9.2 To 9.18)
9.2 Scope 9.2.1 Provisions of this Chapter shall apply to members prestressed with wires, strands, or bars conforming to the specifications of prestressing tendons given in Sec 9.5.1.3. 9.2.2 All provisions of this Code not specifically excluded, and not in conflict with provisions of this Chapter 9, shall apply to prestressed concrete. 9.3 Definitions, Symbols and Notation 9.3.1 Definitions ACTION Mechanical force or environmental effect to which the structure (or structural component) is subjected. ANALYSIS Acceptable methods of evaluating the performance indices or verifying the compliance of specific criteria. ANCHORAGE In post-tensioning, a mechanical device used to anchor the tendon to the concrete; in pretensioning, a device used to anchor the tendon until the concrete has reached a pre-determined strength, and the prestressing force has been transferred to the concrete; for reinforcing bars, a length of reinforcement, or a mechanical anchor or hook, or combination thereof at the end of a bar needed to transfer the force carried by the bar into the concrete. ANCHORAGE BLISTER A build-up area on the web, flange, or flange-web junction for the incorporation of tendon anchorage fittings. ANCHORAGE ZONE The portion of the structure in which the prestressing force is transferred from the anchorage device on to the local zone of the concrete, and then distributed more widely in the general zone of the structure. AT JACKING At the time of tensioning the prestressing tendons. AT LOADING The maturity of the concrete when loads are applied. Such loads include prestressing forces and permanent loads but generally not live loads. AT TRANSFER Immediately after the transfer of prestressing force to the concrete. AUTOGENEOUS SHRINKAGE Volume decrease due to loss of water in the hydration process causing negative pore pressure in concrete. BIOLOGICAL DEGRADATION The physical or chemical degradation of concrete due to the effect of organic matters such as bacteria, lichens, fungi, moss, etc. BONDED MEMBER A prestressed concrete member in which tendons are bonded to the concrete either directly or through grouting. BONDED POST- TENSIONING Post-tensioned construction in which the annular space around the tendons is grouted after stressing, thereby bonding the tendon to the concrete section. BONDED TENDON Prestressing tendon that is bonded to concrete either directly or through grouting. BURSTING FORCE Tensile forces in the concrete in the vicinity of the transfer or anchorage of prestressing forces. CAST-IN-PLACE CONCRETE Concrete placed in its final position in the structure while still in a plastic state. CHARACTERISTIC STRENGTH Unless otherwise stated in this Code, the characteristic strength of material refers to the value of the strength below which none of the test results should fall below by more than 15% or 3.5 MPa for ≤35 MPa concrete, and 10% or 3.5 MPa for ≥35 MPa concrete, whichever is larger. CHEMICAL ADMIXTUREs Admixtures which are usually used in small quantities typically in the form of liquid and can be added to the concrete both at the time of mixing and before placing to improve various concrete properties such as workability, air content and durability, etc. CLOSELY SPACED ANCHORAGES Anchorage devices are defined as closely spaced if their centre to centre spacing does not exceed 1.5 times the width of the anchorage devices in the direction considered. CLOSURE A placement of cast-in-place concrete used to connect two or more previously cast portions of a structure. COMPOSITE CONSTRUCTION Concrete components or concrete and steel components interconnected to respond to force effects as a unit. COMPRESSION- CONTROLLED SECTION A cross-section in which the net tensile strain in the extreme tension steel at nominal resistance is less than or equal to the compression-controlled strain limit. COMPRESSION- CONTROLLED STRAIN LIMIT The net tensile strain in the extreme tension steel at balanced strain conditions. CONCRETE COVER The specified minimum distance between the surface of the reinforcing bars, strands, post-tensioning ducts, anchorages, or other embedded items, and the surface of the concrete. CONFINEMENT A condition where the disintegration of the concrete under compression is prevented by the development of lateral and/or circumferential forces such as may be provided by appropriate reinforcing steel or composite tubes, or similar devices. CONFINEMENT ANCHORAGE Anchorage for a post-tensioning tendon that functions on the basis of containment of the concrete in the anchorage zone by special reinforcement. CREEP Time dependent deformation of concrete under permanent load. CREEP COEFFICIENT The ratio of creep strain to elastic strain in concrete. CREEP IN CONCRETE Increase in strain with time in concrete subjected to sustained stress. CURVATURE FRICTION Friction resulting from bends or curves in the specified prestressing tend stage at which the compressive stresses on profile. DAMAGE CONTROL A means to ensure that the limit state requirement is met for restorability or reparability of a structure. DECOMPRESSION The stage at which the compressive stresses, induced prestress, are overcome by the tensile stresses. DEFORMABILITY A term expressing the ability of concrete to deform. DEGREE OF DETERIORATION The extent to which the performance of a structure is degraded or the extent to which the deterioration has progressed from the time of construction, as a result of its exposure to the environment. DESIGN LIFE Assumed period for which the structure is to be used satisfactorily for its intended purpose or function with anticipated maintenance but without substantial repair being necessary. DETERIORATION INDEX An index selected for estimating and evaluating the extent of the deterioration process. DETERIORATION PREDICTION Prediction of the future rate of deterioration of a structure based on results of inspection and relevant records made during the design and construction stages. DEVIATION SADDLE A concrete block build-out in web, flange, or web-flange junction used to control the geometry of or to provide a means for changing direction of, external tendons. DRYING SHRINKAGE Volume decrease due to loss of moisture from concrete in the hardened state which is usually serious in hot and dry environment. DURABILITY DESIGN Design to ensure that the structure can maintain its required functions during service life under environmental actions. DURABILITY GRADE The extent of durability to which the structure shall be maintained in order to satisfy the required performance during its design life. This affects the degree and frequency of the remedial actions to be carried out during that life. DYNAMIC APPROACH An approach based on dynamic analysis to assess the overall forces on a structure liable to have a resonant response to wind action. DYNAMIC RESPONSE FACTOR Factor to account for the effects of correlation and resonant response. EARLY AGE STATE The state of concrete from final setting until the achievement of the required characteristic strength. EFFECTIVE PRESTRESS Stress remaining in prestressing tendons after all losses have occurred, excluding effects of dead load and superimposed load. ENVIRONMENTAL ACTIONS An assembly of physical, chemical or biological influences which may cause deterioration to the materials making up the structure, which in turn may adversely affect its serviceability, restorability and safety. FATIGUE LOADS Repetitive loads causing fatigue in the material which reduces its strength, stiffness and deformability. FINAL PRESTRESS Stress which exists after substantially all losses have occurred. FINAL TENSION The tension in the steel corresponding to the state of the final prestress. FORMWORK Total system of support for freshly placed concrete including the mould or sheathing, all supporting members, hardware and necessary bracings. FUNCTION The task which a structure is required to perform. GENERAL ZONE Region adjacent to a post-tensioned anchorage within which the prestressing force spreads out to an essentially linear stress distribution over the cross section of the component. GROUT A mixture of cementitious material and water with or without admixtures. INITIAL PRESTRESS The prestress in the concrete at transfer. INITIAL TENSION The maximum stress induced in the prestressing tendon at the time of stressing operation. JACKING FORCE Temporary force exerted by device that introduces tension into prestressing tendons. LIMIT STATE A critical state specified using a performance index, beyond which the structure no longer satisfies the design performance requirements. LIMITS OF DISPLACEMENT Allowable deformation of structure in terms of such parameters as inter-storey drift and relative horizontal displacement, to control excessive deflection, cracking and vibration. LONG-TERM PERFORMANCE INDEX Index defining the remaining capacity of a structure in performing its design functions during the design life. LOCAL ZONE The volume of concrete that surrounds and is immediately ahead of the anchorage device and that is subjected to high compressive stresses. MAINTENANCE A set of activities taken to ensure that the structure continues to perform its functions satisfactorily during the design life. MECHANICAL FORCES An assembly of concentrated or distributed forces acting on a structure, or deformations imposed on it. MODEL Mathematical description or experimental setup simulating the actions, material properties and behavior of a structure. MONITORING Continuous recording of data pertaining to deterioration and/or performance of structure using appropriate equipment. NOMINAL STRENGTH OF MATERIAL The characteristic values of the strength of materials used for calculation, in absence of the available statistical data. NORMAL CONCRETE Concrete which is commonly used in construction; it does not include special constituent materials other than Portland cement, water, fine aggregate, coarse aggregate and common mineral and chemical admixtures; it does not require any special practice for its manufacturing and handling. OVERALL PERFORMANCE INDEX Index indicating the overall performance of the structure. PARTIAL PERFORMANCE INDEX Index indicating a partial performance of the structure. PARTIAL SAFETY FACTOR FOR MATERIAL For analysis purposes, the design strength of a material is determined as the characteristic strength divided by a partial safety factor. PERFORMANCE Ability (or efficiency) of a structure to perform its design functions. PERFORMANCE INDEX Index indicating structural performance quantitatively. PERMANENT ACTIONS Self-weights of structures inclusive of permanent attachments, fixtures and fittings. PLASTIC SHRINKAGE Shrinkage arising from loss of water from the exposed surface of concrete during the plastic state, leading to cracking at the exposed surface. PLASTIC STATE The state of concrete from just after placing until the final setting of concrete. POST- TENSIONING Method of prestressing in which tendons are tensioned after concrete has hardened. PRESTRESSED CONCRETE Reinforced concrete in which internal stresses have been introduced to reduce potential tensile stresses in concrete resulting from loads. PRETENSIONING Method of prestressing in which tendons are tensioned before concrete is placed. SHRINKAGE LOSS The loss of stress in the prestressing steel resulting from the shrinkage of concrete. RELIABILITY Ability of a structure to fulfill specified requirements during its design life. REMAINING SERVICE LIFE Period from the point of inspection to the time when the structure is no longer useable, or does not satisfactorily perform the functions determined at the time of design. REMEDIAL ACTION Maintenance action carried out with the objective of arresting or slowing down the deterioration process, restoring or improving the performance of a structure, or reducing the danger of damage or injury to the users or any third party. REPAIR Remedial action taken with the objective of arresting or slowing down the deterioration of a structure, or reducing the possibility of damage to the users or third party. RESTORABILITY Ability of a structure to be repaired physically and economically when damaged under the effects of considered actions. Also known as REPAIRABILITY. ROBUSTNESS Ability of a structure to withstand damage by events like fire, explosion, impact, instability or consequences of human errors. Also known as STRUCTURAL INSENSITIVITY. SAFETY Ability of a structure to ensure that no harm would come to the users and to people in the vicinity of the structure under any action. SERVICE LIFE The length of time from the completion of a structure until the time when it is no longer usable because of its failure to adequately perform its design functions. SERVICEABILITY Ability of a structure to provide adequate services or functionality in use under the effects of considered actions. SETTLEMENT OF CONCRETE Sinking of the concrete surface after placing due to bleeding and/or escaping of the entrapped and entrained air in the concrete. SPECIAL CONCRETE Concrete other than normal concrete including light weight concrete, roller compacted concrete, self- compacting concrete, fiber-reinforced concrete, anti- washout under water concrete, etc. STIFF AND FLEXIBLE STRUCURES Stiff structures refer to those that are not sensitive to dynamic effects of wind, while flexible ones are those that are sensitive to such effects. STRENGTHENING Remedial action applied to a structure with the objective of restoring or improving its load bearing capacity to a level which is equal to, or higher than, the original design level.STRESS AT TRANSFER The stress in both the prestressing tendon and the concrete at the stage when the prestressing tendon is released from the prestressing mechanism. TEMPERATURE CRACKING Cracking caused by thermal stress which arises from differential temperatures in the concrete mass. TENDON Steel element such as wire, cable, bar, rod, or strand, or a bundle of such elements, used to impart prestress to concrete. THRESHOLD LEVEL OF PERFORMANCE Minimum acceptable level of performance of a structure. TRANSFER Act of transferring stress in prestressing tendons from jacks or pretensioning bed to concrete member. TRANSFER LENGTH The distance required at the end of a pretensioned tendon for developing the maximum tendon stress by bond. ULTIMATE LIMIT STATE Limit state for safety. VARIABLE ACTION Action due to a moving object on the structure as well as any load whose intensity is variable, including traffic load, wave load, water pressure, and load induced by temperature variation. WOBBLE FRICTION Friction caused by unintended deviation of prestressing sheath or duct from its specified profile. WORKABILITY The term expressing the ease with which concrete can be placed, compacted and filled. 9.3.2 Notation and Symbols
= Area of the part of cross-section between flexural tension face and centre of gravity of gross section, mm2 -Z = Cross-sectional area of a structural member measured to the outside edges of transverse reinforcement, mm2 -U = Gross area of concrete section, mm2. For a hollow section, -U is the area of the concrete only and does not include the area of the void(s) -\ = Area of prestressed reinforcement in tension zone, mm2 - = Area of nonprestressed tension reinforcement, mm2 -r = Area of compression reinforcement, mm2 = Clear cover of reinforcement, mm ~ = Dead loads, or related internal moments and forces • = Moment of inertia of cross-section resisting externally applied factored loads, mm4 • = Moment of inertia of cracked section transformed to concrete, mm4, Sec 6. •U = Moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, mm4 •! = Effective moment of inertia for computation of deflection, mm4 = Wobble friction coefficient per meter of prestressing tendon ‹ = Live loads, or related internal moments and forces p{ = Maximum moment in member due to service loads at stage deflection is computed, N-mm p = Moment causing flexural cracking at section due to externally applied loads, N-mm pf{v = Maximum factored moment at section due to externally applied loads, N-mm pk = Factored moment at section, N-mm j = Tensile force in concrete due to unfactored dead load plus live load (D + L), N Ž. = Prestressing tendon force at jacking end, N Ž•ª = Inherent or possessed performance index Ž•X = Inherent or possessed performance index Žv = Prestressing tendon force at any point x ্থ = Nominal shear strength provided by concrete, N ্থম = Nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment, N ্থ্ব = Nominal shear strength provided by concrete when diagonal cracking results from excessive principal tensile stress in web, N ্থি = Shear force at section due to unfactored dead load, N ্থম = Factored shear force at section due to externally applied loads occurring simultaneously with pf{v, N ্থয = Nominal shear strength, N ্থ = Vertical component of effective prestress force at section, N ্থ = Nominal shear strength provided by shear reinforcement, N ্থশ = Factored shear force at section, N Y = Shorter overall dimension of rectangular part of cross-section = Depth of equivalent rectangular stress block, mm y = Width of compression face of member, mm = Distance from extreme compression fiber to centroid of nonprestressed tension reinforcement, mm 0r = Distance from extreme compression fiber to centroid of compression reinforcement, mm = Nominal diameter of bar, wire, or prestressing strand, mm 0= Distance from extreme compression fiber to centroid of prestressed reinforcement, mm • = Base of Napierian logarithm r = Specified compressive strength of concrete, N/mm2 g r = Compressive strength of concrete at transfer of prestress, N/mm2 w = Stress due to unfactored dead load, at extreme fiber of section where tensile stress is caused by externally applied loads, N/mm2 ! = Compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads, N/mm2 \ = Average compressive stress in concrete due to effective prestress force only (after allowance for all prestress losses), N/mm2 \ = Stress in prestressed reinforcement at nominal strength, N/mm2 \k = Specified tensile strength of prestressing tendons, N/mm2 \ = Specified yield strength of prestressing tendons, N/mm2 = Modulus of rupture of concrete, N/mm2 ! = Effective stress in prestressed reinforcement (after allowance for all prestress losses), N/mm2 = Extreme fiber stress in tension in the pre-compressed tensile zone calculated at service loads using gross section properties, N/mm2 (MPa) = Specified yield strength of nonprestressed reinforcement, N/mm2 = Specified yield strength of transverse reinforcement, N/mm2 ℎ = Overall thickness of member, mm ℎ` = Overall thickness of flange of flanged section, mm ে = Length of span of two-way flat plates in direction parallel to that of the reinforcement being determined, mm ‡v = Length of prestressing tendon element from jacking end to any point Ÿ, metre = Spacing of shear or torsion reinforcement in direction parallel to longitudinal reinforcement, mm = Longer overall dimension of rectangular part of cross-section = Distance from centroidal axis of gross section, neglecting reinforcement, to extreme fibre in tension u = Total angular change of prestressing tendon profile in radians from tendon jacking end to a point Ÿ ে = Factor relating depth of equivalent rectangular compressive stress block to neutral axis depth ¡
= A factor for type of prestressing steel ¦ = Curvature friction coefficient ¥ = Modification factor reflecting the reduced mechanical properties of lightweight concrete, all relative to normal weight concrete of the same compressive strength (i.e., ¥ = 1.0 for normal weight concrete and 0.75 for all lightweight concrete. Else, ¥ shall be determined based on volumetric proportions of lightweight and normal weight aggregates, but shall not exceed 0.85.) = Ratio of nonprestressed tension reinforcement = -/(y0) r = Ratio of compression reinforcement = -r /(y0)
= Ratio of prestressed reinforcement = -\/Õy0\Ù
•
= Strength reduction factor
Z
/r Zr
r/ür Z\
\\/r p ω α p ω , Z^ = Reinforcement indices for flanged sections computed for Z, Zand Zr except that y shall be the web width, and reinforcement area shall be that required to develop compressive strength of web only. For other symbols and units of quantities, reference may be made to Chapter 6. 9.4 Analysis and Design 9.4.1 General
9.4.1.1 Prestressed members shall be designed for adequate strength in
accordance with the provisions of this Chapter.9.4.1.2 Unless specifically excluded or superseded by the provisions of this
Chapter, all other relevant provisions of this Code shall apply to prestressed concrete.9.4.1.3 Design of prestressed members shall be based on strength and on the
behavior at service conditions at all stages that will be critical during the life of the structure from the time prestress is first applied.9.4.1.4 Stress concentrations due to prestressing shall be considered in design.
9.4.1.5 Provisions shall be made for effects on adjoining construction of elastic
and plastic deformations, deflections, changes in length and rotations due to prestressing. Effects of creep, temperature and shrinkage shall also be considered.9.4.1.6 The possibility of buckling in a member between points where there is
intermittent contact between prestressing steel and an oversized duct and buckling in thin webs and flanges shall be considered.9.4.1.7 In computing section properties before bonding of prestressing steel,
effect of loss of area due to open ducts shall be considered.9.4.1.8 Thermal gradient and differential shrinkage shall be considered in
composite construction using prestressed concrete members.9.4.1.9 In evaluating the slenderness effects during lifting of slender beams,
consideration shall be given to beam geometry, location of lifting points, method of lifting and tolerances in construction. All beams which are lifted on vertical or inclined slings shall be checked for lateral stability and lateral moment on account of tilting of beam. Reference may be made to specialist literature in this regard. 9.4.2 Design Assumptions9.4.2.1 Strength design of prestressed members for flexure and axial loads shall
be based on assumptions given in Sections 9.4.2.2 to 9.4.2.7 and shall satisfy the applicable conditions of equilibrium and compatibility of strains.9.4.2.2 Strains in steel and concrete shall be assumed to be directly
proportional to the distance from the neutral axis except for Deep Beams.9.4.2.3 If nonprestressed reinforcement conforming to Sec 5.3.2 is used then,
stress in such reinforcements below , shall be taken as times steel strain. For strains greater than that corresponding to , stress in reinforcement shall be considered independent of strain and equal to .9.4.2.4 Maximum usable strain at extreme concrete compression fiber shall be
assumed equal to 0.003.9.4.2.5 The relationship between concrete compressive stress distribution and
concrete strain shall be assumed to be rectangular, trapezoidal, parabolic, or any other shape that results in prediction of strength in substantial agreement with results of comprehensive tests9.4.2.6 Requirements of Sec 9.4.2.5 are satisfied by an equivalent rectangular
concrete stress distribution defined by the following: (a) Concrete stress of 0.85fc′ shall be assumed uniformly distributed over an equivalent compression zone bounded by edges of the cross section and a straight line located parallel to the neutral axis at a distance a=β1c from the fiber of maximum compressive strain. (b) Distance from the fiber of maximum strain to the neutral axis, $ is measured in a direction perpendicular to the neutral axis. (প) ঋড়ৎ ৎ নবঃবিবহ ১৭.৫ ধহফ ২৮ গচধ, ে ংযধষষ নব:ধশবহ ধং ০.৮৫. ঋড়ৎ ৎ ধনড়াব ২৮ গচধ, ে ংযধষষ নব ৎবফঁপবফ ষরহবধৎষু ধঃ ধ ৎধঃব ড়ভ ০.০৫ ভড়ৎ বধপয ৭ গচধ ড়ভ ংঃৎবহমঃয রহ বীপবংং ড়ভ ২৮ গচধ, নঁঃ ে ংযধষষ হড়ঃ নব:ধশবহ ষবংং than 0.65.9.4.2.7 For investigation of stresses at transfer of prestress, at service loads,
and at cracking loads, elastic theory shall be used with the following assumptions: (i) Strains vary linearly with depth through the entire load range. (ii) At cracked sections, concrete resists no tension. 9.4.3 Classification of Prestressed Concrete Members Prestressed concrete flexural members shall be classified as Class U (uncracked), Class T (transition) and Class C (cracked) based on , the computed extreme fiber stress in tension in the pre-compressed tensile zone calculated at service load as follows: (a) Class U: ≤0.62 ′ (b) Class T: 0.62 ′ ≤ ≤1.0 ′ (c) Class C: > 1.0 ′ Prestressed two-way slab systems shall be designed as class U with ≤ 0.50 ′ 9.4.4 Shapes of Beams and Girders For prestressed concrete non-composite beams/girders, the frequently used shapes are: (a) Symmetrical I-section, (b) Unsymmetrical I-section, (c) T-section, (d) Inverted T-section, (e) Box section and (f) Solid/hollow rectangular section. Commentary: The suitability of selecting a particular shape will depend on the specific design requirement and economy of construction. In general, T or equal or unequal I- section are common choices to achieve economy in steel and concrete. Due consideration to the simplicity of formwork is also required. 9.4.5 Material Properties for Design9.4.5.1 Concrete Preparation and Design: Concrete shall be prepared, conveyed,
placed/cast, cured, tested and maintained following appropriate sections of Chapter 5 of the Code. Relevant applicable standards are mentioned in Chapter 5 and also listed in Table 6.9.9. Unless specifically applicable to prestressed concrete, general design requirements of normal concrete are those of Chapter 6 of the Code.9.4.5.2 Class: The Class of concrete is defined by the specified strength of
concrete cylinder r at 28 days. For example, Class 20 indicates concrete cylinder crushing strength of r = 20 N/mm2. Commonly, the classes of concrete shall be in steps of 5 N/mm2 as given by: Class 20, 25, 30 35… … … … 65 and 70 etc. although concrete in between these classes may also be permitted (like class 21, 24, 28, 31, 38, 42, and 49 etc.).9.4.5.3 Modulus of Elasticity, : Modulus of elasticity, for concrete shall be
permitted to be taken as . 0.043 ′ (in N/mm2) for values of between 1440 and 2560 kg/m3. For normal weight concrete, may be permitted to be taken as 4700 r.9.4.5.4 Modulus of Rupture, : Modulus of rupture, for concrete shall be
permitted to be taken as 0.62 ür where ¥ = 1 for normal weight concrete and0.75 for all lightweight concrete.
9.4.5.5 Reinforcing steel: Appropriate applicable standards for reinforcing steel
are given in Chapter 5 and also listed in Table 6.9.10. Unless specifically applicable to prestressed concrete, general design requirements of reinforcing steel are those that has been laid down in Chapter 6 of the Code.9.4.5.6 Modulus of elasticity, : Where it is not possible to ascertain the
modulus of elasticity of reinforcing steel by test and from the manufacturer of steel, the modulus of elasticity of reinforcing steel may be permitted to be taken as = 200,000 N/mm2.9.4.5.7 Prestressing Steel: Appropriate applicable standards for prestressing
steel are listed in Table 6.9.11.9.4.5.8 Modulus of elasticity, : Where it is not possible to ascertain the
modulus of elasticity of pain/ indented steel wire and prestressing steel (bar or strand) by test and from the manufacturer of steel, the values of given in Table 6.9.1 may be used: Table 6.9.1: Modulus of Elasticity of Prestressing Steel and Cold Drawn Wire Type of steel Modulus of elasticity, Es (kN/mm2) Plain/indented cold-drawn wire High tensile steel bars rolled or heat-treated Strands 9.5 Serviceability Requirements – Flexural Members 9.5.1 Stress in Concrete At Transfer Stresses in concrete immediately after prestress transfer (before time- dependent prestress losses occur) are as follows: (a) Extreme fiber stress in compression except as permitted in (b) shall not exceed 0.60g r (b) Extreme fiber stress in compression at ends of simply support members shall not exceed 0.70g r (c) Where computed concrete tensile strength, exceeds0.5 r at ends of simply supported members, or 0.25 r at other locations, additional bonded reinforcement shall be provided in the tensile zone to resist the total tensile force in concrete computed with the assumption of an uncracked section. Allowable stresses in concrete For Class U and Class T prestressed flexural members, stresses in concrete at service loads (based on uncracked section properties and after allowance for all prestress losses) shall not exceed the following: (a) Extreme fiber stress in compression due to prestress plus 0.45r sustained load (b) Extreme fiber stress in compression due to prestress 0.60r plus total load 9.5.2 Permissible stresses in Sections 9.5.1 and 9.5.2 shall be permitted to be exceeded if shown by test or analysis that performance will not be impaired. 9.5.3 Reinforcement Spacing9.5.3.1 For Class C prestressed flexural members not subject to fatigue or to
aggressive exposure, the spacing s of bonded reinforcement nearest the extreme tension face shall not exceed that for normal Reinforced Concrete, as given below: = 380(280/) −2.5 (6.9.1) But, not greater than 300(280/), where cc is the least distance from the surface of reinforcement or prestressing steel to the tension face. If there is only one bar or wire nearest to the extreme tension face, s used in the above equation is the width of the extreme tension face. Calculated stress in reinforcement closest to the tension face at service loads shall be computed based on the unfactored moment. It shall be permitted to take as q ½ . For structures subject to fatigue or exposed to corrosive environments, investigations, judgment and precautions are required.9.5.3.2 The spacing requirements Sec 9.5.3.1 shall be met by nonprestressed
reinforcement and bonded tendons. (a) The spacing of bonded tendons shall not exceed 2/3rd of the maximum spacing permitted for nonprestressed reinforcement. Where both reinforcement and bonded tendons are used to meet the spacing requirement, the spacing between a bar and a tendon shall not exceed 5/6th of that permitted by 9.5.3.1. See also (c) below. (b) In applying Eq. 6.9.1 to prestressing tendons, ∆\ shall be substituted for , where ∆\ shall be taken as the calculated stress in the prestressing steel at service loads based on a cracked section analysis minus the decompression stress w. It shall be permitted to take w equal to the effective stress in the prestressing steel !. See also (c) below. (c) In applying Eq. 6.9.1 to prestressing tendons, the magnitude of ∆\ shall not exceed 250 N/mm2. When ∆\ is less than or equal to 140 N/mm2, the spacing requirements of Sec 9.5.3.2(a) and (b) shall not apply. (d) Where depth ℎ of a beam exceeds 900 mm, the area of longitudinal skin reinforcement consisting of untensioned reinforcing steel or bonded tendons shall be uniformly distributed along both side faces of the member as required by Sec 6.3.6.7. The spacing shall be determined using Sections 9.5.3.1 and 9.5.3.2 (a), (b) and (c). It shall be permitted to include such reinforcement in strength computations if a strain compatibility analysis is made to determine stress in the individual bars or wires. 9.5.4 Permissible Stresses in Prestressing Steel Tensile stress in prestressing tendons shall not exceed the following: (a) Due to prestressing steel jacking force 0.94\ but not greater than the lesser of 0.80\k and the maximum value recommended by the manufacturer of prestressing steel or anchorage devices. (b) Immediately after prestress transfer 0.82\ but not greater than 0.74\k. (c) Post-tensioning tendons, at anchorage devices and couplers, immediately after force transfer 0.70\k 9.6 Losses of Prestress Effective stress in prestressing steel is usually subject to different losses at different stages. Superimposed loads can result in gain of prestress due to bending of the member which shall be taken into consideration if significant. To determine effective stress in the prestressing steel, !, allowance for the following sources of loss of prestress shall be considered: 9.6.1 Immediate Losses (a) Loss due to elastic shortening of concrete; (b) Loss due to prestressing steel seating at transfer (Anchorage slip); (c) Loss due to friction (for post-tensioned concrete only). 9.6.2 Long-term Losses (a) Loss due to relaxation of prestressing steel stress; (b) Loss due to creep of concrete; (c) Loss due to shrinkage of concrete. Unless otherwise determined by actual tests, allowance for these losses shall be made in accordance with the provisions of Sections 9.6.3 to 9.6.8. 9.6.3 Loss due to Elastic Shortening of Concrete (a) The loss of prestress due to immediate elastic shortening of adjacent concrete upon transfer of initial prestress shall be calculated as specified in this section. For pretensioning, the loss of prestress in the tendons at transfer shall be calculated on a modular ratio basis using the stress in the adjacent concrete. (b) For members with post-tensioned tendons which are not stressed simultaneously, there is a progressive loss of prestress during transfer due to the gradual application of the prestressing forces. This loss of prestress shall be calculated on the basis of half the product of the stress in the concrete adjacent to the tendons averaged along their lengths and the modular ratio. Alternatively, the loss of prestress may be exactly computed based on the sequence of tensioning. 9.6.4 Loss due to Prestressing Steel Seating at Transfer (Anchorage Slip) (a) Any loss of prestress which may occur due to slip of wire or strand during anchoring or due to straining of the anchorage shall be allowed for in the design. (b) Necessary additional elongation may be provided for at the time of tensioning to compensate for this loss. 9.6.5 Loss due to Relaxation of Prestressing Steel Stress (a) The relaxation losses in prestressing steel shall be determined from experiments. When experimental values are not available, the relaxation losses, considering normal relaxation steel, may be assumed as given in Table 6.9.2. Table 6.9.2: Relaxation Losses for Prestressing Steel at 1000 Hours at 27oC Initial Stress Relaxation Loss N/mm2 0.5\k 0.6\k 0.7\k 0.8\k For tendons at higher temperature or subject to large lateral loads, greater relaxation losses may be allowed, subject to the advice of the metallurgy specialist. (b) No reduction in the value of the relaxation losses should be made for a tendon with a load equal to or greater than the relevant jacking force that has been applied for a short duration prior to the anchoring of the tendon. 9.6.6 Loss due to Creep of Concrete (a) Creep occurs due to superimposed permanent dead load added to the member after it has been prestressed. Creep of concrete may be assumed to be proportional to the stress provided the stress in concrete does not exceed 40 percent of its compressive strength. (b) In the absence of test data, the ultimate creep strain may be estimated from the following values of creep coefficient, which is the ratio of the ultimate creep strain to the elastic strain at the age of loading. Table 6.9.3 shows the values at different days. Table 6.9.3: Creep Coefficient of Concrete Age at Loading Creep coefficient 7 days 2.2 28 days 1.6 1 year 1.1 (c) The ultimate creep strain estimated as above does not include the elastic strain. For the calculation of deformation at some stage before the total creep is reached, it may be assumed that 50 percent of the total creep takes place in the first month after loading and about 75 percent of the total creep takes place in the first six months after loading. For post-tensioning the creep coefficients shall be taken as 80% of those given here. (d) The loss of prestress due to creep of concrete shall be determined for all the permanently applied loads including the prestress. Loss due to stresses of short duration including live load and erection stresses may be ignored. (e) The loss of prestress due to creep of concrete shall be obtained as the product of the modulus of elasticity of the prestressing steel and the ultimate creep strain of the concrete fiber integrated along the centre-line of the prestressing steel over its entire length. (f) The total creep strain during any specific period shall be assumed to be the creep strain due to sustained stress equal to the average of the stresses at the beginning and end of the period. 9.6.7 Loss due to Shrinkage of Concrete (a) In the absence of test data, the approximate value of shrinkage strain in concrete for design purposes shall be assumed as follows: For pretensioning : 0.0003 For post-tensioning : ০.০০০২/[েঠ ক্ষ্ণ(ন্ + ২)] Where, t = age of concrete at transfer in days. Other standard procedures like AASHTO LRFD Specifications may be used. (b) For the calculation of deformation of concrete at some stage before the maximum shrinkage occurs it may be assumed that 50 percent of the shrinkage takes place during the first month and about 75 percent of the shrinkage takes place in the first six months after drying of concrete starts. (c) The loss of prestress due to shrinkage of concrete shall be obtained as the product of the modulus of elasticity of steel and the shrinkage strain of concrete. 9.6.8 Loss due to Friction (For Post-tensioned Tendons Only) (a) The design shall take into consideration all losses in prestress that may occur during tensioning due to friction between the post- tensioning tendons and the surrounding concrete or any fixture attached to the steel or concrete. (ন) ঞযব াধষঁব ড়ভ ঢ়ৎবংঃৎবংংরহম ভড়ৎপব Žা ধঃ ধ ফরংঃধহপব াে সবঃৎব ভৎড়স:যব jacking end and acting in the direction of the tangent to the curve of the cable shall be calculated from the relation: Žv = Ž.•Ø(#eð’ \Ö) (6.9.2) ডযবহ ( াে + ্বঁ) রং মৎবধঃবৎ:যধহ ০.৩, Žা সধু নব পড়সঢ়ঁঃবফ ভৎড়স Žv = ª] ‘#eð’\Ö (6.9.3) For use in Equations 6.9.2 and 6.9.3, the values of wobble friction coefficient and curvature friction coefficient µ shall be experimentally determined or obtained from the tendon manufacturer, and verified during tendon stressing operations. (c) Values of and ¦ used in the design shall be shown on design drawings (d) In absence of test results or manufacturer’s recommendation, the following values of ¦ and shown in Table 6.9.4 may be taken as a guide: Table 6.9.4: Friction Coefficients (K and µ) for Post-Tensioned Tendons Types of Tendons Coefficient, K per meter Curvature coefficient, µ per radian Grouted Tendons in metal sheathing Wire tendons 0.0033-0.0049 0.15-0.25 High-strength bars 0.0003-0.0020 0.08-0.30 7-wire strand 0.0016-0.0066 0.15-0.25 Unbonded tendons Mastic coated Wire tendons 0.0033-0.0066 0.05-0.15 7-wire strand 0.0033-0.0066 0.05-0.15 Pre-greased Wire tendons 0.001-0.0066 0.05-0.15 7-wire strand 0.001-0.0066 0.05-0.15
9.6.9
Values of wobble and curvature friction coefficients used in design shall
be shown on design drawings.
9.6.10 The effect of reverse friction shall be taken into consideration in such
cases where the initial tension applied to a prestressing tendon is partially released (e.g., anchorage slip) and action of friction in the reverse direction causes significant alteration in the distribution of stress along the length of the tendon.9.6.11 Where loss of prestress in a member occurs due to connection of
member to adjoining construction, such loss of prestress shall be allowed for in design. 9.7 Control of Deflection 9.7.1 For prestressed concrete flexural members, designed in accordance with the provisions of this Chapter, immediate deflection shall be computed by usual methods or formulas for elastic deflections, and the moment of inertia of gross concrete section, gI , shall be permitted to be used for Class U flexural members. 9.7.2 For Class C and Class T flexural members, deflection calculations shall be based on cracked transformed section analysis. It shall be permitted to base calculations on an effective moment of inertia, eI as given in Eq. 6.9.4a. •! = ¸ ¹±º ¹» ¼ ½ •U + ¾1 − ¸ ¹±º ¹» ¼ ½ ¿ • (6.9.4a) p = `º ÀÁ # (6.9.4b) = 0.62 ¥ r (6.9.4c) Deflection computed in accordance with Sec 9.7.1 shall not exceed the limits stipulated in Table 6.6.2, Chapter 6. 9.7.3 Additional long-term deflection of prestressed concrete members shall be computed taking into account stresses in concrete and steel under sustained load and including effects of creep and shrinkage of concrete and relaxation of steel. 9.8 Flexural Strength 9.8.1 Design moment strength of flexural members shall be computed by the strength methods of the Code. For prestressing steel, ps f shall be substituted for yf in strength computations. 9.8.2 As an alternative to a more accurate determination of ps f based on strain compatibility, the following approximate values of ps f shall be permitted to be used if se f is not less than . 0.5 pu f (a) For members with bonded tendons \ = \k ¾1 − ÔÐ\à
±Å + w w (Z −Zr)a¿ (6.9.5) Where, Z = +Ï
±Å , Zr = +ÅÏ
±Å and ¡\ is 0.55 for \/\k not less than 0.80; 0.40 for \/\k not less than 0.85; and 0.28 for \/\k not less than 0.90. If any compression reinforcement is taken into account when calculating \ by Eq. 6.9.5: The term ¾ \ à
`±Å +
w
w (Z − Zr)¿ shall be taken not less than 0.17 and d’ shall be
no greater than 0.15dp.
(b) For members with unbonded tendons and with a span-to-depth ratio of 35
or less:
\ = ! + 70 +
`±Å
²²+
(6.9.6)
But \ in Eq. 6.9.6 shall not be taken greater than the lesser of \ and
(! + 420).
(c) For members with unbonded tendons and with a span-to-depth ratio
greater than 35:
p
ρ
cf
se
f
ps
f
(6.9.7)
But, \ in Eq. 6.9.7 shall not be taken greater than the lesser of \ and
(! + 210)
9.8.3
Non prestressed reinforcement conforming to Sec 5.3 Chapter 5 of this
Part, if used with prestressing steel, shall be permitted to be considered to
contribute to the tensile force and to be included in moment strength
computations at a stress equal to
.
yf
Other non prestressed reinforcement shall
be permitted to be included in strength computations only if a strain
compatibility
analysis
is
performed
to
determine
stresses
in
such
reinforcement.
9.9
Limits For Flexural Reinforcement
9.9.1
Prestressed concrete sections shall be classified as either tension-
controlled, transition, or compression-controlled sections, in accordance with a.
and b. below.
(a) Sections are compression-controlled if the net tensile strain in the
extreme tension fiber , is equal to or less than the compression-
controlled strain limit when the concrete in compression reaches its
assumed strain limit of 0.003. The compression-controlled strain
limit is the net tensile strain in the reinforcement at balanced strain
conditions. For Grade 420 reinforcement, and for all prestressed
reinforcement, it shall be permitted to set the compression-
controlled strain limit to 0.002.
(b) Sections are tension-controlled if the net tensile strain in the extreme
tension steel, , is equal to or greater than 0.005 when the concrete
in compression reaches its assumed strain limit of 0.003. Sections
with between the compression-controlled strain limit and 0.005
constitute a transition region between compression-controlled and
tension-controlled sections. Appropriate strength reduction factor, •,
from
Sec 9.9.2 shall apply.
9.9.2
The appropriate strength reduction factor, , shall apply as given in (a)
to (f) below.
(a) Tension-controlled sections
0.90
(b) For compression-controlled sections
(i)
Members with spiral reinforcement as defined in Sec 6.2.3.2.2 0.75
(ii) Other reinforced members
0.65
(c) Shear and torsion
0.75
(d) Post-tensioned anchorage zones
0.85
(e) Strut and tie models
0.75
(f)
Flexural sections in pre-tensioned members where strand embedment
length is less than the development length
(i)
From the end of the member to the end of the transfer length 0.75
(ii) From the end of transfer length to the end of the development
length, • shall be taken as 0.75 to 0.90
Where bonding of the strand does not extend to the end of the member, strand
embedment shall be assumed to begin at the end of the debonded length.
9.9.3
Total amount of prestressed and non-prestressed reinforcement in
members with bonded prestressed reinforcement shall be adequate to develop
a factored load at least 1.2 times the cracking load computed on the basis of the
modulus of rupture
,
cf
as given in Sec 9.4.5.4. This provision shall be
permitted to be waived for flexural members with shear and flexural strength at
least twice the required strength (U) calculated for the factored loads and forces
in such combinations as are stipulated in Chapter 2, Loads.
9.9.4
Minimum Bonded Reinforcement
9.9.4.1 A minimum area of bonded reinforcement shall be provided in all
flexural members with unbonded tendons as required by Sections 9.9.4.2 and 9.9.4.3.9.9.4.2 Except as provided in Sec 9.9.4.3, minimum area of bonded
reinforcement shall be computed by - = 0.004- (6.9.8) Where, Act is area of that part of cross-section between the flexural tension face and center of gravity of gross-section. (a) Bonded reinforcement required by Eq. 6.9.8 shall be uniformly distributed over pre-compressed tensile zone as close as practicable to extreme tension fibre. (b) Bonded reinforcement shall be required regardless of service load stress conditions.9.9.4.3 For two-way flat slab systems, minimum area and distribution of
bonded reinforcement shall be as required in (a), (b) and (c) below. (a) Bonded reinforcement shall not be required in positive moment areas where , the extreme fibre stress in tension in the precompressed tensile zone at service loads (after allowance for all prestress losses), does not exceed 0.17 r. (b) In positive moment areas where computed tensile stress in concrete at service load exceeds 0.17 r minimum area of bonded reinforcement shall be computed by - = m± ². `Ï (6.9.9) Where, the value of used in Eq. 6.9.9 shall not exceed 420 MPa. Bonded reinforcement shall be uniformly distributed over precompressed tensile zone as close as practicable to the extreme tension fibre. (c) In negative moment areas at column supports, the minimum area of bonded reinforcement As in the top of the slab in each direction shall be computed by - = 0.00075- (6.9.10) Where, - is the larger gross cross-sectional area of the slab-beam strips in two
orthogonal equivalent frames intersecting at a column in a two-way slab.
9.9.4.4 Bonded reinforcement required by Eq. 6.9.10 shall be distributed
between lines that are 1.5ℎ outside opposite faces of the column support. At least four bars or wires shall be provided in each direction. Spacing of bonded reinforcement shall not exceed 300 mm.9.9.4.5 Minimum length of bonded reinforcement required by Sections 9.9.4.2
and 9.9.4.3 shall be as required in Sec 9.9.4.5 (a), (b) and (c). (a) In positive moment areas, minimum length of bonded reinforcement ংযধষষ নব ড়হব-ঃযরৎফ:যব পষবধৎ ংঢ়ধহ ষবহমঃয, যে ধহফ পবহঃবৎবফ রহ ঢ়ড়ংরঃরাব moment area. (b) In negative moment areas, bonded reinforcement shall extend one-sixth ঃযব পষবধৎ ংঢ়ধহ, যে ড়হ বধপয ংরফব ড়ভ ংঁঢ়ঢ়ড়ৎঃ. (c) Where bonded reinforcement is provided for •ph in accordance with Sec 9.8.3 or for tensile stress conditions as per Sec 9.9.4.3 (b), minimum length also shall conform to provisions of Chapter 6. 9.10 Statically Indeterminate Structures9.10.1 Frames and continuous construction of prestressed concrete shall be
designed for satisfactory performance at service load conditions and for adequate strength.9.10.2 Performance at service load conditions shall be determined by elastic
analysis, considering reactions, moments, shears, and axial forces induced by prestressing, creep, shrinkage, temperature change, axial deformation, restraint of attached structural elements, and foundation settlement.9.10.3 Moments used to compute required strength shall be the sum of the
moments due to reactions induced by prestressing (with a load factor of 1.0) and the moments due to factored loads. Adjustment of the sum of these moments shall be permitted as allowed in Sec 9.10.4.9.10.4 Redistribution of moments in continuous prestressed flexural members
shall be: (a) Where bonded reinforcement is provided at supports in accordance with Sec 9.9.4, it shall be permitted to decrease negative or positive moments calculated by elastic theory for any assumed loading, in accordance with Sec 9.10.4 (b) and (c) below. (b) Except where approximate values for moments are used, it shall be permitted to decrease factored moments calculated by elastic theory at sections of maximum negative or maximum positive moment in any span of continuous flexural members for any assumed loading arrangement by not more than 1000 percent, with a maximum of 20 percent. (c) Redistribution of moment shall be made only when is equal to or greater than 0.0075 at the section at which moment is reduced.9.10.5 The reduced moment shall be used for calculating redistributed
moments at all other sections within the spans. Static equilibrium shall be maintained after redistribution of moments for each loading arrangement. 9.11 Compression Members - Combined Flexure And Axial Load9.11.1 Prestressed Concrete Members Subject to Combined Flexure and Axial
Load With or without non-prestressed reinforcement, Prestressed concrete members subject to combined flexure and axial load shall be proportioned by the strength design methods of this Code. Effects of prestress, creep, shrinkage, and temperature change shall be included.9.11.2 Limits for Reinforcement of Prestressed Compression Members
9.11.2.1 Members with average compressive stress in concrete less than 1.6 N/mm2, due to effective prestress force only, shall have minimum reinforcement in accordance with Sections 6.3.9.1, 6.3.9.2 for columns and Sec 6.6.3 for walls and minimum transverse reinforcement for compression members of Chapter 6. 9.11.2.2 Except for walls, members with average compressive stress in concrete due to effective prestress force only, equal to or greater than 1.6 N/mm2 shall have all tendons enclosed by spirals or lateral ties in accordance with (a) through (d). (a) Spirals shall conform to the spiral reinforcement requirement for compression members of this Code and Sec 9.11.3. (b) Lateral ties shall be at least No. 10 in size or welded wire reinforcement of equivalent area, and shall be spaced vertically not to exceed 48 tie bar or wire diameters, or the least dimension of the compression member. (c) Ties shall be located vertically not more than half a tie spacing above top of footing or slab in any story, and not more than half a tie spacing below the lowest horizontal reinforcement in members supported above. (d) Where beams or brackets frame into all sides of a column, ties shall be terminated not more than 75 mm below lowest reinforcement in such beams or brackets. 9.11.2.3 For walls with average compressive stress in concrete due to effective prestress force only equal to or greater than 1.6 N/mm2, minimum reinforcement required by Sec 6.6.3 shall not apply where structural analysis shows adequate strength and stability.9.11.3 Volumetric Spiral Reinforcement Ratio
Volumetric spiral reinforcement ratio, s shall be not less than the value given by = 0.45 ¸ ßÁ ß±R −1¼±Å Ï#
(6.9.11)
Where, the value of in Eq. 6.9.11 shall not exceed 700 N/mm2. For greater
than 420 N/mm2, lap splices according to Sec 9.9.3.1(a) shall not be used.
(a) Spiral reinforcement shall be spliced, if needed, by any one of the
following methods:
Lap splices not less than the larger of 300 mm and the length indicated
in Sec 8.1.9.3 (a) to (e) of Chapter 8 and summarized below:
(i) deformed uncoated bar or wire
(ii) plain uncoated bar or wire
(iii) epoxy-coated deformed bar or wire
(iv) plain uncoated bar or wire with a standard stirrup or tie hook in
accordance with Sec 8.1.9.3 (d) of Chapter 8 at ends of lapped spiral
reinforcement.
(ন) ঞযব:বৎস ুংঃধহফধৎফ যড়ড়শচ্ ধং ঁংবফ রহ:যরং ঈড়ফব ংযধষষ সবধহ ড়হব ড়ভ:যব
following:
(i) 180-degree bend plus 401 extension, but not less than 65 mm at
free end of bar.
(ii) 90-degree bend plus 1201 extension at free end of bar.
(c) For stirrup and tie hooks
(i) No. 16 bar and smaller, 90o bend plus 601 extension at free end of
bar; or
(ii) No. 19, No. 22 bar and No. 25 bar, 90o bend plus 1201 extension at
free end of bar; or
(iii) No. 25 bar and smaller, 135o bend plus 601 extension at free end of
bar.
9.12
Slab Systems
9.12.1 Factored moments and shears in prestressed slab systems reinforced
for flexure in more than one direction shall be determined in accordance with provisions of Sec 6.5.7 Chapter 6 or by more detailed design procedures. 9.12.2 n M of prestressed slabs with loads and load combinations required by Chapter 2 and 6 at every section shall be greater than or equal to u M considering Sections 9.10.3 and 9.10.4. n V (design strength) of prestressed slabs at columns following Chapter 6 shall be greater than or equal to u V (the required strength, Chapter 2).9.12.3 At service load conditions, all serviceability limitations, including limits
on deflections, shall be met, with appropriate consideration of the factors listed in Sec 9.10.2.9.12.4 For uniformly distributed loads, spacing of tendons or groups of
tendons in at least one direction shall not exceed the smaller of eight times the slab thickness and 1.5 m. Spacing of tendons also shall provide a minimum average effective prestress of 0.9 N/mm2 on the slab section tributary to the tendon or tendon group. For slabs with varying cross section along the slab span, either parallel or perpendicular to the tendon or tendon group, the minimum average effective prestress of 0.9 N/mm2 is required at every cross section tributary to the tendon or tendon group along the span. Concentrated loads and opening in slabs shall be considered when determining tendon spacing.9.12.5 In slabs with unbonded tendons, bonded reinforcement shall be
provided in accordance with Sections 9.9.4.3 to 9.9.4.5.9.12.6 Except as permitted in Sec 9.12.7, in slabs with unbonded tendons, a
minimum of two 12.7 mm diameter or larger, seven-wire post-tensioned strands shall be provided in each direction at columns, either passing through or anchored within the region bounded by the longitudinal reinforcement of the column. Outside column and shear cap faces, these two structural integrity tendons shall pass under any orthogonal tendons in adjacent spans. Where the two structural integrity tendons are anchored within the region bounded by the longitudinal reinforcement of the column, the anchorage shall be located beyond the column centroid and away from the anchored span.9.12.7 Prestressed slabs not satisfying Sec 9.12.6 shall be permitted provided
they contain bottom reinforcement in each direction passing within the region bounded by the longitudinal reinforcement of the column and anchored at exterior supports as required by Sec 6.5.3.8 Chapter 6. The area of bottom reinforcement in each direction shall be not less than 1.5 times that required by Eq. 6.9.12 as given below. -,fgh = ².q±Å Ï
y^0
(6.9.12)
and not less than 2.1y^0/, where y^ is the width of the column face through
which the reinforcement passes. Minimum extension of these bars beyond the
column or shear cap face shall be equal to or greater than the bar development
length required by Sec 8.2.