strength $\phi R_n$ as determined from (b) through (f) above as applicable. If the concentrated load, tension or compression exceeds the criteria for $\phi R_n$ of (b) or (c) above respectively, stiffeners need not be extended more than one-half the depth of the web, except as follows : If concentrated compressive loads are applied to the members and if the load exceeds the compressive strength of the web $\phi R_n$ given in (d) or (f) above, the stiffener shall be designed as axially compressed members (columns) in accordance with the requirements of Sec 10.8.5.2 with an effective length equal to 0.75*h*, a cross-section composed of two stiffeners and a strip of the web having a width of $25t_w$ at interior stiffeners and $12t_w$ at the ends of members. When the load normal to the flange is tensile, the stiffeners shall be welded to the loaded flange. When the load normal to the flange is compressive, the stiffeners shall either bear on or be welded to the loaded flange. #### 10.8.11.2 Ponding The roof system shall be investigated for ponding in accordance with the provisions of Sec 10.7.11.2. #### 10.8.11.3 Torsion For limiting values of normal and shear stresses, due to torsion and other loading, the provisions of Sec 10.8.8.2 shall apply. Some constrained local yielding may be permitted. ### 10.8.12 Seismic Design Provisions #### 10.8.12.1 Scope This section specifies special seismic design provisions for the design and construction of structural steel members and connections in buildings for which the design forces resulting from earthquake motions have been determined on the basis of energy dissipation in the nonlinear range of response. These special seismic requirements are to be applied in conjunction with the Load Factor Design method. The special seismic design provisions apply only to buildings in Zone 3 and to buildings in Zone 2 having an importance factor *I* greater than 1.0. #### 10.8.12.2 Seismic Zoning Seismic zoning provisions shall be as stipulated in Chapter 2, Loads. #### 10.8.12.3 Loads and Load Combinations The design loads shall be the minimum factored loads and their combinations specified in Chapter 2, Loads. #### 10.8.12.4 Storey Drift and Building Separations Storey drift shall be calculated using the appropriate effects consistent with the structural system and the method of analysis. Limits on storey drift shall be in accordance with Sec 1.5.6, Chapter 1, General Design Requirements. #### 10.8.12.5 Materials Steel used in seismic force resisting systems shall be as listed in Sec 10.3.1. For buildings over one storey in height, the steel used in seismic resisting systems described in Sec 10.8.14.7, 10.8.14.8 and 10.8.14.9 shall be limited to the following ASTM Specifications : A36, A441, A500 (Grades B and C), A501, A572 (Grades 42 and 50), and A588. For base plates, ASTM A283 Grade D can be used in lieu of the other plate materials listed above. #### 10.8.12.6 Column Requirements a) Columns in earthquake resisting frames shall comply with the requirements of Sec 10.8.5 and 10.8.8. When $P_u/\phi P_n > 0.5$ column axial design strength shall be limited by the following requirements. i) Axial compression loads : $$ 1.2 P_D + 0.5 P_L + 1.0 P_{E'} \leq \phi P_n \tag{10.8.137} $$ **Exception :** The load factor on *L* used to determine $P_L$ in Eq (10.8.137) shall be equal to 1.0 for garages, areas occupied as places of public assembly and all areas where the live load is greater than 5.0 kN/m². ii) Axial tension loads : $$ 0.9 P_D + 1.0 P_{E'} \leq \phi P_n \tag{10.8.138} $$ iii) The required axial strengths in Eq (10.8.137) and (10.8.138) need not exceed either of the following: A. The maximum loads that can be transferred to the column, considering 1.25 times the design strengths of the connecting beam or brace elements of the structure. B. The limit as determined by the foundation capacity to resist overturning uplift. b) Column Splices : Column splices shall have sufficient strength to develop the column axial loads given in (i), (ii) and (iii) above as well as the load combinations specified in Sec 2.7.5.2 of Chapter 2, Loads. i) In column splices using either complete or partial penetration welded joints, changes in thickness and width of flanges and webs are permitted without providing bevelled transitions. ii) Splices using partial penetration welded joints shall not be within 900 mm of the beam to column connection. Column splices that are subjected to net tension forces shall comply with the more critical of the following: A. The lesser design strength of $\phi_w F_w A_w$ or $\phi_w F_{BM} A_w$ (see Sec 10.9.2.4) for partial penetration welded joints shall be at least 150 per cent of the required strength. B. The design strength of welds shall not be less than $0.5 F_{yc} A_f$ where $F_{yc}$ is the yield strength of the column material and $A_f$ is the flange area of the smaller column connected. #### 10.8.12.7 Requirements for Ordinary Moment Frames (OMF) a) Design Strength : Ordinary moment frames (OMF), where permitted according to the provisions of this Code, shall have the design strength to resist the load combinations specified in Sec 2.7.5.2 of Chapter 2, Loads. The design strength of such members shall be determined using the LFD method. b) Joint Requirements : All beam to column connections in OMF which resist earthquake forces shall meet one of the following requirements : i) FR (fully restrained) connections conforming with Sec 10.8.12.8(b). ii) FR connections with design strengths of the connections meeting the requirements of (a) above using the load combinations 7 and 8 specified in Sec 2.7.5.2 of Chapter 2, Loads. iii) Either FR or PR (partially restrained) connections are permitted provided : A. The design strengths of the members and connections meet the requirements of (a) above. B. The connections have been demonstrated by cyclic tests to have adequate rotation capacity at a storey drift calculated at a horizontal load of E′. C. The additional drift due to PR connections shall be considered in design. FR and PR connections are described in detail in Sec 10.4. #### 10.8.12.8 Requirements for Special Moment Frames (SMF) a) Scope : Special moment frames (SMF), shall be used when required by the provisions of this Code. For buildings in Seismic Zone 2 having an importance factor I greater than 1.0, only the requirements of (b), (c), (g), and (h) below shall be applicable. b) Beam to Column Joints i) The required flexural strength $M_u$ of each beam to column joint shall be the lesser of the following quantities : A. The plastic bending moment $M_p$ of the beam. B. The moment resulting from the panel zone nominal shear strength $V_n$ as determined using Eq (10.8.139). The joint need not develop either of the strengths defined above if it can be shown that under an amplified frame deformation of E′/E times that produced by load combinations 5 and 6 specified in Sec 2.7.5.2 of Chapter 2, Loads, the design strength of the members at the connection are adequate to support the vertical loads, and the required lateral force resistance is provided by other means. ii) The required shear strength $V_u$ of a beam to column joint shall be determined using the load combination $1.2D + 0.5L$ plus the shear resulting from $M_u$, as defined in (i) above, on at least one end of the beam. The required shear strength need not exceed the shear resulting from the load combination 7 specified in Sec 2.7.5.2 of Chapter 2, Loads. iii) The design strength $\phi R_n$ of a beam to column joint can be considered adequate to develop the required flexural strength $M_u$ of the beam if it conforms to the following : A. The beam flanges are welded to the column using complete penetration welded joints. B. The beam web joint shall have a design shear strength $\phi V_n$ greater than the required shear $V_u$ and conform to either : 1. Where the nominal flexural strength of the beam $M_n$ considering only the flanges is greater than 70 per cent of the nominal flexural strength of the entire beam section i.e., $$ \left[ 10^{-6} b_f t_f (d - t_f) F_{yf} \geq 0.7 M_p \right], $$ the web joint may be made by means of welding or slip-critical high strength bolting. 2. Where a slip-critical high strength bolted joint in a beam does not meet the flexural criteria in (i) above the required strength of added web welding shall be at least 20 per cent of the nominal flexural strength of the beam web. The required beam shear strength shall be developed by further welding or by slip-critical high strength bolting. iv) Alternate joint configurations : Joint configurations utilizing welds or high strength bolts, but not conforming to (iii) above, may be used if shown by test or calculations to meet the criteria of (i) above. Where conformance is shown by calculation, the design strength of the joint shall be 125 per cent of the design strengths of the connecting elements. c) Panel Zone of Beam to Column Connections (Beam Web Parallel to Column Web) i) Shear strength : The required shear strength $V_u$ of the panel zone shall be based on the beam bending moments determined from the load combinations 5 and 6 specified in Sec 2.7.5.2 of Chapter 2, Loads. $V_u$ need not exceed that determined from $0.9 \sum \phi_b M_p$ of the beams framing into the column flanges at the connection. The design shear strength $\phi_v V_n$ of the panel zone shall be determined by the following formula : $$ \phi_v V_n = 0.55 \times 10^{-3} \phi_v F_y d_c t_p \left[ 1 + \frac{3 b_{cf} t_{cf}^2}{d_b d_c t_p} \right], \text{ where for this case } \phi_v = 0.8 \tag{10.8.139} $$ ii) Panel zone thickness : The panel zone thickness $t_z$ shall conform to the following : $$ t_z \geq (d_z + w_z)/90 \tag{10.8.140} $$ For this purpose $t_z$ shall not include any doubler plate thickness unless the doubler plate is connected to the web with plug welds adequate to prevent local buckling of the plate. iii) Panel zone doubler plates : Doubler plates provided to increase the design strength of the panel zone or to reduce the web depth-thickness ratio shall be placed close to the column web and welded across the plate width top and bottom with a minimum fillet weld as specified in Table (6.10.9). The doubler plates shall be fastened to the column flanges using either butt or fillet welded joints to develop the design shear strength of the doubler plate. d) Beam Limitations i) Beam Flange Area : Abrupt changes in beam flange areas are not permitted within possible plastic hinge regions. ii) Width-thickness Ratios : Beams shall comply with the limiting width thickness ratio stipulated in Table 6.10.5 in lieu of those in Table 6.10.4. e) Continuity Plates : Continuity plates shall be provided if the nominal column local flange bending strength as given by Eq (10.8.127) is less than $1.8 \times 10^{-3} F_{yb} b_f t_{bf}$. Continuity plates shall be fastened by welds to both the flanges and webs or doubler plates of columns. f) Column-Beam Moment Ratio : At any beam to column connection, one of the following relationships shall be satisfied : **Table 6.10.5** **Limiting Width-Thickness Ratios for Compression Elements** | Description of Element | Width-Thickness Ratio | Limiting Width-Thickness Ratios | | ----------------------------------------------------------------------------------------------------------- | --------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Flanges of I-shaped nonhybrid sections and channels in flexure; Flanges of I-shaped hybrid beams in flexure | $b/t$ | $136/\sqrt{F_y}$ | | Webs in combined flexural and axial compression | $h_c/t_w$ | For $P_u/\phi_b P_y \leq 0.125$: $\dfrac{1365}{\sqrt{F_y}} \left[ 1 - \dfrac{1.54 P_u}{\phi_b P_y} \right]$     For $P_u/\phi_b P_y > 0.125$: $\dfrac{500}{\sqrt{F_y}} \left[ 2.33 - \dfrac{P_u}{\phi_b P_y} \right] \geq \dfrac{665}{\sqrt{F_y}}$ | $$ \frac{\sum Z_c (F_{yc} - P_{uc}/A_g)}{\sum Z_b F_{yb}} \geq 1.0, \text{ where } P_{uc} \text{ (in compression)} \geq 0 \tag{10.8.141} $$ $$ \frac{\sum Z_c (F_{yc} - P_{uc}/A_g)}{1000 V_n d_b \left( H/[H - d_b] \right)} \geq 1.0, \text{ where } P_{uc} \text{ (in compression)} \geq 0 \tag{10.8.142} $$ In Eq (10.8.142), $V_n$ is the nominal strength of the panel zone as determined from Eq (10.8.139), $d_b$ is the average overall depth of the beams framing into the connection, and *H* is the average of the storey heights above and below the connection. These requirements need not apply in the following cases, provided that the columns conform to the requirements of (d) above: i) For columns with $P_{uc} < 0.3 \times 10^{-3} F_y A_g$. ii) For columns in any storey that has a total design lateral shear strength 50 per cent greater than that of the storey above. iii) For any column not included in the design to resist the required seismic shears, although the column is included in the design to resist axial overturning forces. g) Beam to Column Connection Restraint i) Restrained Connections : A. Column flanges at a beam to column connection require lateral support only at the level of the top flanges of the beams when a column can be shown to remain outside of the panel zone. This can be satisfied by one of the following conditions : 1. The ratios given by Eq (10.8.141) or (10.8.142) are greater than 1.25. 2. The column remains elastic for load combination 7 specified in Sec 2.7.5.2 of Chapter 2, Loads. B. When a column cannot be shown to remain elastic outside of the panel zone, the following provisions apply : 1. The column flanges shall be laterally supported at the levels of both top and bottom beam flanges. 2. Each column flange lateral support shall be designed for a required strength equal to 1.5 per cent of the nominal beam flange strength $(F_y b_f t_f)$. 3. Column flanges shall be laterally supported either directly or indirectly by means of the column web or beam flanges. ii) Unrestrained Connections : A column containing a beam to column connection with no lateral support transverse to the seismic frame at the connection shall be designed using the distance between adjacent lateral supports as the column height and conform to Sec 10.8.8.1, except that : A. The required column strength shall be determined from the load combination 5 specified in Sec 2.7.5.2 of Chapter 2, where E is the least of : 1. The amplified earthquake force E′. 2. 125 per cent of the frame design strength based on either beam or panel zone design strengths. B. The nominal column axial strength $P_n$ shall be based on a pin ended column. C. The *L/r* for these columns shall not exceed 60. D. The required column moment $M_{uy}$ shall include that caused by the beam flange force specified in i(B-2) above plus the added P-Delta moment due to the resulting column flange displacement. h) Lateral Support of Beams : Both flanges of beams shall be laterally supported directly or indirectly. The unbraced length between lateral supports shall not exceed $17237 r_y/F_y$. In addition, lateral supports shall be placed at concentrated loads where a hinge may form. #### 10.8.12.9 Requirements for Concentrically Braced Frames (CBF) a) Scope : The provisions of this section apply to all braced frames except Eccentric Braced Frames (EBF) designed in accordance with Sec 10.8.12.10. Those members which resist seismic forces totally or partially by shear and flexure shall be designed in accordance with Sec 10.8.12.8. b) Bracing Members i) Slenderness : Bracing members shall have an $L/r \leq 1890/\sqrt{F_y}$ in Seismic Zone 3 except as permitted in (e) below. ii) Compressive Design Strength : The design strength of a bracing member in axial compression shall be determined by $0.8 \phi_c P_n$. iii) Lateral Force Distribution : In Seismic Zone 3, the summation of the horizontal components of lateral seismic force in tension or alternatively in compression along any line of bracing shall not exceed 70% of the total force on that line, unless the nominal strength $P_n$ of the member in compression is larger than the required strength $P_u$ resulting from the application of the load combinations 7 and 8 specified in Sec 2.7.5.2 of Chapter 2, Loads. A line of bracing, for the purpose of this provision, is defined as a single line or parallel lines whose offset is within 10 per cent of the building dimension perpendicular to the line of bracing. iv) Width-thickness Ratios : Width-thickness ratios of stiffened and unstiffened compression elements in braces shall comply with Sec 10.8.3. Braces shall be compact or noncompact, but not slender members. Circular hollow sections shall have an outside diameter to wall thickness ratio not exceeding $8965/F_y$. Rectangular tubes shall have the flat width to wall thickness not exceeding $290/\sqrt{F_y}$, unless the tube walls are stiffened. v) Built-up Member Stitches : For all built-up braces, the first bolted or welded stitch on each side of the mid-length of a built-up member shall be designed to transmit a force equal to 50% of the nominal strength of one element to the adjacent element. Not less than two stitches shall be equally spaced about the member centre line. c) Bracing Connections i) Forces : The required strength of bracing joints (including beam to column joints if part of the bracing system) shall be the least of the following : A. The design axial tension strength of the bracing member. B. The force in the brace resulting from the load combinations 7 and 8 specified in Sec 2.7.5.2 of Chapter 2, Loads. C. The maximum force that can be transferred to the brace by the system. ii) Net Area : In bolted brace joints, the minimum ratio of effective net section area to gross section area shall be limited by : $$ A_e / A_g = \frac{1.2 \alpha P_u^*}{\phi_t P_n} $$ where $\alpha$ = Fraction of the member force from (i) above, that is transferred across a particular net section. $P_u^*$ = Required axial strength of the brace as determined in (i) above. $\phi_t$ = Resistance factor for tension = 0.75. iii) Gusset Plates A. For braces that can buckle in the plane of the gusset plate, the gusset and other parts of the connection shall have a design strength equal to or greater than the nominal in-plane bending strength of the brace. B. For braces which can buckle out-of-plane of the gusset plate, the brace shall terminate on the gusset a minimum of two times the gusset thickness from a line about which the gusset plate can bend unrestrained by the column or beam joints. The gusset plate shall be designed to carry the compressive design strength of the brace member without local buckling of the gusset plate. For braces designed for axial load only, the bolts or welds shall be designed to transmit the brace forces along the centroids of the brace elements. d) Special Bracing Configuration Requirements i) V Bracing A. The design strength of V brace members shall be at least 1.5 times the required strength using load combinations 5 and 6 specified in Sec 2.7.5.2 of Chapter 2, Loads. B. A beam intersected by V braces shall be continuous between columns. C. A beam intersected by V braces shall be capable of supporting all tributary dead and live loads assuming the bracing is not present. D. The top and bottom flanges of the beam at the point of intersection of V braces shall be designed to support a lateral force equal to 1.5 per cent of the nominal beam flange strength $(F_y b_f t_f)$. ii) K Bracing A. In Seismic Zone 3, K bracing shall be prohibited except for those framing systems meeting the requirements of (e) below. B. In Seismic Zone 2, with importance factor I greater than 1.0, K bracing shall meet the requirements for V bracing. e) Low Buildings : Braced frames not meeting the requirements of (b) through (d) above may be used in buildings not over two storeys and in roof structures if load combinations 7 and 8 specified in Sec 2.7.5.2 of Chapter 2, Loads, are used for determining the required strength of the members and connections. #### 10.8.12.10 Requirements for Eccentrically Braced Frames (EBF) a) Scope : Eccentrically braced frames shall be designed so that under earthquake loading, yielding will occur primarily in the links. The diagonal braces, the columns, and the beam segments outside of the links shall be designed to remain essentially elastic under the maximum forces that can be generated by the fully yielded and strain hardened links. In EBF, plastic hinges shall not develop in columns at floor beam levels up to an amplified frame displacement of E′/E times that produced by E. b) Links i) Links shall comply with the width-thickness ratios in Table 6.10.5. ii) The specified minimum yield stress of steel used for links shall not exceed $F_y = 345 \text{ N/mm}^2$. iii) The web of a link shall be single thickness without doubler plate reinforcement and without openings. iv) The required shear strength of the link $V_u$ shall not exceed the design shear strength of the link $\phi_v V_n$ defined as the lesser of $\phi_v V_y$ or $2000 \phi_b M_p / e$, where $V_y = 0.6 \times 10^{-3} F_y d t_w$, $\phi_b = \phi_v = 0.9$ and $e$ = link length, except as limited by (vi) below. v) If the required axial strength $P_u$ in a link is less than or equal to $0.15 P_y$, where $P_y = 10^{-3} A_g F_y$, the effect of axial force on the link design shear strength need not be considered. vi) If the required axial strength $P_u$ in a link exceeds $0.15 P_y$, the following additional limitations shall apply : A. The link design shear strength shall be the lesser of $\phi_v V_{ya}$ or $2000 \phi_b M_{pa}/e$, where $$ V_{ya} = V_y \sqrt{1 - (P_u/P_y)^2} $$ $$ M_{pa} = 1.18 M_p \left[ 1 - (P_u/P_y) \right] $$ and $\phi_b = \phi_v = 0.9$ B. The length of the link in mm, shall not exceed : $$ \left[ 1.15 - 0.5 (P_u/V_y)(A_w/A_g) \right] 1600 M_p/V_y \text{ for } (P_u/V_y)(A_w/A_g) \geq 0.3 \text{ and } $$ $$ 1600 M_p/V_y \text{ for } (P_u/V_y)(A_w/A_g) < 0.3 $$ where $A_w = d t_w$. vii) The link rotation angle is the plastic angle between the link and the beam outside of the link when the total storey drift is E′/E times the drift determined using the specified base shear V. Except as noted in d(iii) below, the link rotation angle shall not exceed the following values : A. 0.09 radian for links of length $1600 M_p/V_y$ or less, provided the fundamental period of the EBF is equal to or greater than 1.0 second; otherwise the link rotation angle shall not exceed 0.08 radian. B. 0.02 radian for links of length $2600 M_p/V_y$ or greater. C. Linear interpolation shall be used for links of length between $1600 M_p/V_y$ and $2600 M_p/V_y$. c) Link Stiffeners i) Full depth web stiffeners shall be provided on both sides of the link web at the diagonal brace ends of the link. These stiffeners shall have a combined width not less than $(b_f - 2t_w)$ and a thickness not less than $0.75 t_w$ nor 10 mm, whichever is larger, where $b_f$ and $t_w$ are the link flange width and link web thickness, respectively. ii) Links shall be provided with intermediate web stiffeners as follows : A. Links of lengths $1600 M_p/V_y$ or less shall be provided with intermediate web stiffeners spaced at intervals not exceeding $(30 t_w - d/5)$ for a link rotation angle of 0.09 radian or $(52 t_w - d/5)$ for link rotation angles of 0.03 radian or less. Linear interpolation shall be used for values between 0.03 and 0.09 radians. B. Links of length greater than $2600 M_p/V_y$ and less than $5000 M_p/V_y$ shall be provided with intermediate web stiffeners placed at a distance of $1.5 b_f$ from each end of the link. C. Links of length between $1600 M_p/V_y$ and $2600 M_p/V_y$ shall be provided with intermediate web stiffeners meeting the requirements of (A) and (B) above. D. No intermediate web stiffeners are required in links of lengths greater than $5000 M_p/V_y$. E. Intermediate link web stiffeners shall be full depth. For links less than 625 mm in depth, stiffeners are required on only one side of the link web. The thickness of one sided stiffeners shall not be less than $t_w$ nor 10 mm, and the width shall be not less than $\left[ (b_f/2) - t_w \right]$. For links 625 mm in depth or greater, similar intermediate stiffeners are required on both sides of the web. iii) Fillet welds connecting link stiffener to the link web shall have a design strength adequate to resist a force of $A_{st} F_y$, where $A_{st}$ equals the area of the stiffener. The design strength of fillet welds fastening the stiffener to the flanges shall be adequate to resist a force of $A_{st} F_y / 4$. d) Link to Column Connections : Where a link is connected to a column, the following additional requirements shall apply : i) Links connected to columns shall not exceed the length of $1600 M_p/V_y$ unless it can be demonstrated that the link to column connection is adequate to develop the required inelastic rotation of the link. ii) The link flanges shall have complete penetration welded joints to the column. The connection of the link web to the column shall be welded to develop the design axial, shear and flexural strength of the link web. iii) Where the link is connected to the column web, the link flanges shall have complete penetration welded joints to connection plates and the web connection shall be welded to develop the design axial, shear and flexural strength of the link web. The link rotation angle shall not exceed 0.015 radian for any link length. e) Lateral Support of Link : Lateral supports shall be provided at both the top and bottom flanges of link at the ends of the link. End lateral supports of links shall have a design strength of 4% of the link flange nominal strength computed as $F_y b_f t_f$. f) Diagonal Brace and Beam Outside of Link i) The required axial and moment strengths of each diagonal brace and the beam outside of the link shall be the axial forces and moments generated by 1.5 times the design shear strength of the link as defined in (b) above. The nominal strengths of the diagonal brace and of the beam outside of the link, as determined by Sec 10.8.8.1 shall exceed the required strengths as defined above. ii) Diagonal brace to link connections shall develop the nominal strength of the brace and transfer this force to the beam. No part of the brace to beam connection shall extend over the link length. If the brace resists a portion of the link end moment as described above, the brace to beam connection shall be designed as fully restrained (Type FR). iii) The beam outside of the link shall be provided with sufficient lateral support to maintain the stability of the beam under the forces generated by at least 1.5 times the design shear strength of the link. Lateral supports shall be provided at both top and bottom flanges of the beam and shall have a strength to resist at least 1.5 per cent of the beam flange nominal strength computed as $F_y b_f t_f$. iv) The width-thickness ratio of brace shall satisfy Sec 10.8.12.9b(iv). g) Beam to Column Connections : Beam to column connections away from links are permitted to be designed as a pin in the plane of the web. The connection shall have a strength to resist rotation about the longitudinal axis of the beam based on two equal and opposite rotation forces of at least 1.5 per cent of the beam flange nominal strength computed as $F_y b_f t_f$ acting laterally on the beam flanges. h) Required Column Strength : The required strength of columns shall be determined by load combinations 5 and 6 specified in Sec 2.7.5.2 of Chapter 2, Loads, except that the moments and axial loads introduced into the column at the connection of a link or brace shall not be less than those generated by 1.25 times the design strength of the link. ## 10.9 CONNECTIONS, JOINTS AND FASTENERS This section provides the requirements for the design of connectors i.e. bolts, welds, rivets, etc. and connecting elements such as plates, stiffeners, gussets, angles, brackets, etc. ### 10.9.1 Design Provisions #### 10.9.1.1 Design Basis a) In Working Stress Design connections shall be designed such that the calculated stress in the connectors or connecting elements for service loads shall not exceed the allowable stress stipulated in Sec 10.7 and 10.9. b) In Load Factor Design the connections shall be designed such that the required strength in the connectors and connecting elements for factored loads shall not exceed the design strength. #### 10.9.1.2 Simple Connections Simple Connections may be designed for the reaction shears only. It shall accommodate end rotations of unrestrained (simple) beams and to accomplish this, inelastic deformation in the connection is permitted. #### 10.9.1.3 Moment Connections End connections of restrained beams, girders and trusses shall be designed for the combined effect of forces resulting from moment and shear induced by the rigidity of the connections. #### 10.9.1.4 Compression Members with Bearing Joints When columns bear on bearing plates or are finished to bear at splices, there shall be sufficient connectors to hold all parts securely in place. When other compression members are finished to bear, the splice material and its connectors shall be arranged to hold all parts in line and shall be designed for 50% of the strength of the member in Working Stress Design and for 50% of the factored strength of the member in Load Factor Design. In Working Stress Design compression joints shall be proportioned to resist any tension developed by the specified lateral loads acting in conjunction with 75% of the calculated dead load stress and no live loads. In Load Factor Design compression joints shall be proportioned to resist any tension developed by the factored load combination 6 specified in Sec 2.7.5.2 of Chapter 2, Loads. #### 10.9.1.5 Minimum Connections Except for lacing, sagbars and girts, all connections shall be proportioned to support a service load not less than 27 kN in Working Stress Design while in Load Factor Design the connection shall be proportioned to support a factored load not less than 45 kN. #### 10.9.1.6 Splices in Heavy Sections The following requirement applies to ASTM A6 Group 4 and 5 rolled shapes, or shapes built up by welding plates more than 50 mm thick together to form the cross-section, and where the cross-section is to be spliced and subjected to primary tensile stresses due to tension or flexure. When the individual elements of the cross section are spliced prior to being joined to form cross-section in accordance with Sec 3.4.6 of AWS D1.1, the applicable provisions of AWS D1.1 shall apply in lieu of the requirements of this section. When tensile forces in these sections are to be transmitted through splices by full penetration groove welds, weld access hole details as given in Sec 10.9.1.7, welding preheat requirements as given in Sec 10.9.2.6 and thermal cut surface preparation and inspection requirements as given in Sec 10.11.2.2 shall be applicable. At tension splices in these sections, weld tabs and backing shall be removed and the surfaces ground smooth. When splicing these sections, and where the section is to be used as a primary compression member, all weld access holes required to facilitate groove welding operations shall satisfy the requirements of Sec 10.9.1.7. Alternatively, splicing of such members subjected to compression, including members which are subjected to tension due to wind or seismic loads, may be accomplished using splice details which do not induce large weld shrinkage strains such as partial-penetration flange groove welds with fillet-welded surface lap plate splices on the web, or with bolted or combination of bolted and fillet welded lap plate splices. #### 10.9.1.7 Beam Copes and Weld Access Holes All weld access holes required to facilitate welding operations shall have a length from the toe of the weld preparation not less than $1\frac{1}{2}$ times the thickness of the material in which the hole is made. The height of the access hole shall be adequate for deposition of sound weld metal in the adjacent plates and provide clearance for weld tabs. In hot rolled shapes and built-up shapes, all beam copes and weld access holes shall be shaped free of notches or sharp reentrant corners except that, when fillet web to flange welds are used in built-up shapes, access holes are permitted to terminate perpendicular to the flange. For Group 4 and 5 shapes and built-up shapes of material more than 50 mm thick, the thermally cut surfaces of beam copes and weld access holes shall be ground to bright metal and inspected by either magnetic particle or dye penetrant methods. If the curved transition portion of weld access holes and beam copes are formed by predrilled or sawed holes, that portion of the access hole or cope need not be ground. Weld access holes and beam copes in other shapes need not be ground nor inspected by dye penetrant or magnetic particle. #### 10.9.1.8 Placement of Welds, Bolts and Rivets Groups of welds, bolts or rivets at the ends of any member which transmit axial stress into that member shall be sized so that the centre of gravity of the group coincides with the centre of gravity of the member, unless provision is made for the eccentricity. The foregoing provision is not applicable to end connections of statically loaded single-angle, double-angle and similar members. Eccentricity between the gravity axes of such members and the gauge lines for their riveted or bolted end connections may be neglected in statically loaded members. #### 10.9.1.9 Bolts in Combination with Welds In new work, A307 bolts or high strength bolts used in bearing type connections shall not be considered as sharing the stress in combination with welds. Welds, if used, shall be provided to carry the entire stress in the connection. High strength bolts designed for slip-critical connections may be considered as sharing the stress with the welds. In making welded alterations to structures, existing rivets and high strength bolts tightened to the requirements for slip-critical connections are permitted for carrying stresses resulting from loads present at the time of alteration, and the welding need only be adequate to carry the additional load. #### 10.9.1.10 High strength Bolts in Slip-critical Connections in Combination with Rivets In both new work and alterations, high strength bolts in slip-critical connections may be considered as sharing the load with rivets. #### 10.9.1.11 Limitations of Bolted and Welded Connections Fully tensioned high strength bolts (see Table 6.10.12) or welds shall be used for the following connections : Column splices in all tier structures 60 m or more in height, Column splices in tier structures 30 m to 60 m in height, if the least horizontal dimension is less than 40% of the height, Column splices in tier structures less than 30 m in height, if the least horizontal dimension is less than 25% of the height, Connections of all beams and girders to columns and of any other beams and girders on which the bracing of columns is dependent, in structures over 40 m in height, In all structures carrying cranes of over 50 kN capacity : roof truss splices and connections of trusses to columns, column splices, column bracing, knee braces and crane supports, Connections for supports of running machinery or of other live loads which produce impact or reversal of stress, and Any other connections stipulated on the design plans. In all other cases, connections may be made with high strength bolts tightened to the snug-tight condition or with A307 bolts. For the purpose of this section, the height of a tier structure shall be taken as the vertical distance from the curb level to the highest point of the roof beams in the case of flat roofs, or to the mean height of the gable in the case of roofs having a rise of more than 1 in $4\frac{1}{2}$. Where the curb level has not been established, or where the structure does not adjoin a street, the mean level of the adjoining land shall be used instead of curb level. Penthouses may be excluded in computing the height of the structure. ### 10.9.2 Welds All provisions of the AWS D1.1 : Structural Welding Code - Steel, except its Sec 2.3.2.4, 2.5, 8.13.1, 9 and 10 shall apply to work executed under this specification. #### 10.9.2.1 Groove Welds a) Effective Area : The effective area of groove welds shall be considered as the effective length of the weld times the effective throat thickness. The effective length of a groove weld shall be the width of the part joined. The effective throat thickness of a complete penetration groove weld shall be the thickness of the thinner part joined. The effective throat thickness of a partial-penetration groove weld shall be as shown in Table 6.10.6. **Table 6.10.6** **Effective Throat Thickness of Partial Penetration Groove Welds** | Welding Process | Welding Position | Included Angle at Root of Groove | Effective Throat Thickness | | ---------------------------------------------------------------- | ---------------- | --------------------------------------- | --------------------------- | | Shielded metal arc; Submerged arc; Gas metal arc; Flux-cored arc | All | J or U joint | Depth of chamfer | | | All | Bevel or V joint $\geq 60°$ | Depth of chamfer | | | All | Bevel or V joint $< 60°$ but $\geq 45°$ | Depth of chamfer minus 3 mm | The effective throat thickness of a flare groove weld when flush to the surface of a bar or 90° bend in a formed section shall be as shown in Table 6.10.7. Random sections of production welds for each welding procedure, or such test sections as may be required by design documents, shall be used to verify that the effective throat is consistently obtained. b) Limitations : The minimum effective throat thickness of a partial penetration groove weld shall be as shown in Table 6.10.8. Minimum effective throat thickness is determined by the thicker of the two parts joined, except that the weld size need not exceed the thickness of the thinnest part joined though a larger size is required by calculation. For this exception, particular care shall be taken to provide sufficient preheat for soundness of the weld. **Table 6.10.7** **Effective Throat Thickness of Flare Groove Welds** | Type of Weld | Radius (R) of Bar or Bend | Effective Throat Thickness | | ------------------ | ------------------------- | -------------------------- | | Flare bevel groove | All | $\dfrac{5}{16} R$ | | Flare V-groove | All | $\dfrac{1}{2} R^*$ | \* Use $\dfrac{3}{8} R$ for Gas Metal Arc Welding (except short circuiting transfer process) when $R \geq 12$ mm **Table 6.10.8** **Minimum Effective Throat Thickness of Partial Penetration Groove Welds** | Material Thickness of Thicker Part Joined, mm | Minimum Effective Throat Thickness, mm | | --------------------------------------------- | -------------------------------------- | | To 6 inclusive | 3 | | Over 6 to 12 | 5 | | Over 12 to 20 | 6 | | Over 20 to 40 | 8 | | Over 40 to 60 | 10 | | Over 60 to 150 | 12 | | Over 150 | 16 | #### 10.9.2.2 Fillet Welds a) Effective Area : The effective area of fillet welds shall be taken as the effective length times the effective throat thickness. The effective length of fillet welds, except fillet welds in holes and slots, shall be the overall length of full size fillets, including returns. The effective throat thickness of a fillet weld shall be the shortest distance from the root of the joint to the face of the diagrammatic weld, except that for fillet welds made by the submerged arc process, the effective throat thickness shall be taken equal to the leg size for 10 mm and smaller fillet welds, and equal to the theoretical throat plus 3 mm, for fillet welds larger than 10 mm. For fillet welds in holes and slots, the effective length shall be the length of the centre line of the weld along the centre of the plane through the throat. In the case of overlapping fillets, the effective area shall not exceed the nominal cross-sectional area of the hole or slot in the plane of the faying surface. b) Limitations : The minimum size of fillet welds shall be as shown in Table 6.10.9. Minimum weld size is dependent upon the thicker of the two parts joined, except that the weld size need not exceed the thickness of the thinner part. For this exception particular care shall be taken to provide sufficient preheat for soundness of the weld. Weld sizes larger than the thinner part joined are permitted if required by calculated strength. In the as-welded condition the distance between the edge of the base metal and the toe of the weld may be less than 1.5 mm provided the weld size is clearly verifiable. **Table 6.10.9** **Minimum Size of Fillet Welds** | Material Thickness of Thicker Part Joined (mm) | Minimum Size of Fillet Weld \* (mm) | | ---------------------------------------------- | ----------------------------------- | | To 6 inclusive | 3 | | Over 6 to 12 | 5 | | Over 12 to 20 | 6 | | Over 20 | 8 | \* Leg dimension of fillet welds. Single-pass welds must be used. The maximum size of fillet welds that is permitted along edges of connected parts shall be: Not greater than the thickness of the material for less than 6 mm thick material. Not greater than the thickness of the material minus 1.5 mm for material 6 mm or more in thickness, unless the weld is especially designated on the drawings to be built out to obtain full-throat thickness. The minimum effective length of fillet welds designed on the basis of strength shall be not less than 4 times the nominal size, or else the size of the weld shall be considered not to exceed $\dfrac{1}{4}$ of its effective length. If longitudinal fillet welds are used alone in end connections of flat bar tension members, the length of each fillet weld shall be not less than the perpendicular distance between them. The transverse spacing of longitudinal fillet welds used in end connections of tension members shall not exceed 200 mm, unless the member is designed on the basis of effective net area in accordance with Sec 10.6.3. Intermittent fillet welds are permitted to transfer calculated stress across a joint or faying surfaces when the strength required is less than that developed by a continuous fillet weld of the smallest size, and to join components of built-up members. The effective length of any segment of intermittent fillet welding shall be not less than 4 times the weld size, with a minimum of 40 mm. In lap joints, the minimum lap shall be 5 times the thickness of the thinner part joined, but not less than 25 mm. Lap joints joining plates or bars subject to axial stress shall be fillet welded along the end of both lapped parts, except where the deflection of the lapped parts is sufficiently restrained to prevent opening of the joint under maximum loading. Fillet welds in holes or slots may be permitted to transmit shear in lap joints or to prevent the buckling or separation of lapped parts and to join components of built-up members. Such fillet welds may overlap, subject to the provisions of this section. Fillet welds in holes or slots are not to be considered plug or slot welds. Side or end fillet welds terminating at ends or sides, respectively, of parts or members shall, wherever practicable, be returned continuously around the corners for a distance not less than 2 times the nominal size of the weld. This provision shall apply to side and top fillet welds connecting brackets, beam seats and similar connections, on the plane about which bending moments are computed. For framing angles and simple end-plate connections which depend upon flexibility of the outstanding legs for connection flexibility, end returns shall not exceed 4 times the nominal size of the weld. Fillet welds which occur on opposite sides of a common plane shall be interrupted at the corner common to both welds. End returns shall be indicated on the design and detail drawings. #### 10.9.2.3 Plug and Slot Welds a) Effective Area : The effective shearing area of plug and slot welds shall be considered as the nominal cross-sectional area of the hole or slot in the plane of the faying surface. b) Limitations : Plug or slot welds are permitted to transmit shear in lap joints or to prevent buckling of lapped parts and to join component parts of built-up members. The diameter of the hole for a plug weld shall not be less than the thickness of the part containing it plus 8 mm, rounded to the next higher value nor greater than the minimum diameter plus 3 mm or $2\dfrac{1}{2}$ times the thickness of the weld. The minimum centre to centre spacing of plug welds shall be 4 times the diameter of the hole. The minimum spacing of lines of slot welds in a direction transverse to their length shall be 4 times the width of the slot. The minimum centre to centre spacing in a longitudinal direction on any line shall be 2 times the length of the slot. The length of slot for a slot weld shall not exceed 10 times the thickness of the weld. The width of the slot shall be not less than the thickness of the part containing it plus 8 mm, rounded to the next higher value, nor shall it be larger than $2\dfrac{1}{4}$ times the thickness of the weld. The ends of the slot shall be semicircular or shall have the corners rounded to a radius not less than the thickness of the part containing it, except those ends which extend to the edge of the part. The thickness of plug or slot welds in material 16 mm or less in thickness shall be equal to the thickness of the material. In material over 16 mm thick, the thickness of the weld shall be at least $\dfrac{1}{2}$ the thickness of the material but not less than 16 mm. #### 10.9.2.4 Allowable Stresses or Design Strength For Working Stress Design the welds shall be proportioned to meet the stress requirements given in Table 6.10.10. For Load Factor Design the design strength of welds shall be the lower value of $\phi F_{BM}$ and $\phi F_w$, when applicable. The values of $\phi$, $F_{BM}$, $F_w$ and the limitations thereon are given in Table 6.10.11. **Table 6.10.10** **Allowable Stress on Welds(1)** | Type of Weld and Stress | Allowable Stress | Required Weld Strength Level(2, 3) | | ----------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------ | | **Complete-penetration Groove Welds** | | | | Tension normal to effective area | Same as base metal | "Matching" weld metal shall be used | | Compression normal to effective area | Same as base metal | Weld metal with a strength level equal to or less than "matching" weld metal is permitted | | Tension or compression parallel to axis of weld | Same as base metal | (same as above) | | Shear on effective area | 0.30 x nominal tensile strength of weld metal, N/mm² | (same as above) | | **Partial-penetration Groove Welds(4)** | | | | Compression normal to effective area | Same as base metal | Weld metal with a strength level equal to or less than "matching" weld metal is permitted | | Tension or compression parallel to axis of weld(5) | Same as base metal | (same as above) | | Shear parallel to axis of weld | 0.30 x nominal tensile strength of weld metal, N/mm² | (same as above) | | Tension normal to effective area | 0.30 x nominal tensile strength of weld metal (N/mm²), except tensile stress on base metal shall not exceed 0.60 x yield stress of base metal | (same as above) | | **Fillet Welds** | | | | Shear on effective area | 0.30 x nominal tensile strength of weld metal, N/mm² | Weld metal with a strength level equal to or less than "matching" weld metal is permitted. | | Tension or compression parallel to axis of weld(5) | Same as base metal | (same as above) | | **Plug and Slot Welds** | | | | Shear parallel to faying surfaces (on effective area) | 0.30 x nominal tensile strength of weld metal, N/mm² | Weld metal with a strength level equal to or less than "matching" weld metals is permitted | Notes: (1) The design of connected material is governed by Sec 10.7.4 through 10.7.7. (2) For "Matching" weld metal, see Table 4.1.1 of AWS D1.1. (3) Weld metal one strength level stronger than "matching" weld metal may be permitted. (4) See Sec 10.9.2.1(b) for a limitation on use of partial penetration groove welded joints. (5) Fillet welds and partial penetration groove welds joining the component elements of built-up members, such as flange to web connections, may be designed without regard to the tensile or compressive stress in these elements parallel to the axis of the welds. #### 10.9.2.5 Combination of Welds If two or more of the general types of weld (groove, fillet, plug, slot) are combined in a single joint, the effective capacity of each shall be separately computed with reference to the axis of the group in order to determine the allowable capacity of the combination. #### 10.9.2.6 Preheat for Heavy Shapes For ASTM A6 Group 4 and 5 shapes and welded built-up members made of plates more than 50 mm thick, a preheat equal to or greater than 175°C shall be used when making groove weld splices. #### 10.9.2.7 Matching Steel The choice of electrode for use with complete-penetration grove welds subjected to tension normal to the effective area shall be according to the requirements for matching steel stipulated in AWS D1.1 : Structural Welding Code-Steel. ### 10.9.3 Bolts, Rivets and Threaded Parts #### 10.9.3.1 High strength Bolts Except as otherwise provided in this Code, use of high strength bolts shall conform to the provisions of the RCSC Specification for Structural Joints Using ASTM A325 or A490 Bolts of AISC. **Table 6.10.11** **Design Strength of Welds** | Types of Weld and Stress(1) | Material | Resistance Factor $\phi$ | Normal Strength $F_{BM}$ or $F_w$ | Required Weld Strength Level(2, 3) | | ----------------------------------------------------- | --------------------------- | ------------------------ | --------------------------------- | ----------------------------------------------------------------------------------------- | | **Complete Penetration Groove Weld** | | | | | | Tension normal to effective area | Base | 0.90 | $F_y$ | "Matching" weld must be used | | Compression normal to effective area | Base | 0.90 | $F_y$ | Weld metal with a strength level equal to or less than "matching" may be used. | | Tension or compression parallel to axis of weld | | | | | | Shear on effective area | Base
weld electrode | 0.90
0.80 | $0.60F_y$
$0.60F_{EXX}$ | | | **Partial Penetration Groove Welds** | | | | | | Compression normal to effective area | Base | 0.90 | $F_y$ | Weld metal with a strength level equal to or less than "matching" may be used. | | Tension or compression parallel to axis of weld(4) | | | | | | Shear parallel to axis of weld | Base(5)
weld electrode | 0.75 | $0.60F_{EXX}$ | | | Tension normal to effective area | Base
weld electrode | 0.90
0.80 | $F_y$
$0.60F_{EXX}$ | | | **Fillet Welds** | | | | | | Shear on effective area | Base(5)
weld electrode | 0.75 | $0.60F_{EXX}$ | Weld metal with a strength level equal to or less than "matching" weld metal may be used. | | Tension or compression parallel to axis of weld(4) | Base | 0.90 | $F_y$ | | | **Plug or Slot Welds** | | | | | | Shear parallel to faying surfaces (on effective area) | Base(5)
weld electrode | 0.75 | $0.60F_{EXX}$ | Weld metal with a strength level equal to or less than "matching" weld metal may be used. | Notes: (1) For definition of effective area, see Sec 10.9.2. (2) For "matching" weld metal, see Table 4.1.1 of AWS D1.1. (3) Weld metal one strength level stronger than "matching" weld metal may be permitted. (4) Fillet welds and partial penetration groove welds joining component elements of built-up members, such as flange-to-web connections, may be designed without regard to the tensile or compressive stress in these elements parallel to the axis of the welds. (5) The design of connected material is governed by Sec 10.9.4.2. If required to be tightened to more than 50% of their minimum specified tensile strength, ASTM A449 bolts in tension and bearing type shear connections shall have an ASTM F436 hardened washer installed under the bolt head, and the nuts shall meet the requirements of ASTM A563. When assembled, all joint surfaces, including those adjacent to the washers, shall be free of scale, except tight mill scale. Except as noted below, all A325 and A490 bolts shall be tightened to a bolt tension not less than that given in Table 6.10.12. Tightening shall be done by the turn-of-nut method, a direct tension indicator or by calibrated wrench. Bolts in connections not subjected to tension loads, where slip can be permitted and where loosening or fatigue due to vibration or load fluctuation are not design considerations, need only to be tightened to the snug-tight condition. The snug-tight condition is defined as the tightness attained by a few impacts of an impact wrench or the full effort of a worker with an ordinary spud wrench and must bring the connected plies into firm contact. For Load Factor Design, the nominal strength value given in Table 6.10.13 for bearing type connections shall be used for bolts tightened to the snug-tight condition. Bolts to be tightened only to the snug-tight conditions shall be clearly indicated on the design and drawings. #### 10.9.3.2 Size and Use of Holes a) The maximum sizes of holes for bolts are given in Table 6.10.14 except that larger holes, required for tolerance on location of anchor bolts in concrete foundations, are permitted in column base details. **Table 6.10.12** **Minimum Bolt Tension, kN(1, 2)** | Diameter, mm | Nominal Size, in ASTM A325 or A490 | A325 Bolts | A490 Bolts | | ------------ | ---------------------------------- | ---------- | ---------- | | 12 | $\dfrac{1}{2}$ | 53 | 67 | | 16 | $\dfrac{5}{8}$ | 85 | 107 | | 20 | $\dfrac{3}{4}$ | 125 | 156 | | 22 | $\dfrac{7}{8}$ | 173 | 218 | | 25 | 1 | 227 | 285 | | 28 | $1\dfrac{1}{8}$ | 249 | 356 | | 32 | $1\dfrac{1}{4}$ | 316 | 454 | | 35 | $1\dfrac{3}{8}$ | 378 | 538 | | 38 | $1\dfrac{1}{8}$ | 458 | 658 | Notes: (1) Equal to 0.70 of minimum tensile strength of bolts, rounded off to nearest kN, as specified in ASTM specifications for A325 and A490 bolts with UNC threads. (2) The pretension values are based on nominal sizes in inch of ASTM bolts with UNC thread. **Table 6.10.13** **Design Strength of Fasteners** | Description of Fasteners | Tensile Strength: Resistance Factor $\phi$ | Tensile Strength: Nominal Strength, N/mm² | Shear Strength in Bearing type Connections: Resistance Factor $\phi$ | Shear Strength in Bearing type Connections: Nominal Strength, N/mm² | | ------------------------------------------------------------------------------------------------------- | ------------------------------------------ | ----------------------------------------- | -------------------------------------------------------------------- | ------------------------------------------------------------------- | | A307 bolts | 0.75 | 310 (1) | 0.60 | 186 (2, 4) | | A325 bolts, when threads are not excluded from shear planes | 0.75 | 620 | 0.60 | 372 (4) | | A325 bolts, when threads are excluded from shear planes | 0.75 | 620 | 0.60 | 495 (4) | | A490 bolts, when threads are not excluded from shear planes | 0.75 | 775 | 0.60 | 465 (4) | | A490 bolts, when threads are excluded from the shear planes | 0.75 | 775 | 0.60 | 620 (4) | | Threaded part meeting the requirements of Sec 10.3, when threads are not excluded from the shear planes | 0.75 | $0.75F_u$ (1, 3) | 0.65 | $0.45F_u$ | | Threaded parts meeting the requirements of Sec 10.3, when threads are excluded from the shear planes | 0.75 | $0.75F_u$ (1, 3) | 0.65 | $0.60F_u$ | | A502 Gr. 1. hot-driven rivets | 0.75 | 310 (1) | 0.65 | 250 (4) | | A502 Gr. 2 & 3 hot-driven rivets | 0.75 | 410 (1) | 0.65 | 330 (4) | Notes: (1) Static loading only. (2) Threads permitted in shear planes. (3) The nominal tensile strength of the threaded portion of an upset rod, based upon the cross-sectional area at its major thread diameter, $A_b$ shall be larger than the nominal body area of the rod before upsetting times $F_y$. (4) When bearing type connections used to splice tension members have a fastener pattern whose length, measured parallel to the line of force, exceeds 1250 mm, tabulated values shall be reduced by 20%. b) Standard holes shall be provided in member to member connections, unless oversized, short-slotted or long-slotted holes in bolted connections are approved by the engineer. Finger shims up to 6 mm may be introduced into slip-critical connections designed on the basis of standard holes without reducing the allowable shear of the fastener. c) Oversized holes are permitted in any or all plies of slip-critical connections, but they shall not be used in bearing type connections. Hardened washers shall be installed over oversized holes in an outer ply. d) Short-slotted holes are permitted in any or all plies of slip-critical or bearing type connections. The slots are permitted without regard to direction of loading in slip-critical connections, but the length shall be normal to the direction of the load in bearing-type connections. Washers shall be installed over short-slotted holes in an outer ply; when high strength bolts are used, such washers shall be hardened. e) Long-slotted holes are permitted in only one of the connected parts of either a slip-critical or bearing-type connection at an individual faying surface. Long-slotted holes may be used without regard to direction of loading in slip-critical connections, but shall be normal to the direction of load in bearing type connections. Where long-slotted holes are used in an outer ply, plate washers or a continuous bar with standard holes, having a size sufficient to completely cover the slot after installation, shall be provided. In high strength bolted connections, such plate washers or continuous bars shall be not less than 8 mm thick and shall be of structural grade material, but need not be hardened. If hardened washers are required for use of high strength bolts, the hardened washers shall be placed over the outer surface of the plate washer or bar. f) When A 490 bolts over 25 mm diameter are used in slotted or oversize holes in external plies, a single hardened washer conforming to ASTM F436, except with 8 mm minimum thickness, shall be used in lieu of the standard washer. **Table 6.10.14** **Nominal Hole Dimensions** | Bolt Dia mm | Standard (Dia) mm | Oversize (Dia) mm | Short-slot (Width × length) | Long-slot (Width × length) | | :---------- | :---------------- | :---------------- | :-------------------------- | :------------------------- | | 12 | 14 | 16 | 14 × 18 | 14 × 32 | | 16 | 18 | 21 | 18 × 22 | 18 × 40 | | 20 | 21 | 24 | 21 × 25 | 21 × 48 | | 22 | 24 | 27 | 24 × 28 | 24 × 56 | | 25 | 27 | 32 | 27 × 33 | 27 × 64 | | ≥28 | d + 1.5 | d + 8 | (d+1.5) × (d+10) | (d+1.5) × (2.5×d) | #### 10.9.3.3 Effective Bearing Area The effective bearing area of bolts, threaded parts and rivets shall be the diameter multiplied by the length in bearing, except that for countersunk bolts and rivets $\frac{1}{2}$ the depth of the countersink shall be deducted. #### 10.9.3.4 Tension and Shear In Working Stress Design the allowable tension and shear stresses on bolts, threaded parts and rivets shall be as given in Table 6.10.15 of the nominal body area of rivets (before driving) or the unthreaded nominal body area of bolts and threaded parts other than upset rods (see foot note h, Table 6.10.15). In Load Factor Design the design strength of bolts, threaded parts shall be taken as the product of the resistance factor $\phi$ and the nominal strength given in Table 6.10.13 of the unthreaded nominal body area of bolts and threaded parts other than upset (see footnote (3) of Table 6.10.13). High strength bolts supporting applied load by direct tension shall be so proportioned that their average tensile stress, computed on the basis of nominal bolt area and independent of any initial tightening force, will not exceed the appropriate stress given in Table 6.10.15 and the design strength given in Table 6.10.13 for Working Stress Design and Load Factor Design respectively. The applied load shall be the sum of any tension resulting from prying action produced by deformation of the connected parts and external service load in case of Working Stress Design or factored load in case of Load Factor Design. #### 10.9.3.5 Combined Tension and Shear in Bearing Type Connections a) In Working Stress Design, bolts and rivets subjected to combined shear and tension shall be so proportioned that the tension stress $F_t$, in N/mm² on the nominal body area $A_b$ produced by forces applied to the connected parts, shall not exceed the values computed from the expressions in Table 6.10.16 where $f_v$, the shear stress produced by the same forces, shall not exceed the value for shear given in Table 6.10.15. When allowable stresses are increased for wind or seismic loads in accordance with Sec 10.7.2.2, the constants in the expressions listed in Table 6.10.16 shall be increased by 33% but the coefficient applied to $f_v$ shall not be increased. b) In Load Factor Design, bolts and rivets subjected to combined tension and shear shall be so proportioned that the tension stress $f_t$ produced by factored loads on the nominal body area $A_b$ does not exceed the values computed from the expressions in Table 6.10.17. The value of $f_v$, the shear produced by the same factored loads, shall not exceed the values of shear for Load Factor Design given in Sec 10.9.3.4. #### 10.9.3.6 Combined Tension and Shear in Slip-critical Joints a) In Working Stress Design for A325 and A490 bolts used in slip-critical connections, the maximum shear stress allowed by Table 6.10.15 shall be multiplied by the reduction factor $(1-f_t/A_y T_b)$ where $f_t$ is the average tensile stress due to a direct load applied to all of the bolts in a connection and $T_b$ is the pretension load of the bolt specified in Table 6.10.12. When allowable stresses are increased for wind or seismic load in accordance with the provision of Sec 10.7.2.2, the reduced allowable shear stress shall be increased by 33%. **Table 6.10.15** **Allowable Shear Stress on Fasteners, N/mm²** | Description of Fasteners | Allowable Tension (Ft) | Allowable Shear (Fs) | | | Bearing type Connections | | | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------- | -------------------- | ------------------- | -------------------------------- | ---------------------------------------------------- | -------- | | | | | Standard size Holes | Oversize and Short-slotted Holes | Long-slotted Holes (Transverse Load / Parallel Load) | | | A502, Gr. 1, hot-driven Rivets | 159(5) | | | | | 120(6) | | A502, Gr. 2 and 3, hot-driven rivets | 200(5) | | | | | 152(6) | | A307 bolts | 138(5) | | | | | 69(6,7) | | Threaded parts meeting the requirements of Sec 10.3.1 and 10.3.2, and A449 bolts meeting the requirements of Sec 10.3.2, and when threads are not excluded from shear planes | 0.33F\_b(5, 8) | | | | | 0.17F\_u | | Threaded parts meeting the requirements of Sec 10.3.1 and 10.3.2, and A449 bolts meeting the requirements of Sec 10.3.2 when threads are excluded from shear planes | 0.33 F\_u(5) | | | | | 0.22F\_u | | A325 bolts, when threads are not excluded from shear planes | 303 | 117 | 103 | 83 | 69 | 145(6) | | A325 bolts, when threads are excluded from shear planes | 303 | 117 | 103 | 83 | 69 | 207(6) | | A490 bolts, when threads are not excluded from shear planes | 372 | 145 | 124 | 103 | 90 | 193(6) | | A490 bolts, when threads are excluded from shear planes | 372 | 145 | 124 | 103 | 90 | 276(6) | Notes: (1) See Sec 10.7.2.2. (2) Class A (slip coefficient 0.33). Clean mill scale and blast-cleaned surfaces with Class A coatings. When specified by the Engineer, the allowable shear stress, $F_v$, for slip-critical connections having special faying surface conditions may be increased to the applicable value given in the RCSC Specification. (3) For limitations on use of oversized and slotted holes, see Sec 10.9.3.2. (4) Direction of load application relative to long axis of slot. (5) Static loading only. (6) When bearing-type connections used to splice tension members have a fastener pattern whose length, measured parallel to the line of force, exceeds 1250 mm, tabulated values shall be reduced by 20%. (7) Threads permitted in shear planes. (8) The tensile capacity of the threaded portion of an upset rod, based upon the cross-sectional area at its major thread diameter $A_b$ shall be larger than the nominal body area of the rod before upsetting times $0.60F_u$. b) In Load Factor Design the design shear resistance of slip-critical joints shall be determined by using the values from Table 6.10.18 multiplied by $\phi = 1.0$, except $\phi = 0.85$ for the long-slotted holes when the load is in the direction of the slot. The shear on the bolt due to service loads shall be less than the tabulated **Table 6.10.16** **Allowable Tension Stress (Ft) for Fasteners in Bearing-type Connections** | Description of Fasteners | Threads Included in Shear Plane | Threads Excluded from Shear Plane | | ----------------------------------------- | ------------------------------- | --------------------------------- | | A307 bolts | 180 − 1.8f\_s ≤ 140 | | | A325 bolts | $\sqrt{(303)^2 − 4.39f_s^2}$ | $\sqrt{(303)^2 − 2.15f_s^2}$ | | A490 bolts | $\sqrt{(372)^2 − 3.75f_s^2}$ | $\sqrt{(372)^2 − 1.82f_s^2}$ | | Threaded parts, A449 bolts over 40 mm dia | 0.43F\_u − 1.8f\_s ≤ 0.33F\_u | 0.43F\_u − 1.4f\_s ≤ 0.33F\_u | | A502 Gr. 1 rivets | 207 − 1.3f\_s ≤ 160 | | | A502 Gr. 2 rivets | 262 − 1.3f\_s ≤ 200 | | **Table 6.10.17** **Tension Design Stress Limit (φFt), N/mm², for Fasteners in Bearing Type Connections** | Description of Fasteners | Threads Included in the Shear Plane | Threads Excluded from the Shear Plane | | ---------------------------------------------- | ----------------------------------- | ------------------------------------- | | A307 bolts | 270 − 1.8f\_s ≤ 207 | | | A325 bolts | 585 − 1.8f\_s ≤ 470 | 585 − 1.4f\_s ≤ 470 | | A490 bolts | 730 − 1.8f\_s ≤ 580 | 730 − 1.4f\_s ≤ 580 | | Threaded parts, A449 bolts over 40 mm diameter | 0.73F\_u − 1.8f\_s ≤ 0.56F\_u | 0.73F\_u − 1.4f\_s ≤ 0.56F\_u | | A502 Gr. 1 rivets | 304 − 1.3f\_s ≤ 234 | | | A502 Gr. 2 rivets | 407 − 1.3f\_s ≤ 310 | | When a bolt in a slip-critical connection is subjected to a service tensile force T, the nominal resistance in Table 6.10.18 shall be multiplied by the reduction factor $(1 − T/T_b)$ where $T_b$ is the minimum pretension load from Table 6.10.12. **Table 6.10.18** **Nominal Slip-critical Shear Strength, N/mm², of High Strength Bolts(1)** | Type of Bolt | Standard Size Holes | Oversize and Short Slotted Holes | Long slotted Holes(2) | | ------------ | ------------------- | -------------------------------- | --------------------- | | A325 | 117 | 103 | 83 | | A490 | 145 | 124 | 103 | Notes: (1) Class A (slip coefficient 0.33). Clean mill scale and blast-cleaned surfaces with class A coatings. (2) Tabulated values are for the case of load application transverse to the slot. When the load is parallel to the slot, multiply tabulated values by 0.85. #### 10.9.3.7 Bearing at Bolt Holes a) For shear connections in Working Stress Design the allowable bearing on the projected area of bolts and rivets at the bolt holes for two or more bolts in the line of force shall be as follows, provided the end distance in the line of force is more than $1\frac{1}{2}d$ and the centre to centre distance of bolts is more than $3d$. i) In standard or short-slotted holes $$ F_p = 1.2F_u \tag{10.9.1} $$ ii) In long-slotted holes perpendicular to the direction of load $$ F_p = 1.0F_u \tag{10.9.2} $$ On the projected area of the bolt or rivet closest to the edge in standard or short-slotted holes with the edge distance less than $1\frac{1}{2}d$ and in all connections with a single bolt in the line of force: $$ F_p = LtF_u/2d \leq 1.2F_u \tag{10.9.3} $$ If deformation around the hole is not a design consideration and adequate spacing and edge distance are provided as required by Sec 10.9.3.8 and 10.9.3.9, the following equation is permitted in lieu of Eq (10.9.3): $$ F_p = 1.5F_u \tag{10.9.4} $$ and the limit in Eq 10.9.3 shall be increased to $1.5F_u$. b) For shear connections in Load Factor Design the design bearing strength on two or more bolts in the line of force is $\phi R_n$ ($\phi = 0.75$) provided the end distance in the line of force is more than $1\frac{1}{2}d$ and the centre to centre distance of bolts is more than $3d$. i) In standard or short-slotted holes $$ R_n = 2.4 \times 10^{-3} d t F_u \tag{10.9.5} $$ ii) In long-slotted holes perpendicular to the direction of load $$ R_n = 2.0 \times 10^{-3} d t F_u \tag{10.9.6} $$ For the bolts closest to the edge, in all connections not covered by Eq (10.9.5) and (10.9.6), the design bearing of a single bolt or two or more bolts in line of force, each with an end distance less than $1\frac{1}{2}d$, shall be determined by $\phi R_n$ where $\phi = 0.75$. $$ R_n = \frac{Lt F_u}{1000} \tag{10.9.7} $$ If deformation around the bolt hole is not a design consideration and adequate spacing and edge distance as required by Sec 10.9.3.8 and 10.9.3.9 is provided, the following expression may be used in lieu of Eq 10.9.5 and 10.9.6, where $\phi = 0.75$. $$ R_n = 3.0 \times 10^{-3} d t F_u \tag{10.9.8} $$ #### 10.9.3.8 Minimum Spacing The distance between centres of standard, oversized or slotted fastener holes shall not be less than $2\frac{1}{2}$ times the nominal diameter of the fastener (a distance of $3d$ is preferred) nor less than that required by the following, if applicable. a) In Working Stress Design the centre to centre distance of holes, s, along a line of transmitted forces shall not be less than $3d$ when $F_p$ is determined by Eq (10.9.1) and (10.9.2). Otherwise, the distance between centres of holes shall not be less than the following: i) For standard holes: $$ s \leq 2000P/F_y(1 + d/2) \tag{10.9.9} $$ ii) For oversized and slotted holes: the distance required for standard holes in (i) above, plus the applicable increment $C_1$ from Table 6.10.19, but the clear distance between holes shall not be less than one bolt diameter. b) In Load Factor Design the centre to centre distance of holes, s, along a line of transmitted forces shall not be less than $3d$ when $R_n$ is determined by Eq (10.9.5) and (10.9.6). Otherwise, the distance between centres of holes shall not be less than the following : $$ s \leq \frac{1000P}{\phi F_y t} + \frac{d}{2} \tag{10.9.10} $$ where $\phi = 0.75$ #### 10.9.3.9 Minimum Edge Distance a) In Working Stress Design the distance from the centre of a standard hole to an edge of a connected part shall be not less than the applicable value from Table 6.10.20 or the value from Eq (10.9.11), as applicable. Along a line of transmitted force, the distance from the centre of a standard hole to the edge of the connected part $L_c$ shall be not less than $$ L_c \leq 2000P/F_u t \tag{10.9.11} $$ **Table 6.10.19** **Values of Spacing Increment C₁, mm** | Nominal Dia of Fastener | Oversize Holes | Slotted Holes | | Parallel to Line of Force | | ----------------------- | -------------- | ------------------------------ | ----------- | ------------------------- | | | | Perpendicular to Line of Force | Short Slots | Long Slots(1) | | ≤ 22 | 3 | 0 | 5 | 1½d − 1.5 | | 25 | 5 | 0 | 6 | 36 | | ≥ 28 | 6 | 0 | 16 | 1½d − 1.5 | Note: (1) When length of slot is less than the maximum allowed in Table 6.10.14, C₁ may be reduced by the difference between the maximum and actual slot lengths. b) In Load Factor Design the distance from the centre of a standard hole to the edge of the connected part shall be not less than the applicable value from Table 6.10.20 nor the value from Eq 10.9.12, as applicable. Along a line of transmitted force, the distance from the centre of a standard hole to the edge of the connected part $L_c$ shall be not less than $1\frac{1}{2}d$ when $R_n$ is determined by Eq (10.9.5) and (10.9.6). Otherwise, the edge distance shall be not less than $$ L_c \leq \frac{1000P}{\phi F_u t} \tag{10.9.12} $$ where $\phi = 0.75$ **Table 6.10.20** **Minimum Edge Distance, mm** **(Centre of Standard Hole to Edge of Connected Part)** | Nominal Bolt or Rivet Dia (mm) | At Sheared Edges | At Rolled Edges of Plates, Shapes or Bars, Gas-cut or Saw-cut Edges(2) | | ------------------------------ | ---------------- | ---------------------------------------------------------------------- | | 12 | 22 | 20 | | 16 | 28 | 22 | | 20 | 32 | 25 | | 22 | 38(3) | 28 | | 25 | 45(3) | 32 | | 28 | 50 | 38 | | 32 | 57 | 41 | | Over 32 | 45 × dia | 32 × dia | Notes: (1) For oversized or slotted holes, see Table 6.10.21 (2) All edge distances in this column may be reduced 3 mm when the hole is at a point where stress does not exceed 25% of the maximum design strength in the element. (3) These may be 32 mm at the ends of beam connection angles. For both the Working Stress and the Load Factor Design methods, the distance from the centre of an oversized or slotted hole to an edge of a connected part shall be not less than that required for a standard hole plus the applicable increment $C_2$ from Table 6.10.21. **Table 6.10.21** **Values of Edge Distance Increment C₂, mm** | Nominal Dia of Fastener (mm) | Oversized Holes | Slotted Holes | | Parallel to Edge | | ---------------------------- | --------------- | --------------------- | -------------- | ---------------- | | | | Perpendicular to Edge | Short Slots | Long Slots(1) | | ≤ 22 | 1.5 | 3 | | | | 25 | 3 | 3 | $\frac{3}{4}d$ | 0 | | ≤ 28 | 3 | 5 | | | Note: (1) When length of slot is less than maximum allowable (See Table 6.10.14), C₂ may be reduced by one-half the difference between the maximum and actual slot lengths. #### 10.9.3.10 Maximum Edge Distance and Spacing The maximum distance from the centre of any rivet or bolt to the nearest edge of parts in contact shall be 12 times the thickness of the connected part under consideration, but shall not exceed 150 mm. Bolted joints in unpainted steel exposed to atmospheric corrosion require special limitations on pitch and edge distance. For unpainted, built-up members made of weathering steel which will be exposed to atmospheric corrosion, the spacing of fasteners connecting a plate and a shape or two-plate components in contact shall not exceed 14 times the thickness of the thinnest part 175 mm, and the maximum edge distance shall not exceed eight times the thickness of the thinnest part 125 mm. ### 10.9.4 Shear Rupture #### 10.9.4.1 Working Stress Design At beam end connections where the top flange is coped, and in similar situations where failure might occur by shear along a plane through the fasteners, or by a combination of shear along a plane through the fasteners plus tension along a perpendicular plane : $$ F_s = 0.30F_u \tag{10.9.13} $$ acting on the net shear area $A_c$ and, $$ F_t = 0.50F_u \tag{10.9.14} $$ acting on the net tension area $A_t$. The minimum net failure path on the periphery of welded connections shall be checked. #### 10.9.4.2 Load Factor Design The design strength for the limit state of rupture along a shear failure path in main members shall be taken as $\phi F_n A_{ns}$ where $\phi = 0.75$ $$ F_n = 0.6 F_u \tag{10.9.15} $$ ### 10.9.5 Connecting Elements This section covers the design of connecting elements, such as stiffeners, gussets, angles and brackets and the panel zones of beam to column connections. #### 10.9.5.1 Eccentric Connections Axially stressed intersecting members shall have their gravity axes intersect at one point, if practicable; if not, provision shall be made for bending and shearing stresses due to the eccentricity. #### 10.9.5.2 Design a) In Working Stress Design for situations where failure might occur by shear along a plane through the fasteners, or by a combination of shear along a plane through the fasteners plus tension along a perpendicular plane, see Sec 10.9.4.1. b) In Load Factor Design the design strength $\phi R_n$ of welded, bolted and riveted connecting elements statically loaded in tension (i.e. splice and gusset plates) shall be the lower value obtained according to the limit state of yielding, fracture of the connecting element and block shear rupture. i) For yielding of the connecting element $$ \phi = 0.90 $$ $$ R_n = \frac{A_g F_y}{1000} \tag{10.9.16} $$ ii) For fracture of the connecting element where $A_n \leq 0.85A_g$ $$ \phi = 0.75 $$ $$ R_n = \frac{A_g F_u}{1000} \tag{10.9.17} $$ iii) For Block Shear Rupture : Block shear is a failure mode in which the resistance is determined by the sum of the shear strength on a failure path and the tensile strength on the perpendicular segment. When ultimate strength on the net section is used to determine the resistance on one segment, yielding on the gross section shall be used on the perpendicular segment; $\phi = 0.75$. Design strength shall be the larger of the two failure mode. At beam end connections where the top flange is coped, and in similar situations, failure can occur by shear along a plane through the fasteners, acting in combination with tension along a perpendicular plane. In such case, the ultimate strength on the net section (shear or tension) shall be used to determine the resistance of one segment and yielding on the gross section (shear or tension) shall be used on the perpendicular segment, with $\phi = 0.75$ for both. By alternating the choice of which segment resistance is based on ultimate strength two possible values of design strength are obtained. The larger value shall be taken as the design strength. For all other connecting elements, the design strength $\phi R_n$ shall be determined for the applicable limit state to insure that the design strength is equal to or greater than the required strength where $R_n$ is the nominal strength appropriate to the geometry and type of loading on the connecting element. The shear limit state is governed by : $$ \phi = 0.80 $$ $$ R_n = 0.7 \times 10^{-3} A_g F_y \tag{10.9.18} $$ ### 10.9.6 Fillers In welded construction, any filler 6 mm or more in thickness shall extend beyond the edges of the splice plate and shall be welded to the part on which it is fitted with sufficient weld to transmit the splice plate stress and shall be long enough to avoid overstressing the filler. Any filler less than 6 mm thick shall have its edges flush with the edges of the splice plate and the weld size shall be the sum of the size necessary to carry the splice plus the thickness of the filler plate. When bolts or rivets carrying loads pass through fillers thicker than 6 mm, except in slip-critical connections, the fillers shall be extended beyond the splice material and the filler extension shall be secured by enough bolts or rivets to distribute the total stress in the member uniformly over the combined section of the member and the filler, or an equivalent number of fasteners shall be included in the connection. ### 10.9.7 Splices Groove welded splices in plate girders and beams shall develop the full strength of the smaller spliced section. Other types of splices in cross-sections of plate girders and beams shall develop the strength required by the stresses at the point of splice. ### 10.9.8 Bearings #### 10.9.8.1 In Working Stress Design the allowable bearing stress $F_p$ on contact area of milled surfaces and ends of fitted bearing stiffeners; on projected area of pins in reamed, drilled or bored holes shall be $$ F_p = 0.90F_y \tag{10.9.19} $$ On expansion rollers and rockers, N/mm² $$ F_p = \left( \frac{F_y - 90}{20} \right) 0.66d \tag{10.9.20} $$ #### 10.9.8.2 In Load Factor Design the strength of surfaces in bearing is $\phi R_n$, where $\phi = 0.75$ and $R_n$ is defined below for various types of bearing. a) Milled or Finished Surfaces : For milled surfaces, pins in reamed, drilled or bored holes, and ends of fitted bearing stiffeners, $$ R_n = 2.0 \times 10^{-3} F_y A_{pb} \tag{10.9.21} $$ b) Expansion Roller and Rockers : For expansion rollers and rockers, $$ R_n = 1.5(F_y - 90)d/20 \tag{10.9.22} $$ ### 10.9.9 Column Bases and Bearing on Supports Proper provision shall be made to transfer the column loads and moments to the foundations : #### 10.9.9.1 In Working Stress Design, the stresses due to service loads shall not exceed the following : On brick in cement mortar $F_p = 1.72 \text{ N/mm}^2$ On the full area of a concrete support $F_p = 0.35f_c'$ On less than the full area of a concrete support $F_p = 0.35f_c' \sqrt{A_2/A_1} \leq 0.70f_c'$ #### 10.9.9.2 In Load Factor Design, the design bearing reactions due to factored loads on concrete shall not exceed $\phi c F_p'$. On the full area of concrete support $F_p = 0.85f_c'A_1$ On less than the full area of concrete support $F_p = 0.85f_c'A_1 \sqrt{A_2/A_1}$ where $\phi_c = 0.60$, and $$ \sqrt{A_2/A_1} \leq 2 ; $$ ### 10.9.10 Anchor Bolts Anchor bolts shall be designed to provide resistance to all conditions of tension and shear at the bases of columns, including the net tensile components of any bending moment which may result from column, base restraint. ## 10.10 SERVICEABILITY REQUIREMENTS This section provides the serviceability requirements under normal usage. Allowable limits for selected parameters affecting serviceability are specified below. ### 10.10.1 Camber If any special camber is necessary it shall be indicated in the design documents. Trusses of 25 m or greater in span generally shall be cambered for approximately the dead load deflection. Crane girders of 23 m or greater in span generally shall be cambered for approximately the dead load deflection plus $\frac{1}{4}$ the live load deflection. Beams and trusses detailed without specified camber shall be fabricated so that after erection any camber due to rolling or shop assembly shall be upward. If camber involves the erection of any member under a preload, this shall be noted in the design documents. ### 10.10.2 Expansion and Contraction Provision shall be made for expansion and contraction appropriate to the service conditions of the structure. ### 10.10.3 Deflection and Vibration #### 10.10.3.1 Deflection Beams and girders supporting floors and roofs shall be proportioned with due regard to the deflection produced by the design loads. Beams and girders supporting plastered ceilings shall be so designed that the maximum live load deflection does not exceed $\frac{L}{360}$. #### 10.10.3.2 Vibration Beams and girders supporting large open floor areas free of partitions or other sources of damping shall be designed with due regard for vibration. ### 10.10.4 Corrosion When appropriate, structural components shall be designed to tolerate corrosion or shall be protected against corrosion that impairs the strength or serviceability of the structure. Exposed beams shall be sealed against corrosion of interior surfaces and spaced sufficiently apart to permit cleaning and painting. ## 10.11 FABRICATION, ERECTION AND QUALITY CONTROL ### 10.11.1 Shop Drawings Shop drawings shall incorporate complete information necessary for the fabrication of the components of the structure, including the location, type and size of all welds, bolts and rivets. It shall be prepared in advance of the actual fabrication. These drawings shall be clearly distinguished between shop and field welds and bolts and shall clearly indicate type of high strength bolted connection such as snug tight or fully tensioned bearing, or slip-critical. Shop drawings shall be made in conformity with the best practice and with due regard to speed and economy in fabrication and erection. ### 10.11.2 Fabrication #### 10.11.2.1 Cambering, Curving and Strengthening Local application of heat or mechanical means to introduce or correct camber, curvature and straightness are permitted. The temperature of heated areas, as measured by approved methods, shall not exceed 565°C for A852 steel, 590°C for A514 steel nor 650°C for other steels. #### 10.11.2.2 Thermal Cutting Thermally cut free edges subject to substantial tensile stress shall be free of gouges greater than 5 mm. Gouges greater than 5 mm deep and sharp notches shall be removed by grinding or repaired by welding. Thermally cut edges which are to have weld deposited upon them, shall be reasonably free of notches or gouges. All reentrant corners shall be shaped to a smooth transition. Beam copes and weld access holes shall meet the geometrical requirements of Sec 10.9.1.7. Beam copes and weld access holes in ASTM A6 Group 4 and 5 shapes and welded built-up shapes with material thickness greater than 50 mm, shall be preheated to a temperature of not less than 65°C prior to thermal cutting. #### 10.11.2.3 Smoothing of Edges Smoothing or finishing of sheared or thermally cut edges of plates or shapes will not be required unless specially called for in the design documents or included in a stipulated edge preparation for welding. #### 10.11.2.4 Welded Construction The technique of welding, the workmanship, appearance and quality of welds and the methods used in correcting nonconforming work shall be in accordance with AWS D1.1 : Structural Welding Code–Steel. #### 10.11.2.5 High–strength Bolted Construction All parts of bolted members shall be pinned or bolted and held together rigidly without assembling. Use of a drift pin in bolt holes during assembly shall not distort the metal or enlarge the holes. Poor matching of holes shall not be acceptable. If the thickness of the material is not greater than the nominal diameter of the bolt plus 3 mm, the holes may be punched; otherwise the holes shall be either drilled or sub-punched and reamed. The die for all sub-punched holes, shall be at least 1.5 mm smaller than the nominal diameter of the bolt. Holes in A514 steel plates over 12 mm thick shall be drilled. Surfaces of high strength bolted parts in contact with the bolt head and nut shall not have a slope of more than 1:20 respect to a perpendicular to bolt axis. Where the slope of the surface exceeds 1:20, a beveled washer shall be used to compensate for the lack of parallelism. High strength bolted parts shall fit solidly together when assembled and shall not be separated by gaskets or any other interposed compatible materials. When assembled, all joint surfaces, including surface adjacent to the bolt head and nut, shall be free of scale, except tight mill scale, and shall be free of direct or other foreign material. Burrs that would prevent solid seating of the connection parts in the snug-tight condition shall be removed. Contact surfaces within slip-critical connections shall be free of oil, paint, or other coatings. #### 10.11.2.6 Compression Joints Compression joints which depend on contact bearing as part of the splice capacity shall have the bearing surfaces of individual fabricated pieces prepared by milling, sawing or other suitable means. #### 10.11.2.7 Dimensional Tolerances Dimensional tolerances shall be as specified in the Code of Standard Practice of the American Institute of Steel Construction. #### 10.11.2.8 Finishing of Column Base Columns base and base plates shall be finished in accordance with the following requirements : a) Rolled steel bearing plates 50 mm or less in thickness are permitted without milling, provided a satisfactory contact bearing is obtained; rolled steel bearing plates over 50 mm but not over 100 mm in thickness may be straightened by pressing, or if presses are not available, by milling of all bearing surfaces except as noted in (iii) and (iv) below, to obtain a satisfactory contact bearing; rolled steel bearing plates over 100 mm thick shall be milled for all bearing surfaces (except as noted in (iii) and (iv) below). b) Column bases other than rolled steel bearing plates shall be milled for all bearing surfaces (except as noted in (iii) and (iv) below). c) The bottom surfaces of bearing plates and column bases which are grouted to insure full bearing contact on foundations need not be milled. d) The top surfaces of base plates with columns full-penetration welded need not be pressed or milled. ### 10.11.3 Erection #### 10.11.3.1 Alignment of Column Bases Column bases shall be set level and to correct elevation with full bearing on concrete or masonry. #### 10.11.3.2 Bracing The frame of steel skeleton buildings shall be carried up true and plumb within the limits defined in the Code of Standard Practice of the American Institute of Steel Construction. Temporary bracing shall be provided in accordance with the requirements of the Code of Standard Practice wherever necessary to take care of all loads to which the structure may be subject, including equipment and the operation of the same. Such bearing shall be left in place as long as may be required for safety. Wherever erection equipment or other loads are supported during erection, proper provision shall be made to take care of stresses resulting from such loads. #### 10.11.3.3 Alignment No permanent bolting or welding shall be performed until the elements have been properly aligned. #### 10.11.3.4 Fit of Column Compression Joints Lack of contact bearing not exceeding a gap of 1.5 mm, regardless of the type of splice used (partial penetration grove welded or bolted), shall be acceptable. If the gap exceeds 1.5 mm, and is less than 6 mm, and if an engineering investigation shows that sufficient contact area exists, the gap shall be packed with non tapered steel shims. Shums may be of mild steel, regardless of the grade of the main material. #### 10.11.3.5 Field Welding Shop paint on surfaces adjacent to welds shall be wire-brushed to reduce paint film to a minimum. #### 10.11.3.6 Field Connection As erection progresses, the work shall be securely bolted or welded to take care of all dead, wind and live load forces. ### 10.11.4 Quality Control The fabricator shall provide quality control procedures to the extent that all work is performed in accordance with this specification. In addition to the fabricator's quality control procedures, material and workmanship at all times may be subject to inspection by the Engineer. #### 10.11.4.1 Cooperation As far as possible, all inspection shall be made at the fabricator's plant. The fabricator shall cooperate with the Engineer permitting access for inspection to all places where work is being done. The Engineer shall schedule his work for minimum interruption to the work of the fabrication. #### 10.11.4.2 Rejection Material or workmanship not in reasonable conformance with the provisions of this specification may be rejected at any time during the progress of the work. #### 10.11.4.3 Inspection of Welding The inspection of welding shall be performed in accordance with the provisions of Sec 6 of AWS D1.1 – Standard Welding Code Steel. When nondestructive testing is required, the process, extent and standards of acceptance shall be defined clearly in the design documents. #### 10.11.4.4 Inspection of Slip-critical High strength Bolted Connections The inspection of slip-critical, high strength bolted connections shall be in accordance with the provisions of the Specification for Standard Joints Using ASTM A325 or A490 Bolts of Research Council on Structural Connections. ## 10.12 SURFACE TREATMENT ### 10.12.1 General Surface treatment of steel structures shall include the preparation of surfaces and the application and drying of the paint or galvanization including the protection of the applied treatment against damage. ### 10.12.2 Weather Condition #### 10.12.2.1 Paints Paints shall be applied only on thoroughly dry surfaces and during period of favourable weather. Painting shall not be permitted when the atmospheric temperature is at or below 5°C when using vinyl, alkyd, and organic materials, and 10°C when using inorganic zinc, or when the humidity exceeds 85 percent at the site of the work, or when freshly painted surfaces may be damaged by rain, fog, or dew, or when it can be anticipated that the atmospheric temperature will drop below 5°C during the drying period. #### 10.12.2.2 During inclement weather , painting may be done inside an enclosure with artificially controlled atmospheric dust, or when such painting within limits suitable for painting. #### 10.12.2.3 All blast cleaning, except that performed within closed buildings, and all painting shall be preferably performed during daylight hours. ### 10.12.3 Cleaning of Surfaces #### 10.12.3.1 All exposed surfaces of structural steel, except galvanized surfaces, shall be cleaned and painted. #### 10.12.3.2 All surfaces of new structural steel or surfaces which are to be painted with inorganic zinc shall be blast cleaned. #### 10.12.3.3 In repainting existing steel structures where partial cleaning is required, the method of cleaning shall be specified. Any damage to sound painted surfaces, on areas not designated for treatment, shall be repaired. #### 10.12.3.4 Cleaning methods shall conform to the following. a) Blast Cleaning i) Abrasives used for blast cleaning shall be either clean dry sand, mineral grit, steel shot, or steel grit, and shall be suitable to produce satisfactory results. ii) Unwashed beach sand containing salt or excessive amounts of silt shall not be allowed. iii) All dirt, mill scale, rust, old paint, and other foreign materials shall be removed from steel surfaces by an approved blast cleaning apparatus. iv) Blast cleaned surfaces shall be primed or treated the same day blast cleaning is done. If cleaned surfaces rust or are contaminated with foreign materials before painting, they shall be re-cleaned. b) Steam Cleaning i) All dirt, grease, chalky paint or other foreign materials which may have accumulated on the previously painted or galvanized surfaces shall be removed with a steam cleaning apparatus which shall precede all other phases of cleaning. It is not intended that sound paint be removed by this process. Any paint which becomes loose, curled, lifted, or loses its bond with the preceding coat or coats after steam cleaning, shall be removed to expose sound paint or metal surface. ii) A detergent shall be added to the feed water of the steam generator. The detergent shall be of such composition and shall be added in such quantity that the cleaning as provided in the above is accomplished. iii) Any residue, detergent, or other foreign material which may accumulate on cleaned surfaces shall be removed by flushing with fresh water. iv) Steam cleaning shall not be performed more than two weeks prior to painting. v) Subsequent painting shall not be performed until the cleaned surfaces are thoroughly dry and in no case less than 24 hours after cleaning. c) Hand Cleaning i) Wire brushes, either hand or powered scraping tools, power grinders, or sandpaper shall be used to remove all dirt, loose rust and mill scale, or paint which is not firmly bonded to the metal surfaces. ii) Pneumatic chipping hammers shall not be used. ### 10.12.4 Application #### 10.12.4.1 Painting shall be done in a neat and workmanlike manner. Unless otherwise specified, paint shall be applied by brush, spray, roller or any combination thereof peculiar to the paint being applied. #### 10.12.4.2 Each application of paint shall be thoroughly cured and any skip, thin areas, or other deficiencies corrected before the succeeding application. The surface of the paint being covered shall be free from moisture, dust, grease, or any other deleterious materials that would prevent the bond of the succeeding applications. In spot painting, old paint which lifts after the first application shall be removed by scraping and the area repainted before the next application. #### 10.12.4.3 Brushes, when used, shall have sufficient body and length of bristle to spread the paint in a uniform film. Paint shall be evenly spread and thoroughly brushed out. #### 10.12.4.4 Rollers, when used, shall be of a type that does not leave a stippled texture in the paint film. #### 10.12.4.5 Mechanical mixers shall be used to mix paint. Prior to applying, the paint shall be mixed for a sufficient length of time to thoroughly mix the pigment and vehicle together, and shall be kept thoroughly mixed during its application. #### 10.12.4.6 Paints shall be formulated ready for application and no thinning will be allowed unless otherwise provided in the application materials specification for the paint being used. #### 10.12.4.7 The dry film thickness of the paint will be measured in place with a calibrated magnetic film thickness gauge. #### 10.12.4.8 The thickness of each application shall be limited to that which will result in uniform drying throughout the paint film. #### 10.12.4.9 Succeeding applications of paint shall be of such shade as to contrast with the paint being covered. #### 10.12.4.10 Zinc-rich primers shall be applied by spray methods. On areas inaccessible to spray application, the paint may be applied by brush or daubers. #### 10.12.4.11 Structures shall be blast cleaned and painted with the total thickness of undercoats before erection. After erection and before applying subsequent paint, all areas where paint has been damaged or has deteriorated and all exposed unpainted surfaces shall be thoroughly cleaned and spot painted with undercoats to the specified thickness. #### 10.12.4.12 Surfaces exposed to the atmosphere and which would be inaccessible for painting after erection shall be painted the full number of applications prior to erection. #### 10.12.4.13 Unless otherwise specified, steelworks in contact with concrete need not be painted. #### 10.12.4.14 Surfaces inaccessible after shop assembly shall be cleaned and painted prior to assembly except for contact surfaces. #### 10.12.4.15 Paint is permitted unconditionally in bearing type connections. For slip-critical connections where the design is based on special faying surface conditions, the surfaces in contact shall not be painted. #### 10.12.4.16 Unless otherwise specified in the design documents, surfaces within 50 mm of any field weld location shall be free of materials that would prevent proper welding or produce toxic fumes during welding. ### 10.12.5 Protection against Damage #### 10.12.5.1 Adequate protective measure shall be taken to prevent damage to the work. #### 10.12.5.2 Paint or paint stains that result in an unsightly appearance on surfaces not designated to be painted shall be removed or obliterated. #### 10.12.5.3 All painted surfaces that are marred or damaged shall be repaired with materials and to a condition equal to that of the coating specified. ### 10.12.6 Painting Galvanized Surfaces #### 10.12.6.1 All galvanized surfaces that are to be painted shall first be cleaned by washing with mineral spirit solvent sufficient to remove any oil, grease, or other materials foreign to the galvanized coating. #### 10.12.6.2 After washing, all areas shall be roughened by abrasive blasting. Galvanizing shall not be removed by this operation. #### 10.12.6.3 After preparation, all galvanized surfaces that are to be painted shall be covered with one application of zinc dust-zinc oxide primer. The zinc dust-zinc oxide paint shall be applied by spraying to produce a complete covering of the galvanized surfaces. #### 10.12.6.4 After the application of zinc dust-zinc oxide paint one application of pretreatment, vinyl wash primer shall be applied to such surfaces. The vinyl wash primer shall be applied by spraying to produce uniform wet film on the surface. ## 10.13 DESIGN DOCUMENTS ### 10.13.1 General This section covers the requirements for presentation of design documents including drawings for construction of steel structures. These requirements shall be met in addition to those specified in Chapter 1, General Design Requirements. ### 10.13.2 Drawings The design plans shall show a complete design with sizes, sections and relative locations of the various members. The stiffeners and bracings shall also be shown. Floor levels, column centres and offset shall be dimensioned. Drawings shall be drawn to a scale large enough to show the information clearly. Design documents shall indicate the type or types of construction as defined in Sec 10.4 including the loads and design requirements necessary for preparation of shop drawings, sheets, moments and axial forces to be resisted by all members and their connections. Where joints are to be assembled with high strength bolts, the design documents shall indicate the connection type (slip-critical, tension or bearing). Camber of trusses, beams and girders, if required, shall be shown in the design documents. ### 10.13.3 Standard Symbols and Nomenclature Welding and inspection symbols used on plans and shop drawings shall preferably be the American Welding Society symbols. Other welding symbols may be used, provided a complete explanation thereof is shown in the design documents. ### 10.13.4 Notation for Welding Notes shall be made in the design documents and on the shop drawings of those points or groups of joints in which the welding sequence and technique of welding shall be carefully controlled to minimize distortion. Weld lengths called for in the design documents and on the shop drawings shall be the net effective lengths. ## Related Appendix **Appendix A** Conversion of Expressions from SI to FPS Units