Chapter 18General Design Requirements

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 927

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18.1 General

The general design requirements for design of prestressed concrete structures shall be as per 17 to 23 of Subsection 5A(C) of Part 6 ‘Structural Design, Section 5 Concrete, Subsection 5A Plain and Reinforced Concrete’ of the Code except as modified and supplemented in 18.2 to 18.6.5.

18.2 Effects of Prestress

The effects of prestress shall also be taken into account in assessing loads and forces.

18.3Deductions for Prestressing Tendons

The deductions for prestressing tendons as in 18.3.1 shall be considered for the determination of area, centroid and moment of inertia of the cross-section.

18.3.1 In calculating area, centroid and moment of inertia of a cross-section, deduction (or addition in case of transformed area of tendons) for prestressing tendons shall be made as follows:

a) In the case of pre-tensioned members, where the prestressing tendons are single wires distributed on the cross-section or strands of wires of relatively small cross-sectional area, allowance for the prestressing tendons need not be made. Where allowance is made, it shall be on the basis of (m-1) times the area of the

prestressing tendons, $m$ being the modular ratio.

b) In the case of post-tensioned members, deductions shall invariably be made for prestressing tendons, cable ducts or sheaths and such other openings whether they are formed longitudinally or transversally. These deductions need not, however, be made for determining the effect of loads applied after the ducts, sheaths or openings have been grouted or filled with concrete. Where such deductions are not made, a transformed area equivalent to $(m-1)$ times the area of the prestressing tendon shall be taken in calculation, m being the modular ratio.

NOTE — m shall be calculated as $E_{s}/E_{c}$ ; for values of $E_{s}$ and $E_{c}$ , see 4.6.1.2.1 and 5.2.3.1, respectively. Wherever necessary, creep effects shall also be taken into consideration.

c) In case of multi-directional prestressing, loss of area due to presence of ungrouted ducts/sheaths placed at an angle to the prestressing tendons under consideration may be made at full area (100 percent) of such ducts. In case, such ducts placed at an angle have been grouted prior to stressing of tendons 50 percent of area of such ducts can be considered as effectively available.

18.4Instability During Erection

In evaluating the slenderness effects during lifting of slender members following factors require consideration:

a) Member geometry,

b) Location of lifting points,

c) Method of lifting, and

d) 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 due to inaccuracies in location of lifting points, and due to the lateral bow.

For calculating the factor of safety against lateral instability $(\gamma_{\mathrm{j}})$ references may be made to specialist literature; the factor shall not be less than two.

For determining the lateral moment due to tilting, realistic values which are not likely to be exceeded in practice shall be assumed for the eccentricity of lifting points and the lateral bow. The maximum tensile stress for $\gamma_{i}/(\gamma_{i}-1)$ times the lateral moment due to tilting shall not exceed $1.5\ N/mm^{2}$ .

18.5Prestressing Requirements

18.5.1 Maximum Initial Prestress

At the time of initial tensioning, the maximum tensile

stress, $f_{\mathrm{pi}}$ immediately behind the anchorages shall not exceed 76 percent of the ultimate tensile strength, $f_{\mathrm{pu}}$ of the wire or bar or strand.

18.5.2 Losses in Prestress

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 from creep of concrete, shrinkage of concrete, relaxation of steel, the shortening (elastic deformation) of concrete at transfer, and friction and slip of anchorage. Unless otherwise determined by actual tests, allowance for these losses shall be made in accordance with the values specified under 18.5.2.1 to 18.5.2.6.

18.5.2.1 Loss of prestress due to creep of concrete

The loss of prestress due to creep of concrete under load shall be determined for all the permanently applied loads including the prestress.

The creep loss due to live load stresses, erection stresses and other stresses of short duration may be ignored. The loss of prestress due to creep of concrete is 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 line of centre of gravity of the prestressing tendon at the section at which creep loss is being calculated for bonded tendons. In case of unbonded tendons, the creep loss is a product of modulus of elasticity of prestressing steel and creep strain calculated by integrating and averaging creep stress along the line of centre of gravity between the anchorage points.

The total creep strain during any specific period shall be assumed for all practical purposes, to be the creep strain due to sustained stress equal to the average of the stresses at the beginning and end of the period.

18.5.2.2 Loss of prestress due to shrinkage of concrete

The loss of prestress due to shrinkage of concrete shall be the product of the modulus of elasticity of prestressing steel and the shrinkage strain of concrete calculated as per 5.2.4.

18.5.2.3 Loss of prestress due to relaxation of steel

The relaxation losses in prestressing steels vary with type of steel, initial prestress, age, and temperature and, therefore, shall be determined from experiments. When experimental values are not available, the relaxation losses may be assumed as given in Table 6.

For long term relaxation losses, the values of relaxation losses given in Table 6 may be multiplied by 3.

For periods less than 1 000 h the value of relaxation loss (expressed as percent of 1 000 h value) shall be as shown below:

Time, h		1	5	20	100	200	500	1 000
Percent of Relaxation Loss at 1 000 h	for Normal Relaxation Steel	34	44	55	70	78	90	100
Percent of Relaxation Loss at 1 000 h	for Low Relaxation Steel	37	47	57	72	79	90	100

For tendons at higher temperatures or subjected to large lateral loads, greater relaxation losses as specified by the engineer-in-charge 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 time prior to the anchoring of the tendon.

Table 6Relaxation Losses for Prestressing Steel at 1 000 h at 20 ± 2 °C (Clause 18.5.2.3)

Sl No.	Initial Stress	Relaxation Loss Percent
Sl No.	Initial Stress	Normal Relaxation (3)	Low Relaxation (4)
i)	$0.5f_p$	0	0
ii)	$0.6f_p$	3.0	1.0
iii)	$0.7f_p$	5.0	2.5
iv)	$0.8f_p$	8.0	4.5

NOTE — $f_{p}$ is the characteristic strength of prestressing steel.

18.5.2.4 Loss of prestress due to elastic shortening of concrete

This type of loss occurs when the prestressing tendons upon release from tensioning devices cause the concrete to be compressed. This loss is proportional to the modular ratio and initial stress in the concrete and shall be calculated as below, assuming that the tendons are located at their centroid:

a) 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 should 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.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5B PRESTRESSED CONCRETE

18.5.2.5 Loss of prestress due to slip in anchorage

Any loss of prestress which may occur due to slip of wires during anchoring or due to the strain of anchorage shall be allowed for in the design.

18.5.2.6 Loss of prestress due to friction

The design shall take into consideration all losses in prestress that may occur during tensioning due to friction between the prestressing tendons and the surrounding concrete or any fixture attached to the steel or concrete.

For straight or moderately curved structures, with curved or straight cables, the value of prestressing force $P_{\mathrm{x}}$ at a distance $x$ metre from tensioning end and acting in the direction of the tangent to the curve of the cable, shall be calculated as below:

P _ {\mathrm{x}} = P _ {0} e ^ {- (\mu \alpha + k x)}

where

$P_{0} =$ prestressing force in the prestressed steel at the tensioning end acting in the direction of the tangent to the force of the cable;

$\alpha =$ cumulative angle through which the tangent to the cable profile has turned between any two points under consideration, in radians;

$\mu =$ coefficient of friction in curve; and

k = coefficient for wobble effect.

The value of $\mu$ and $k$ given below may be adopted for calculating the friction losses:

Type of High Tensile Steel(1)	Type of Duct or Sheath(2)	Values Recommended to be Used in Design
Type of High Tensile Steel(1)	Type of Duct or Sheath(2)	k per metre(3)	μ(4)
Wire cables	Bright metals	0.009 1	0.25
	Galvanized	0.004 6	0.20
	Lead coated	0.004 6	0.18
Uncoated stress relieved strand	Bright metals	0.004 6	0.25
	Galvanized	0.003 0	0.20
	Lead coated	0.003 0	0.18
	Corrugated HDPE	0.002 0	0.17