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# Chapter 9: Prestressed Concrete Structures

## 9.1 Notation

* a = depth of equivalent rectangular stress block, mm
* A = area of the part of cross-section between flexural tension face and centre of gravity of gross section, mm²
* Aps = area of prestressed reinforcement in tension zone, mm²
* As = area of nonprestressed tension reinforcement, mm²
* A's = area of compression reinforcement, mm²
* b = width of compression face of member, mm
* d = distance from extreme compression fibre to centroid of nonprestressed tension reinforcement, mm
* d'' = distance from extreme compression fibre to centroid of compression reinforcement, mm
* dp = nominal diameter of bar, wire, or prestressing strand, mm
* D = dead loads, or related internal moments and forces
* e = base of Napierian logarithm
* fc' = specified compressive strength of concrete, N/mm²
* fcds = compressive strength of concrete at transfer of prestress, N/mm²
* fda = stress due to unfactored dead load, at extreme fibre of section where tensile stress is caused by externally applied loads, N/mm²
* fpe = compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fibre of section where tensile stress is caused by externally applied loads, N/mm²
* fpc = average compressive stress in concrete due to effective prestress force only (after allowance for all prestress losses), N/mm²
* fps = stress in prestressed reinforcement at nominal strength, N/mm²
* fpu = specified tensile strength of prestressing tendons, N/mm²
* fpy = specified yield strength of prestressing tendons, N/mm²
* h = overall thickness of member, mm
* hf = overall thickness of flange of flanged section, mm
* Ie = moment of inertia of cross-section resisting externally applied factored loads, mm⁴
* k = wobble friction coefficient per metre of prestressing tendon
* l = length of span of two-way flat plates in direction parallel to that of the reinforcement being determined, mm
* ℓx = length of prestressing tendon element from jacking end to any point x, metre
* L = live loads, or related internal moments and forces
* Mcs = moment causing flexural cracking at section due to external loads, N⋅mm
* Mmax = maximum factored moment at section due to externally applied loads
* Mu = factored moment at section
* Nu = tensile force in concrete due to unfactored dead load plus live load (D + L)
* s = spacing of shear or torsion reinforcement in direction parallel to longitudinal reinforcement, mm
* Vc = nominal shear strength provided by concrete
* Vcd = nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment
* Vcw = nominal shear strength provided by concrete when diagonal cracking results from excessive principal tensile stress in web
* Vd = shear force at section due to unfactored dead load
* Vf = factored shear force at section due to externally applied loads occurring simultaneously with Mmax
* Vn = nominal shear strength
* Vp' = vertical component of effective prestress force at section
* Vs = nominal shear strength provided by shear reinforcement
* Vsu = factored shear force at section
* Ps = prestressing tendon force at jacking end
* Px = prestressing tendon force at any point x
* x = shorter overall dimension of rectangular part of cross-section
* α = total angular change of prestressing tendon profile in radians from tendon jacking end to any point x
* y = longer overall dimension of rectangular part of cross-section
* yt = distance from centroidal axis of gross section, neglecting reinforcement, to extreme fibre in tension
* β1 = factor defined in Sec 9.5.5(c)
* γp = factor for type of prestressing tendon
  * \= 0.55 for fpy/fpu not less than 0.80
  * \= 0.40 for fpy/fpu not less than 0.85
  * \= 0.28 for fpy/fpu not less than 0.90
* μ = curvature friction coefficient
* ρ = ratio of nonprestressed tension reinforcement = As/bd
* ρ' = ratio of compression reinforcement = A's/bd
* ρp = ratio of prestressed reinforcement = Aps/bdp
* φ = strength reduction factor
* ω = ρfy/fc'
* ω' = ρ'fy/fc'
* ωp = ρp fpm/fc'
* ωw, ωp, ωw' = reinforcement indices for flanged sections computed for ω, ωp, and ω' except that b 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 shall be made to Chapter 6.

## 9.2 Scope

Provisions of this chapter shall apply to members prestressed with wire, strands, or bars conforming to provisions for prestressing tendons in Sec 2.4.6(d) of Part 5.

## 9.3 Definitions

For the purpose of this chapter, the following definitions shall apply.

**ANCHORAGE:** In post-tensioning, a device used to anchor tendon to concrete member; in pretensioning, a device used to anchor tendon during hardening of concrete.

**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.

**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 tendon profile.

**EFFECTIVE PRESTRESS:** Stress remaining in prestressing tendons after all losses have occurred, excluding effects of dead load and superimposed load.

**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.

**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.

**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.

**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.

**TENDON:** Steel element such as wire, cable, bar, rod, or strand, or a bundle of such elements, used to impart prestress to concrete.

**TRANSFER:** Act of transferring stress in prestressing tendons from jacks or pretensioning bed to concrete member.

**TRANSMISSION LENGTH:** The distance required at the end of a pretensioned tendon for developing the maximum tendon stress by bond.

**WOBBLE FRICTION:** Friction caused by unintended deviation of prestressing sheath or duct from its specified profile.

## 9.4 General Requirements

### 9.4.1

Prestressed members shall be designed for adequate strength in accordance with the provisions of this Code.

### 9.4.2

Unless specifically excluded or superseded by the provisions of this chapter, all other relevant provisions of this Code shall apply to prestressed concrete.

### 9.4.3

Design of prestressed members shall be based on strength and on the behaviour at service conditions at all critical load stages.

### 9.4.4

In the design of prestressed concrete members consideration shall be given to the following:

a) Stress concentrations due to prestressing,

b) Effects of temperature and shrinkage,

c) Effects of elastic and plastic deformations, changes in length, deflections and rotations due to prestressing,

d) Possibility of buckling in a member between points where concrete and prestressing tendons are in contact and of buckling in thin webs and flanges,

e) Thermal gradient and differential shrinkage shall be considered in composite construction using prestressed concrete members. Adequate provision for shear connectors in such composite members shall be kept.

### 9.4.5

Loss of area due to open ducts shall be taken into consideration in computing section properties prior to bonding of prestressing tendons.

### 9.4.6

In assessing loads and forces the effects of prestress shall be taken into account.

### 9.4.7

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.

For calculating the factor of safety against lateral instability reference may be made to specialist literature. This factor shall not be less than two.

For determining the lateral moment due to tilting, realistic values shall be assumed for the eccentricity of lifting points and the lateral bow. The maximum tensile stress due to lateral moment arising from tilting shall not exceed 0.75 N/mm².

## 9.5 Design Assumptions

### 9.5.1

Strength design of prestressed members for flexure and axial loads shall be based on assumptions given in Sec 9.5.2 through 9.5.6, and shall satisfy the applicable conditions of equilibrium and compatibility of strains.

### 9.5.2

Strains in steel and concrete shall be assumed to be directly proportional to the distance from the neutral axis.

### 9.5.3

Maximum usable strain at extreme concrete compression fibre shall be assumed to be 0.003.

### 9.5.4

Relationship between concrete compressive stress distribution and concrete strain may be assumed to be of any shape that can be justified by comprehensive tests.

### 9.5.5

Requirements of Sec 9.5.4 may be considered satisfied by an equivalent rectangular concrete stress distribution defined by the following:

a) Concrete stress of 0.85 fc' 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

$$
a = \beta_1 c
$$

from the fibre of maximum compressive strain.

b) Distance c from the fibre of maximum strain to the neutral axis shall be measured in a direction perpendicular to the neutral axis.

c) Factor β1 shall be calculated from

$$
\beta_1 = 0.85 - 0.008(f'_c - 30), \text{ and } 0.65 \leq \beta_1 \leq 0.85
$$

### 9.5.6

Stresses at transfer of prestress, at service loads, and at cracking loads, shall be investigated by the straight-line theory with the following assumptions:

a) Strains vary linearly with depth through the entire load range.

b) At cracked sections, concrete resists no tension.

## 9.6 Control of Deflections

### 9.6.1

For prestressed concrete flexural members, immediate deflection shall be computed by usual methods or formulas for elastic deflections, and the moment of inertia of gross concrete section may be used for uncracked sections.

### 9.6.2

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.

### 9.6.3

For Class 3 members (See Sec 9.7 below), deflection calculations shall be made considering cracked sections.

### 9.6.4

Deflection computed in accordance with Sec 9.6.1, 9.6.2 and 9.6.3 shall not exceed the limits stipulated in Table 6.6.4 of Chapter 6.

## 9.7 Classification of Prestressed Concrete Members

Prestressed concrete members, depending on the amount of tensile stresses permitted under service load, shall be classified as follows:

**Class 1:** No flexural tensile stresses.

**Class 2:** Flexural tensile stress but no visible cracking.

**Class 3:** Flexural tensile stresses but surface width of cracks not exceeding 0.1 mm for members having exposure condition as detailed in note 1 and not exceeding 0.2 mm for all other members.

**Note 1:** Concrete surfaces exposed to sea water spray, de-icing salts (directly or indirectly), corrosive fumes, sewage or other toxic materials e.g. sulphate, abrasive action e.g. sea water carrying solid or flowing water with pH ≤ 4.5 or machinery or vehicles.

## 9.8 Allowable Tensile Stresses in Concrete for Flexural Members

### 9.8.1

Design tensile stresses in flexure at service loads (after allowance for all prestress losses) shall not exceed the following values for different classes of members:

1. **Class 1 members:** No tensile stress.

2. **Class 2 members:** Design tensile stresses shall not exceed the following:

   i) For pretensioned tendons: $f_t = 0.50\sqrt{f'_c}$ (9.8.1)

   ii) For post-tensioned tendons: $f_t = 0.40\sqrt{f'_c}$ (9.8.2)

3. **Class 3 members:** Design tensile stresses shall not exceed the following:

   a) Pretensioned or grouted post-tensioned tendons:

   i) For limiting crack width of 0.1 mm: $f_t = 0.70F\sqrt{f'_c}$ (9.8.3)

   ii) For limiting crack width of 0.2 mm: $f_t = 0.85F\sqrt{f'_c}$ (9.8.4)

   b) Pretensioned tendons distributed in the tensile zone and positioned close to the tension face of the concrete.

   i) For limiting crack width of 0.1 mm: $f_t = 0.90F\sqrt{f'_c}$ (9.8.5)

   ii) For limiting crack width of 0.2 mm: $f_t = 1.00F\sqrt{f'_c}$ (9.8.6)

Factor F used in Eq (9.8.3), (9.8.4), (9.8.5) and (9.8.6) is the depth factor and shall be calculated as:

$$
F = 1.2 - \frac{d}{2000}
$$

The value of F shall not be taken greater than 1.1 nor less than 0.70.

**Note:** Reliable literature should be followed for calculation of crack width.

### 9.8.2

Design tensile stresses in flexure immediately after transfer of prestress shall not exceed the following values for different classes of members:

a) **Class 1 members:** = 1.00 N/mm²

b) **Class 2 members:**

i) For pretensioned member = $0.50\sqrt{f_{cds}}$

ii) For post-tensioned member = $0.40\sqrt{f_{cds}}$

Members with pretensioned tendons should have some tendons or additional reinforcement well distributed throughout the tensile zone of the section. Members with post-tensioned tendons should have additional reinforcement, if required, located near the tension face of the member.

c) **Class 3 members:** The design tensile stress should not, in general, exceed the appropriate value for a Class 2 member. Where this stress is exceeded, the section shall, in design, be considered as cracked.

## 9.9 Allowable Compressive Stresses in Concrete for Flexural Members

### 9.9.1

Stresses at extreme fibre of concrete shall not exceed 0.45 fc' at service loads (after allowance for all prestress losses).

### 9.9.2

Stresses at extreme fibre of concrete shall not exceed 0.60 fcd immediately after transfer of prestress.

### 9.9.3

Allowable compressive stresses in concrete as provided in Sec 9.9.1 and 9.9.2 above may be allowed to be exceeded if shown by test or analysis that performance will not be impaired.

## 9.10 Steel

### 9.10.1

The prestressing steel shall conform to the following standards and the requirements of Part 5 of this Code:

a) Steel wire conforming to BDS 240,

b) Steel wire conforming to ASTM A421,

c) Low-relaxation wire conforming to ASTM A421,

d) High-strength steel bar conforming to ASTM A722,

e) Strand conforming to ASTM A416,

f) Low-relaxation strand conforming to ASTM A416.

### 9.10.2

All prestressing steel shall be clean and free from oil, dirt, scales, splits, harmful scratches, surface flaws, rough, jagged and imperfect edges and other defects likely to impair its use in prestressed concrete. Slight rust may be permitted provided there is no surface pitting visible to the naked eye.

### 9.10.3

Coupling units and other similar fixtures used in conjunction with the wires or bars shall have an ultimate tensile strength of not less than individual strengths of the wires or bars being joined.

### 9.10.4

Where it is not possible to ascertain the modulus of elasticity by test or from the manufacturer of steel, the following values may be adopted:

| Type of Steel                                  | Modulus of Elasticity Es (kN/mm²) |
| :--------------------------------------------- | :-------------------------------- |
| Plain cold-drawn wire                          | 210                               |
| High tensile steel bars rolled or heat-treated | 200                               |
| Strands                                        | 195                               |

### 9.10.5

Reinforcement used as untensioned steel shall be any one of those permitted in reinforced concrete (see Sec 5.3).

## 9.11 Allowable Stresses in Prestressing Steel

Tensile stress in prestressing tendons shall not exceed the following:

a) Due to tendon jacking force: $0.94 f_{pu}$, but not greater than the lesser of 0.80 fpu and the maximum value recommended by the manufacturer of prestressing tendons or anchorages.

b) Immediately after prestress transfer: $0.82 f_{pu}$, but not greater than 0.74 fpu.

c) Post-tensioning tendons, at anchorages and couplers, immediately after tendon anchorage: $0.70f_{pu}$

## 9.12 Losses of Prestress

### 9.12.1

While assessing the stresses in concrete and steel during tensioning operations and later in service, due regard shall be paid to all losses and variations in stress resulting from creep of concrete, shrinkage of concrete, relaxation of steel, elastic shortening of concrete at transfer, friction due to curvature of post-tensioning tendons, and slip of anchorage. Unless otherwise determined by actual tests, allowance for these losses shall be made in accordance with the provisions of Sec 9.12.2 through 9.12.7 below.

In computing losses in prestress when untensioned reinforcement is present, the effect of the tensile stresses developed by the untensioned reinforcement due to shrinkage and creep shall be considered.

### 9.12.2 Loss of Prestress Due to Creep of Concrete

#### 9.12.2.1

Creep of concrete may be assumed to be proportional to the stress provided the stress in concrete does not exceed 40 per cent of its compressive strength.

#### 9.12.2.2

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:

| Age at Loading | Creep Coefficient |
| :------------- | :---------------- |
| 7 days         | 2.2               |
| 28 days        | 1.6               |
| 1 year         | 1.1               |

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 per cent of the total creep takes place in the first month after loading and about 75 per cent of the total creep takes place in the first six months after loading.

#### 9.12.2.3

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.

#### 9.12.2.4

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 fibre integrated along the centreline of the prestressing steel over its entire length.

#### 9.12.2.5

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.

### 9.12.3 Loss of Prestress Due to Shrinkage of Concrete

#### 9.12.3.1

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:

$$
\frac{0.0002}{\log_{10}(t+2)}
$$

where, t = age of concrete at transfer in days.

#### 9.12.3.2

For the calculation of deformation of concrete at some stage before the maximum shrinkage occurs it may be assumed that 50 per cent of the shrinkage takes place during the first month and about 75 per cent of the shrinkage takes place in the first six months after drying of concrete starts.

#### 9.12.3.3

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.

### 9.12.4 Loss of Prestress Due to Relaxation of Steel

The relaxation losses in prestressing steel shall be determined from experiments. When experimental values are not available, the relaxation losses may be assumed as given in Table 6.9.1.

**Table 6.9.1: Relaxation Losses for Prestressing Steel at 1000 Hours at 27°C**

| Initial Stress | Relaxation Loss N/mm² |
| :------------- | :-------------------- |
| 0.5 fpu        | 0                     |
| 0.6 fpu        | 35                    |
| 0.7 fpu        | 70                    |
| 0.8 fpu        | 90                    |

For tendons at higher temperature or subject to large lateral loads, greater relaxation losses as specified by the engineer shall be allowed for. 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.

### 9.12.5 Loss of Prestress Due to Elastic Shortening of Concrete

The loss of prestress due to immediate elastic shortening of adjacent concrete upon transfer of initial prestress shall be calculated as specified in Sec 9.12.5.1 and 9.12.5.2 below.

#### 9.12.5.1

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.

#### 9.12.5.2

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.

### 9.12.6 Loss of Prestress Due to Friction

#### 9.12.6.1

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.

#### 9.12.6.2

The value of prestressing force $P_x$ at a distance $\ell_x$ metres from the jacking end and acting in the direction of the tangent to the curve of the cable, shall be calculated from the relation:

$$
P_x = P_s e^{-(k\ell_x + \mu\alpha)}
$$

(9.12.1)

When $(k\ell_x + \mu\alpha)$ is not greater than 0.3, $P_x$ may be computed from

$$
P_x = \frac{P_s}{1 + k\ell_x + \mu\alpha}
$$

(9.12.2)

For use in Eq (9.12.1) and (9.12.2), the values of wobble friction coefficient k and curvature friction coefficient μ shall be experimentally determined or obtained from the tendon manufacturer, and verified during tendon stressing operations.

#### 9.12.6.3

In the absence of test results or manufacturer's recommendation, the following values of μ and k may be taken as a guide:

a) For straight or moderately curved structures with curved or straight cables, μ may be taken as follows:

0.55 for steel moving on concrete,
0.30 for steel moving on steel,
0.25 for steel moving on lead

and the value of k may be taken as varying from $15 \times 10^{-4}$ to $50 \times 10^{-4}$ per metre.

b) In circular or similar constructions, where circumferential tendons are tensioned by jacks, values of μ for calculating friction may be taken as:

0.45 for steel moving in smooth concrete,
0.25 for steel moving on steel bearers,
0.10 for steel moving on steel rollers.

#### 9.12.6.4

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 and action of friction in the reverse direction causes an alteration in the distribution of stress along the length of the tendon.

#### 9.12.6.5

Values of wobble and curvature friction coefficients used in design shall be shown on design drawings.

#### 9.12.6.6

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.

### 9.12.7 Loss of Prestress Due to Anchorage Slip

Any loss of prestress which may occur due to slip of wire during anchoring or due to straining of the anchorage shall be allowed for in the design. Necessary additional elongation may be provided for at the time of tensioning to compensate for this loss.

## 9.13 Flexural Strength

### 9.13.1

Design moment strength of flexural members shall be computed by the design methods provided in this Code. For prestressing steel, fps shall be substituted for fy in the strength computations.

Equations for the computation of design moment strength shall be as follows:

a) **Sections with Tension Reinforcement only**

i) For rectangular or flanged sections when the compression flange thickness hf is equal to or greater than the depth of the equivalent rectangular stress block, a, the design moment strength φMn may be computed by:

$$
\varphi M_n = \varphi\left[A_{ps}f_{ps}(d_p - a/2) + A_s f_y(d - a/2)\right]
$$

(9.13.1)

$$
\text{where } a = \frac{A_{ps}f_{ps} + A_s f_y}{0.85f'_c b}
$$

or

$$
\varphi M_n = \varphi\left[A_{ps}f_{ps}d_p\left(1-0.59\left(\omega_p + \frac{d}{d_p}\omega\right)\right) + A_s f_y d\left(1-0.59\left(\frac{d_p}{d}\omega_p + \omega\right)\right)\right]
$$

(9.13.2)

When compression flange thickness hf is less than a, the design moment strength φMn may be computed by:

$$
\varphi M_n = \varphi\left[A_{ps}f_{ps}(d_p - a/2) + A_s f_y(d - a/2) + 0.85f'_c h_f(b - b_w)(d_p - h_f/2)\right]
$$

(9.13.3)

$$
\text{where } A_{psw}f_{ps} = A_{ps}f_{ps} + A_s f_y - 0.85f'_c(b - b_w)h_f
$$

and

$$
a = \frac{A_{psw}f_{ps}}{0.85f'_c b_w}
$$

Ayw/fps is the tension reinforcement force required to develop in the web.

b) **Rectangular Sections with Compression Reinforcement:** For rectangular sections with compression reinforcement, the design moment strength φMn shall be computed as follows:

When

$$
\frac{A_{ps}f_{ps} + A_s f_y - A'_s f_y}{bd} \geq 0.85\beta_1 f'_c \frac{d}{d'}\left(\frac{600}{600 - f_y}\right)
$$

$$
\varphi M_n = \varphi\left[A_{ps}f_{ps}(d_p - a/2) + A_s f_y(d - a/2) + A'_s f_y(a/2 - d')\right]
$$

(9.13.4)

$$
\text{where } a = \frac{A_{ps}f_{ps} + A_s f_y - A'_s f_y}{0.85f'_c b}
$$

When the value of (Apsps + Asfy - A'sfy)/bd is less than the value given above, the stress in the compression reinforcement is less than the yield strength fy. In such case, the effects of compression reinforcement may be neglected and the moment strength may be computed by the equation given for a rectangular section with tension reinforcement only. Alternatively, the stress in the compression reinforcement may be determined by a general analysis based on stress and strain compatibility, using the assumptions given in Sec 9.5.

c) **Other Cross-sections:** For other cross-sections, the design moment strength φMn shall be computed by a general analysis based on stress and strain compatibility, using the stress-strain properties of the prestressing steel and the assumptions given in Sec 9.5.

### 9.13.2

In lieu of a more accurate determination of fps based on strain compatibility, the following approximate values of fps may be used if fse is not less than 0.5 fpu:

a) For members with bonded prestressing tendons:

$$
f_{ps} = f_{pu}\left(1 - \frac{\gamma_p}{\beta_1}\left[\rho_p\frac{f_{pu}}{f'_c} + \frac{d}{d_p}(\omega - \omega')\right]\right)
$$

(9.13.5)

If any compression reinforcement is taken into account when calculating fps by Eq (9.13.5), the term

$$
\left[\rho_p\frac{f_{pu}}{f'_c} + \frac{d}{d_p}(\omega - \omega')\right]
$$

shall be taken not less than 0.17 and d' shall not be greater than 0.15dp.

b) For members with unbonded prestressing steel and with a span-to-depth ratio of 35 or less:

$$
f_{ps} = f_{se} + 69 + \frac{f'_c}{100\rho_p}
$$

(9.13.6)

but fps shall not be taken greater than fpy, nor (fse + 414).

c) For members with unbonded prestressing steel and with a span-to-depth ratio greater than 35:

$$
f_{ps} = f_{se} + 69 + \frac{f'_c}{300\rho_p}
$$

(9.13.7)

but fps shall not be taken greater than fpy, nor (fse + 207).

### 9.13.3

Nonprestressed reinforcement conforming to the specifications for prestressing tendons, may be considered to contribute to the tensile force and may be included in moment strength computations at a stress equal to the specified yield strength fy. Other nonprestressed reinforcement may be included in strength computations only if a strain compatibility analysis is made to determine stresses in such reinforcement.

## 9.14 Limits for Reinforcement of Flexural Members

### 9.14.1

Ratio of prestressed and nonprestressed reinforcement used for computation of flexural strength of a prestressed concrete member, except as provided in Sec 9.14.2, shall be such that $\omega_{pe}\left[\omega_p + (d/d_p)(\omega - \omega')\right]$, or $\left[\omega_{pw} + (d/d_p)(\omega_w - \omega'_w)\right]$ is not greater than 0.36β1.

### 9.14.2

When a reinforcement ratio in excess of that specified in Sec 9.14.1 is provided, design moment strength shall not exceed the moment strength based on the compression portion of the moment couple.

The following equations may be used to calculate design moment strength φMn of overreinforced members.

1. For rectangular sections, or flanged sections in which the neutral axis lies within the flange, the design moment strength φMn may be computed by:

$$
\varphi M_n = \varphi\left[f_c bd^2(0.36\beta_1 - 0.08\beta_1^2)\right]
$$

(9.14.1)

2. For flanged sections in which the neutral axis is located outside the flange, the design moment strength φMn may be computed by:

$$
\varphi M_n = \varphi\left[f_c bd_p^2(0.36\beta_1 - 0.08\beta_1^2) + 0.85f'_c h_f(b - b_w)(d_p - 0.5h_f)\right]
$$

(9.14.2)

### 9.14.3

Total amount of prestressed and nonprestressed 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 $f_r = 0.62\sqrt{f'_c}$ except for flexural members with shear and flexural strength at least twice that required by the combination of loads specified in Sec 2.7.

## 9.15 Minimum Bonded Reinforcement

### 9.15.1

A minimum area of bonded reinforcement shall be provided in all flexural members, as required by Sec 9.15.2 and 9.15.3.

### 9.15.2

Except as provided in Sec 9.15.3, minimum area of bonded reinforcement shall be calculated by

$$
A_s = 0.004A
$$

(9.15.1)

This bonded reinforcement shall be uniformly distributed over precompressed tensile zone as close as practicable to extreme tension fibre.

### 9.15.3

For two-way flat plates, defined as solid slabs of uniform thickness, minimum area and distribution of bonded reinforcement shall be as specified in Sec 9.15.3.1 through 9.15.3.3 below.

#### 9.15.3.1

Bonded reinforcement shall not be required in positive moment areas where computed tensile stress in concrete at service load (after allowance for all prestress losses) does not exceed $0.17\sqrt{f'_c}$.

#### 9.15.3.2

In positive moment areas where calculated stress in concrete at service load exceeds $0.17\sqrt{f'_c}$, minimum area of bonded reinforcement shall be computed by

$$
A_s = \frac{2N_u}{f_y}
$$

(9.15.2)

in which the design yield strength fy shall not exceed 410 N/mm². Bonded reinforcement shall be uniformly distributed over precompressed tensile zone as close as practicable to extreme tension fibre.

#### 9.15.3.3

In negative moment areas at column supports, minimum area of bonded reinforcement in each direction shall be computed by

$$
A_s = 0.00075 \ell t
$$

(9.15.3)

where ℓ is the length of span in direction parallel to that of the reinforcement being determined. Bonded reinforcement required by Eq (9.15.3) shall be distributed within a slab width 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.

### 9.15.4 Minimum Length of Bonded Reinforcement

Minimum length of bonded reinforcement required by Sec 9.15.2 and 9.15.3 shall be as specified in Sec 9.15.4.1 through 9.15.4.3 below.

#### 9.15.4.1

In positive moment areas, minimum length of bonded reinforcement shall be one-third the clear span length and centred in positive moment area.

#### 9.15.4.2

In negative moment areas, bonded reinforcement shall extend one-sixth the clear span on each side of the support.

#### 9.15.4.3

Where bonded reinforcement is provided for design moment strength in accordance with Sec 9.13.3 or for tensile stress conditions in accordance with Sec 9.15.3.2, minimum length shall also conform to Sec 8.2.

## 9.16 Transmission Lengths in Pretensioned Members

Transmission length, $\ell_t$, of bonded prestressing steel in pretensioned members shall be calculated by using the following equation:

$$
\ell_t = \frac{K_t d_b}{\sqrt{f'_c}}
$$

(9.16.1)

where Kt is a coefficient for the type of prestressing steel and is selected from the following:

| Type of Steel                                             | Kt  |
| :-------------------------------------------------------- | :-- |
| Plain or indented wire                                    | 650 |
| Crimped wire with total wave height not less than 0.15 db | 440 |
| 7-wire drawn strand                                       | 390 |
| 7-wire standard or super strand                           | 260 |

## 9.17 Spacing Limits of Prestressing Steel and Ducts

### 9.17.1

Clear distance between pretensioning steel at each end of a member shall not be less than 4db for wire, nor 3dp for strands. Closer vertical spacing and bundling of steel may be allowed in the middle portion of the span.

### 9.17.2

Post-tensioning ducts may be bundled if concrete can be satisfactorily placed and if adequate measure is taken to prevent the steel, when tensioned, from breaking through the duct.

### 9.17.3

The minimum clear spacing between individual tendons or post-tensioning ducts shall not be less than 1.33 times the maximum nominal size of aggregates.

## 9.18 Concrete Protection for Reinforcement

### 9.18.1

Concrete cover for nonprestressed reinforcement shall be in accordance with Sec 8.1.8.

### 9.18.2

Concrete cover for prestressed tendon shall not be less than that for nonprestressed reinforcement.

## 9.19 Shear Strength

### 9.19.1 Design of Cross-sections Subjected to Shear

Design of cross-sections subjected to shear shall be based on

$$
V_u \leq \phi V_n
$$

(9.19.1)

where Vu is the factored shear force at section considered and Vn is the nominal shear strength calculated by

$$
V_n = V_c + V_s
$$

(9.19.2)

In the above, $V_c$ is nominal shear strength provided by concrete in accordance with Sec 9.19.2 and $V_s$ is nominal shear strength provided by shear reinforcement in accordance with Sec 9.19.3.

#### 9.19.1.1

In determining shear strength Vn, effect of any openings in members shall be taken into consideration.

#### 9.19.1.2

In determining shear strength Vc, effects of axial tension due to creep and shrinkage in restrained members shall be considered and effects of inclined flexural compression in members with variable depth may be included.

#### 9.19.1.3

The values of fc' shall not exceed 65 N/mm² except as permitted below:

Values of fc' greater than 65 N/mm² shall be permitted in computing Vcd, Vcd and Vcw for prestressed concrete beams having minimum web reinforcement equal to $f'_c/35$ times, but not more than 3 times the amounts required by Sec 9.19.3 (c), (d) or (e).

#### 9.19.1.4

Sections located less than a distance h/2 from face of support may be designed for the same shear Vn as that computed at a distance h/2 when both of the following conditions are satisfied:

a) Support reaction, in the direction of applied shear, introduces compression into end regions of member, and

b) No concentrated load occurs between face of support and location of the section.

### 9.19.2 Shear Strength Provided by Concrete

#### 9.19.2.1

Unless more detailed calculation is made in accordance with Sec 9.19.2.2, shear strength Vc provided by concrete of a member having effective prestress force not less than 40 per cent of the tensile strength of flexural reinforcement, may be calculated by using Eq (9.19.3).

$$
V_c = \left(0.05\sqrt{f'_c} + 4.8\frac{V_ud}{M_u}\right)b_w d
$$

(9.19.3)

but Vc need not be taken less than $0.17\sqrt{f'_c}b_w d$ nor greater than $0.42\sqrt{f'_c}b_w d$, nor the value given in Sec 9.19.2.3 or 9.19.2.4. The quantity Vud/Mu shall not be taken greater than 1.0, where Mu is factored moment occurring simultaneously with Vu at the section considered. When applying Eq (9.19.3), d in the term Vud/Mu shall be the distance from extreme compression fibre to centroid of prestressed reinforcement.

#### 9.19.2.2

Shear strength Vc may be calculated in accordance with (a) and (b) below where Vc shall be the lesser of Vcd or Vcw.

a) Shear strength Vcd shall be computed by

$$
V_{cd} = 0.05\sqrt{f'_c}b_w d + V_d + \frac{V_l M_{cr}}{M_{max}}
$$

(9.19.4)

but Vcd need not be taken less than $0.14\sqrt{f'_c}b_w d$, where

$$
M_{cr} = (I/y_t)(0.5\sqrt{f'_c} + f_{pe} - f_d)
$$

(9.19.5)

and values of Mmax and Vl shall be computed from the load combination causing the maximum moment to occur at the section. For Class 3 members moment of inertia shall be calculated for cracked section.

b) Shear strength Vcw shall be computed by

$$
V_{cw} = (0.29\sqrt{f'_c} + 0.3f_{pe})b_w d + V_p
$$

(9.19.6)

Alternatively, Vcw may be computed as the shear force corresponding to dead load plus live load that results in a principal tensile stress of $0.33\sqrt{f'_c}$ at centroidal axis of member, or at the intersection of flange and web when centroidal axis is in the flange. In composite members, principal tensile stress shall be computed using the cross-section that resists live load.

c) In Eq (9.19.4) and (9.19.6), d shall be the distance from extreme compression fibre to centroid of prestressed reinforcement or 0.8h, whichever is greater.

#### 9.19.2.3

In a pretensioned member in which the section at a distance h/2 from face of support is closer to end of member than the transmission length of the prestressing steel, the reduced prestress shall be considered when computing Vcc. This value of Vcw shall also be taken as the maximum limit for Eq (9.19.3). Prestresses force may be assumed to vary linearly from zero at end of tendon to maximum at a distance equal to the transmission length.

#### 9.19.2.4

In a pretensioned member where bonding of some prestressing steel tendons does not extend to end of member, a reduced prestress shall be considered when computing Vc in accordance with Sec 9.19.2.1 or 9.19.2.2. Value of Vcw calculated using the reduced prestress shall also be taken as the maximum limit for Eq (9.19.3). The prestress force due to bonded steel tendons for which bonding does not extend to the end of member, shall be assumed to vary linearly from zero at the point at which bonding commences to a maximum at a distance from this point equal to the transmission length.

### 9.19.3 Shear Strength Provided by Shear Reinforcement

#### 9.19.3.1

Types of Shear Reinforcement: Shear reinforcement may consist of

a) stirrups perpendicular to axis of member,

b) welded wire fabric with wires located perpendicular to axis of member.

#### 9.19.3.2

Design yield strength of shear reinforcement shall not exceed 410 N/mm².

#### 9.19.3.3

Stirrups and other bars or wires used as shear reinforcement shall extend to a distance d from extreme compression fibre and shall be anchored at both ends according to development of web reinforcement, as specified in Sec 8.2, to develop the design yield strength of reinforcement.

#### 9.19.3.4 Spacing Limits of Shear Reinforcement

a) Spacing of shear reinforcement placed perpendicular to axis of member shall not exceed 0.75h nor 600 mm.

b) When Vu exceeds $0.33\sqrt{f'_c}b_w d$, maximum spacing given above shall be reduced by one-half.

#### 9.19.3.5 Minimum Shear Reinforcement

a) A minimum area of shear reinforcement shall be provided in all prestressed concrete flexural members where factored shear force Vus exceeds one-half the shear strength provided by concrete φVcs, except slab and beams with total depth not greater than 250 mm.

b) Minimum shear reinforcement requirements of (a) above may be waived if shown by tests that the required nominal flexural and shear strengths can be developed when shear reinforcement is omitted.

c) Where shear reinforcement is required by (a) above or by analysis, and where factored torsional moment Tus does not exceed $\phi(0.04\sqrt{f'_c}\sum x^2y)$, minimum area of shear reinforcement for prestressed members, except as provided in (d) below, shall be computed by

$$
A_v = 0.35\frac{b_w s}{f_y}
$$

(9.19.7)

d) For members with an effective prestress force not less than 40 per cent of the tensile strength of the flexural reinforcement, the area of shear reinforcement shall not be less than the smaller Aw as obtained by Eq (9.19.7) and the following:

$$
A_v = \frac{A_{ps}f_{ps}}{80f_y d}\sqrt{\frac{d}{b_w}}
$$

(9.19.8)

e) Where factored torsional moment Tus exceeds $\phi(0.04\sqrt{f'_c}\sum x^2 y)$ and where web reinforcement is required by (a) above or by analysis, minimum area of closed stirrups shall be computed by

$$
A_v + 2A_t = 0.35\frac{b_w s}{f_y}
$$

(9.19.9)

#### 9.19.3.6 Design of Shear Reinforcement

a) Where factored shear force Vus exceeds shear strength φVcs, shear reinforcement shall be provided to satisfy Eq (9.19.1) and (9.19.2), where shear strength Vs shall be computed in accordance with (b) and (c) below.

b) When shear reinforcement perpendicular to axis of member is used,

$$
V_s = \frac{A_v f_y d}{s}
$$

(9.19.10)

where Av is the area of shear reinforcement within a distance s.

c) Shear strength Vs shall not be taken greater than $0.67\sqrt{f'_c}b_w d$.

## 9.20 Compression Members - Combined Flexure and Axial Loads

### 9.20.1

Prestressed concrete members subjected to combined flexure and axial load, with or without nonprestressed reinforcement, shall be proportioned by the strength design methods of this Code for members without prestressing. Effects of prestress, creep, shrinkage, and temperature change shall be included.

### 9.20.2 Limits for Reinforcement of Prestressed Compression Members

#### 9.20.2.1

Members with average prestress fpc less than 1.55 N/mm² shall have minimum reinforcement in accordance with Sec 6.3.6 for columns and Sec 6.9.7 for walls.

#### 9.20.2.2

Except for walls, members with average prestress fpc equal to or greater than 1.55 N/mm² shall have all prestressing steel enclosed by spirals or lateral ties in accordance with the following:

a) Spirals shall conform to spirals for columns in Sec 6.3.6.4 and 6.3.6.5

b) Lateral ties shall be at least 10 mm dia in size or welded wire fabric of equivalent area, and spaced vertically not to exceed 48 tie bar or wire diameters, or least dimension of compression member.

c) Ties shall be located vertically not more than half a tie spacing above top of footing or slab in any storey, and shall be spaced as provided herein to not more than half a tie spacing below lowest horizontal reinforcement in members supported above.

d) Where beams or brackets frame into all sides of a column, ties may be terminated not more than 75 mm below lowest reinforcement in such beams or brackets.

#### 9.20.2.3

For walls with average prestress fpc equal to or greater than 1.55 N/mm², minimum reinforcement required by Sec 6.9.7 shall not apply where structural analysis shows adequate strength and stability.

## 9.21 Frames and Continuous Structures

### 9.21.1

Performance at service load conditions of frames and continuous structures of prestressed concrete shall be determined by elastic analysis, considering reactions, moments, shears, and axial forces produced by prestressing, creep, shrinkage, temperature change, axial deformation, restraint of attached structural elements, and foundation settlement. All the elements shall be designed for satisfactory performance at service load conditions and for adequate strength.

### 9.21.2

Moments to be used to calculate required strength shall be the sum of the moments due to reaction induced by prestressing (with a load factor of 1.0) and the moments due to factored loads including redistribution as permitted in Sec 9.21.3 below.

### 9.21.3

Redistribution of negative moments due to gravity loads in continuous prestressed flexural members shall be in accordance with the following:

a) Where bonded reinforcement is provided at supports in accordance with Sec 9.15.2, negative moments calculated by elastic theory for any assumed loading arrangement may be increased or decreased by not more than

$$
20\left[1 - \frac{\omega_p + (d/d_p)(\omega - \omega')}{0.36\beta_1}\right] \text{ per cent}
$$

b) The modified negative moments shall be used to calculate moments at sections within spans for the same loading arrangement.

c) Redistribution of negative moments shall be made only when the section at which moment is reduced is so designed that $\omega_{p}, [\omega_p + (d/d_p)(\omega - \omega')]$, or $[\omega_{pw} + (d/d_p)(\omega_w - \omega'_w)]$, whichever is applicable, is not greater than 0.24β1.

## 9.22 Slab System

### 9.22.1

Factored moments and shears in prestressed slab systems reinforced for flexure in more than one direction shall be determined in accordance with the provisions of Sec 6.4.6 or by more detailed design procedures.

### 9.22.2

Moment strength of prestressed slabs at every section shall be at least equal to that required for a reinforced concrete structure and that required considering Sec 9.21.2 and 9.21.3.

Shear strength of two-way prestressed slabs at columns shall be at least equal to that required in Sec 6.4.7, except as follows:

For slabs without shear reinforcement, Vc may be computed by Eq (9.22.1) provided the conditions (a), (b) and (c) below are satisfied, otherwise the provisions of Sec 6.4.7.2 shall apply.

a) No portion of the column cross-section shall be closer to a discontinuous edge than 4 times the slab thickness,

b) $f'_c$ in Eq (9.22.1) shall not be taken greater than 35 N/mm²,

c) $f_{pc}$ in each direction shall not be less than 0.86 N/mm², nor greater than 3.45 N/mm².

$$
V_c = (0.083\beta_p\sqrt{f'_c} + 0.3f_{pc})b_o d + V_p
$$

(9.22.1)

where βp is the smaller of 3.5 and (2αs d/bo + 1.5),

* αs shall have the values given in Sec 6.4.7.2,
* bo shall be taken in accordance with Sec 6.4.7.1(b),
* $\bar{f'_c}$ is the average value of fpc for the two directions,
* $V_p$ is the vertical component of all effective prestress forces crossing the critical section.

### 9.22.3

At service load conditions, all serviceability limitations, including specified limits on deflections, shall be met, with appropriate consideration of the factors listed in Sec 9.21.1.

### 9.22.4

For normal live loads and loads uniformly distributed, spacing of prestressing tendons or groups of tendons in one direction shall not exceed 8 times the slab thickness, nor 1.5 m. Spacing of tendons shall also provide a minimum average prestress (after allowance for all prestress losses) of 0.85 N/mm² on the slab section tributary to the tendon or tendon group. A minimum of two tendons shall be provided in each direction through the critical shear section over columns. Special consideration of tendon spacing shall be provided for slabs with concentrated loads.

### 9.22.5

In slabs with unbonded prestressing steel, bonded reinforcement shall be provided in accordance with Sec 9.15.3 and 9.15.4.

## 9.23 Tendon Anchorage Zones

### 9.23.1

End blocks shall be provided in post-tensioned members for support bearing or for distribution of prestressing forces. These shall be at least as wide as the narrow flange of the beam and shall have a length at least equal to three-fourths of the depth of the beam and in any case not less than 600 mm. Transition between end block and normal section of the beam shall have a slope not steeper than 2.5:1.

### 9.23.2

Reinforcement shall be provided in tendon anchorage zones to resist bursting, splitting, and spalling forces induced by tendon anchorage. Regions of abrupt change in section shall be adequately reinforced. In post-tensioned members a closely spaced grid of both vertical and horizontal bars shall be placed near the face of the end block to resist bursting or other forces. Amount of steel in the end grid should follow recommendations of the supplier of the anchorage or specialist literature. Where such recommendations are not available the grid shall consist of at least 12 mm dia bars on 100 mm centres in each direction placed not more than 40 mm from the inside face of anchor bearing plate. Closely spaced reinforcement shall also be placed both vertically and horizontally throughout the length of end block in accordance with accepted methods of end block stress analysis.

### 9.23.3

Post-tensioning anchorages and supporting concrete shall be designed to resist the maximum jacking force for the strength of concrete at time of prestressing.

### 9.23.4

Post-tensioning anchorage zones shall be designed to develop the guaranteed ultimate tensile strength of prestressing steel using a strength reduction factor φ of 0.90 for concrete.

### 9.23.5

In end zones of pretensioned beams, vertical stirrups acting at a unit stress of 138 N/mm² to resist at least 4 per cent of the total prestressing force shall be placed within the distance d/4 at the end of the beam; the end stirrups shall be as close to the end of the beam as practicable. For at least the distance d from the end of the beam, nominal reinforcement shall be placed to enclose the prestressing steel in the bottom flange.

## 9.24 Corrosion Protection for Unbonded Prestressing Tendons

### 9.24.1

Unbonded prestressing tendons shall be completely coated with suitable material to ensure corrosion protection.

### 9.24.2

Tendon covering shall be continuous over the entire unbonded length and shall prevent intrusion of cement paste or loss of coating materials during concrete placement.

## 9.25 Post-Tensioning Ducts

### 9.25.1

Ducts for grouted or unbonded tendons shall be mortar-tight and nonreactive with concrete, tendons, or filler material.

### 9.25.2

Ducts for grouted single wire, strand, or bar tendons shall have an inside diameter at least 6 mm larger than tendon diameter.

### 9.25.3

Ducts for grouted multiple wire, strand, or bar tendons shall have an inside cross-sectional area at least two times the area of the tendons.

## 9.26 Grout for Bonded Prestressing Tendons

### 9.26.1

Grout shall consist of ordinary Portland cement and water for diameter of duct less than 150 mm or Portland cement, sand, and water for diameter of duct larger than 150 mm.

### 9.26.2

Materials for grout shall conform to Sec 9.26.2.1 through 9.26.2.3 below.

#### 9.26.2.1

Portland cement and water shall conform to Sec 2.4.3 and 2.4.4 of Part 5.

#### 9.26.2.2

Sand shall conform to standard specification for aggregates as provided in Sec 2.4.2 of Part 5. Gradation of sand shall be as required to obtain satisfactory workability.

#### 9.26.2.3

Admixtures conforming to the specification provided in Sec 2.4.5 of Part 5 and known to have no injurious effects on grout, steel, or concrete shall be permitted. Calcium chloride, nitrates and sulphates shall not be used.

### 9.26.3 Selection of Grout Proportions

#### 9.26.3.1

Proportions of materials for grout shall be based on either of the following:

a) Results of tests on fresh and hardened grout prior to beginning of grouting operations, or

b) Prior documented experience with similar materials and equipment and under comparable field conditions.

#### 9.26.3.2

Cement used in the work shall correspond to that on which selection of grout proportions was based.

#### 9.26.3.3

Water content shall be the minimum necessary for proper pumping of grout; however, water cement ratio shall not exceed 0.45 by weight.

#### 9.26.3.4

Water shall not be added to increase grout flowability that has been decreased by delayed use of grout.

#### 9.26.3.5

The grout shall not bleed in excess of 2 per cent after 3 hours.

#### 9.26.3.6

The minimum compressive strength of grout shall be: $f'_c$ = 25 N/mm².

### 9.26.4 Mixing and Pumping of Grout

#### 9.26.4.1

Grout shall be mixed in equipment capable of continuous mechanical mixing and agitation that will produce uniform distribution of materials, passed through screens of 1.0 mm nominal aperture size and pumped in a manner that will completely fill tendon ducts. The grout injector shall be capable of continuous operation with a constant pressure of 0.7 N/mm².

#### 9.26.4.2

Temperature of members at time of grouting shall be above 2°C and shall be maintained above 2°C until field cured 50 mm cubes of grout reach a minimum compressive strength of 5.5 N/mm². Grout temperatures shall not be above 32°C during mixing and pumping.

#### 9.26.4.3

The pressure gauge shall be recently calibrated prior to use in grouting.

### 9.26.5 Grouting Procedure

Specialist literature e.g. Guide for Freyssinet Methods or equivalent shall be used for grouting procedure of ducts.

## 9.27 Protection of Prestressing Tendons

Burning or welding operations in the vicinity of prestressing tendons shall be carefully performed, so that tendons are not subjected to excessive temperatures, welding sparks, or ground currents.

## 9.28 Application and Measurement of Prestressing Force

### 9.28.1

Prestressing force shall be determined by both of the following methods:

a) Measurement of tendon elongation. Required elongation shall be determined from average load elongation curves for the prestressing tendons used.

b) Observation of jacking force on a calibrated gauge or load cell or by use of a calibrated dynamometer.

Causes of any difference in force determination between (a) and (b) above, that exceeds 5 per cent for pretensioned members or 7 per cent for post-tensioned construction, shall be ascertained and corrected.

### 9.28.2

Where transfer of force from bulkhead of pretensioning bed to concrete is accomplished by flame cutting, prestressing tendons, cutting points and cutting sequence shall be predetermined to avoid undesired temporary stresses.

## 9.29 Post-Tensioning Anchorage and Couplers

### 9.29.1

Anchorages and couplers for bonded and unbonded prestressing tendons shall develop at least 95 per cent of the specified breaking strength of the tendons, when tested in an unbonded condition, without exceeding anticipated set. For bonded tendons, anchorages and couplers shall be located so that 100 per cent of the specified breaking strength of the tendons shall be developed at critical sections after tendons are bonded in the member.

### 9.29.2

Couplers shall be placed in areas approved by the engineer and enclosed in housing long enough to permit necessary movements.

### 9.29.3

In unbonded construction subject to repetitive loads, special attention shall be given to the possibility of fatigue in anchorages and couplers.

### 9.29.4

Anchorages, couplers, and end fittings shall be permanently protected against corrosion.

## 9.30 Demountable Precast Prestressed Construction

In building structures which are likely to be shifted to other locations during their life time, provisions of demountability may be introduced. The connections must be moment resisting against stresses due to environmental effects besides other stresses.

## 9.31 Cold Drawn Low Carbon Wire Prestressed Concrete (CWPC)

Cold drawn low carbon wire conforming to ASTM A615 or equivalent may be permitted for prestressing provided the mechanical requirements shown in Table 6.9.2 are satisfied.

**Table 6.9.2: Tensile Strength and Elongation of Cold Drawn Wire**

| Dia of Wire (mm) | Minimum Tensile Strength (N/mm²) | Minimum Elongation, per cent |
| :--------------- | :------------------------------- | :--------------------------- |
| 3                | 650                              | 2.0                          |
| 4                | 600                              | 2.5                          |
| 5                | 550                              | 3.0                          |

### Related Appendix

**Appendix A:** Conversion of Expressions from SI to FPS Units