NBC 2016 (SP 7:2016) Volume 1
2016 · PDF page 927
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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.
The effects of prestress shall also be taken into account in assessing loads and forces.
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, 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 times the area of the prestressing tendon shall be taken in calculation, m being the modular ratio.
NOTE — m shall be calculated as ; for values of and , 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.
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 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 times the lateral moment due to tilting shall not exceed .
At the time of initial tensioning, the maximum tensile
stress, immediately behind the anchorages shall not exceed 76 percent of the ultimate tensile strength, of the wire or bar or strand.
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.
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.
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.
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 |
| 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.
| Sl No. | Initial Stress | Relaxation Loss Percent | |
| Normal Relaxation (3) | Low Relaxation (4) | ||
| i) | |||
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.
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 at a distance metre from tensioning end and acting in the direction of the tangent to the curve of the cable, shall be calculated as below:
The considerations affecting the transmission length shall be as follows:
a) The transmission length depends on a number of variables, the most important being the strength of concrete at transfer, the size and
type of tendon, the surface deformations of the tendon. The transmission length of the tendon towards the top of a unit is usually greater than that at the bottom.
The following values may be used, provided the concrete is well-compacted and detailing is as per the relevant provisions of this Section, and its strength at transfer is not less than and the tendon is released gradually:
For plain and indented wire :
For crimped wires : 65φ
Strands :
c) The development of stress in the tendon may be assumed to vary linearly along the length of the member.
NOTES
1 is the diameter of the tendon.
2 The transmission length may vary depending on the site conditions and therefore should be determined from tests carried out under the most unfavourable conditions.
a) On the areas immediately behind external anchorages, the permissible unit bearing stress on the concrete, after accounting for losses due to elastic shortening and seating of anchorages, shall not exceed,
18.6.3.1 The detailing of reinforcement in prestressed concrete shall generally conform to the requirements given in relevant clauses of Part 6 ‘Structural Design, Section 5 Concrete, Subsection 5A Plain and Reinforced Concrete’ of the Code. In addition, the requirements of 18.6.3.2 and 18.6.3.3 shall be satisfied.
a) The amount and spacing of transverse reinforcement shall be governed by shear and torsion considerations. It is, however, desirable to provide transverse reinforcement in the web when the web is thin and cables are located in the web.
b) In the case of all members subjected to dynamic loading, webs shall be provided with transverse reinforcement, not less than 0.3 percent of the sectional area of the web in plan. This percentage of reinforcement may be reduced to 0.2 percent in members where the depth of the web is not more than four times the thickness of the web. These values may be reduced to 0.2 and 0.15 percent, respectively when high strength reinforcement is used.
c) In case of members not subjected to dynamic loading, reinforcement shall be provided when the depth of the web is more than 4 times the thickness. Such reinforcement shall not be less than 0.1 percent of the sectional area of the web in plan. The reinforcement shall be spaced
PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5B PRESTRESSED CONCRETE
at a distance not greater than the clear depth of the web and the size of such reinforcement shall be as small as possible.
d) Reinforcement in the form of links or helix shall be provided perpendicular to the line of heavy compression or shock loading to resist the induced tensile stresses.
a) A minimum longitudinal reinforcement of 0.2 percent of the total concrete area shall be provided in all cases except in the case of pretensioned units of small sections. This reinforcement may be reduced to 0.15 percent in the case of high yield strength deformed reinforcement. The percentage of steel provided, both tensioned and untensioned taken together, should be sufficient so that when the concrete in the precompressed tensile zone cracks, the steel is in a position to take up the additional tensile stress transferred on to it by the cracking of the adjacent fibres of concrete and a sudden failure is avoided.
b) When the depth of the web exceeds 500 mm, longitudinal distribution reinforcement not less than 0.05 percent of the area of the web shall be provided on each face. The spacing of the individual bars of such reinforcement shall not exceed 200 mm.
c) All untensioned longitudinal reinforcement shall be restrained in the lateral direction.
In the design of continuous prestressed concrete structures, due consideration shall be given to the effects of the support restraints on both the external moment and the moment due to prestressing.
Where a butted assembly is used, or where like conditions of abuttal are employed, proper provision shall be made to transfer all shear stresses. Wherever the shear stresses exceed the limits specified under 22.4, this provision shall include keying of all abutting faces.
| 0 |
| 0 |
| ii) | 3.0 | 1.0 |
| iii) | 5.0 | 2.5 |
| iv) | 8.0 | 4.5 |
NOTE — 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
b)
where
prestressing force in the prestressed steel at the tensioning end acting in the direction of the tangent to the force of the cable;
cumulative angle through which the tangent to the cable profile has turned between any two points under consideration, in radians;
coefficient of friction in curve; and
k = coefficient for wobble effect.
The value of and 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 | |
| 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 | |
or , whichever is smaller, where is the cube strength at transfer, is the bearing area and is the punching area.
During tensioning, the allowable bearing stress specified in (a) may be increased by 25 percent, provided that this temporary value does not exceed .
c) The effective punching area shall generally be the contact area of the anchorage devices which, if circular in shape, shall be replaced by a square of equivalent area. The bearing area shall be the maximum area of that portion of the member which is geometrically similar and concentric to the effective punching area.
d) Where a number of anchorages are used, the bearing area shall not overlap. Where there is already a compressive stress prevailing over the bearing area, as in the case of anchorage placed in the body of a structure, the total stress shall not exceed the limiting values specified in (a), (b) and (e). For stage stressing of cables, the adjacent unstressed anchorages shall be neglected when determining the bearing area.
e) The bearing stress specified in (a) and (b) for permanent and temporary bearing stress may be increased suitably if adequate hoop reinforcement complying with manufacturer's recommendations is provided at the anchorages.
f) When the anchorages are embedded in concrete, the bearing stress shall be investigated after accounting for the surface friction between the anchorage and the concrete. The reinforcement details, concrete strength, cover and other dimensions shall conform to manufacturer's specification/specialist literature.
a) The bursting tensile forces in the end blocks, or regions of bonded post-tensioned members, should be assessed on the basis of the tendon jacking load. For unbonded members, the bursting tensile forces should be assessed on the basis of the tendon jacking load or the load in the tendon at the limit state of collapse, whichever is greater (see Annex C).
The bursting tensile force, existing in an individual square end block loaded by a symmetrically placed square anchorage or bearing plate, may be derived from the equation below:
where
b) The force will be distributed in a region extending from to from the loaded face of the end block. Reinforcement provided to sustain the bursting tensile force may be assumed to be acting at its design strength (0.87 times characteristic strength of reinforcement) except that the stress should be limited to a value corresponding to a strain of 0.001 when the concrete cover to the reinforcement is less than .
c) In rectangular end blocks, the bursting tensile forces in the two principal directions should be assessed on the basis of 18.6.2.2. When circular anchorage or bearing plates are used, the side of the equivalent square area should be used. Where groups of anchorages or
bearing plates occur, the end blocks should be divided into a series of symmetrically loaded prisms and each prism treated in the above manner. For designing end blocks having a cross section different in shape from that of the general cross section of the beam, reference should be made to specialist literature.
d) Compliance with the requirements of (a), (b) and (c) will generally ensure that bursting tensile forces along the load axis are provided for. Alternative methods of design which make allowance for the tensile strength of the concrete may be used, in which case reference should be made to specialist literature.
e) Consideration should also be given to the spalling tensile stresses that occur in end blocks where the anchorage or bearing plates are highly eccentric; these reach a maximum at the loaded face.