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6 — Loss of prestress

6 — Loss of prestress

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(c) Creep of concrete;

ation of initial stress level (0.7fpu or higher), type of steel

(stress-relieved or low-relaxation wire, strand, or bar), exposure

conditions, and type of construction (pretensioned, bonded

post-tensioned, or unbonded post-tensioned).

(d) Shrinkage of concrete;

(e) Relaxation of prestressing steel stress;

(f) Friction loss due to intended or unintended

curvature in post-tensioning tendons.

18.6.2 — Friction loss in post-tensioning tendons

R18.6.2 — Friction loss in post-tensioning tendons — Ppx , force in post-tensioning tendons a

distance lpx from the jacking end shall be computed by

The coefficients tabulated in Table R18.6.2 give a range that

generally can be expected. Due to the many types of

prestressing steel ducts and sheathing available, these values

can only serve as a guide. Where rigid conduit is used, the

wobble coefficient K can be considered as zero. For largediameter prestressing steel in semirigid type conduit, the

wobble factor can also be considered zero. Values of the

coefficients to be used for the particular types of

prestressing steel and particular types of ducts should be

obtained from the manufacturers of the tendons. An unrealistically low evaluation of the friction loss can lead to

improper camber of the member and inadequate prestress.

Overestimation of the friction may result in extra

prestressing force. This could lead to excessive camber and

excessive shortening of a member. If the friction factors are

determined to be less than those assumed in the design, the

tendon stressing should be adjusted to give only that

prestressing force in the critical portions of the structure

required by the design.

– ( Kl px + μ p α px )


Where (Klpx + μpαpx) is not greater than 0.3, Ppx shall

be permitted to be computed by

Ppx = Ppj (1 + Klpx + μpαpx)–1

(18-2) — Friction loss shall be based on experimentally determined wobble K and curvature μp friction

coefficients, and shall be verified during tendon

stressing operations.



IN EQ. (18-1) OR (18-2)



Unbonded tendons

Grouted tendons in

metal sheathing



coefficient, K per coefficient, μp per




Ppx = Ppj e


Actual losses, greater or smaller than the computed values,

have little effect on the design strength of the member, but

affect service load behavior (deflections, camber, cracking

load) and connections. At service loads, overestimation of

prestress losses can be almost as detrimental as underestimation, since the former can result in excessive camber and

horizontal movement.

Wire tendons



High-strength bars



7-wire strand



Wire tendons



7-wire strand



Wire tendons



7-wire strand



ACI 318 Building Code and Commentary




COMMENTARY — Values of K and μp used in design shall

be shown on design drawings.

R18.6.2.3 — When the safety or serviceability of the

structure may be involved, the acceptable range of

prestressing steel jacking forces or other limiting requirements

should either be given or approved by the licensed design

professional in conformance with the permissible stresses of

18.4 and 18.5.

18.6.3 — Where loss of prestress in a member occurs

due to connection of the member to adjoining

construction, such loss of prestress shall be allowed

for in design.

18.7 — Flexural strength

R18.7 — Flexural strength

18.7.1 — Design moment strength of flexural

members shall be computed by the strength design

methods of the Code. For prestressing steel, fps shall

be substituted for fy in strength computations.

R18.7.1 — Design moment strength of prestressed flexural

members may be computed using strength equations similar

to those for nonprestressed concrete members. The 1983

Code provided strength equations for rectangular and

flanged sections, with tension reinforcement only and with

tension and compression reinforcement. When part of the

prestressing steel is in the compression zone, a method

based on applicable conditions of equilibrium and compatibility of strains at a factored load condition should be used.

For other cross sections, the design moment strength φMn is

computed by an analysis based on stress and strain

compatibility, using the stress-strain properties of the

prestressing steel and the assumptions given in 10.2.

18.7.2 — As an alternative to a more accurate

determination of fps based on strain compatibility, the

following approximate values of fps shall be permitted

to be used if fse is not less than 0.5fpu .

(a) For members with bonded tendons

f pu d


- ρ p -------- + ------ ( ω – ω′ )

fps = fpu ⎪⎨ 1 – ----fc ′ dp



where ω is ρfy /fc′ , ω′ is ρ′fy /fc′ , and γp is 0.55 for

fpy /fpu not less than 0.80; 0.40 for fpy /fpu not less

than 0.85; and 0.28 for fpy /fpu not less than 0.90.

If any compression reinforcement is taken into

account when calculating fps by Eq. (18-3), the term

f pu d

- + ------ ( ω – ω′ )

ρ p ------fc ′ dp

shall be taken not less than 0.17 and d ′ shall be no

greater than 0.15dp .

R18.7.2 — Equation (18-3) may underestimate the strength

of beams with high percentages of reinforcement and, for

more accurate evaluations of their strength, the strain

compatibility and equilibrium method should be used. Use

of Eq. (18-3) is appropriate when all of the prestressed

reinforcement is in the tension zone. When part of the

prestressed reinforcement is in the compression zone, a

strain compatibility and equilibrium method should be used.

By inclusion of the ω′ term, Eq. (18-3) reflects the increased

value of fps obtained when compression reinforcement is

provided in a beam with a large reinforcement index. When

the term [ρp (fpu /fc′ ) + (d/dp)(ω – ω′)] in Eq. (18-3) is small,

the neutral axis depth is small, the compressive reinforcement does not develop its yield strength, and Eq. (18-3)

becomes unconservative. This is the reason why the term

[ρp (fpu /fc′ ) + (d/dp)(ω – ω′)] in Eq. (18-3) may not be taken

less than 0.17 if compression reinforcement is taken into

account when computing fps. If the compression reinforcement is neglected when using Eq. (18-3), ω′ is taken as zero,

then the term [ρp(fpu /fc′ ) + (d/dp)ω] may be less than 0.17

and an increased and correct value of fps is obtained.

When d′ is large, the strain in compression reinforcement

can be considerably less than its yield strain. In such a case,

the compression reinforcement does not influence fps as

ACI 318 Building Code and Commentary






(b) For members with unbonded tendons and with a

span-to-depth ratio of 35 or less:

f c′

f ps = f se + 70 + ---------------100ρ p


but fps in Eq. (18-4) shall not be taken greater than

the lesser of fpy and (fse + 420).

(c) For members with unbonded tendons and with a

span-to-depth ratio greater than 35:

f c′

f ps = f se + 70 + ---------------300ρ p


but fps in Eq. (18-5) shall not be taken greater than

the lesser of fpy and (fse + 210).

favorably as implied by Eq. (18-3). For this reason, the

applicability of Eq. (18-3) is limited to beams in which d′ is

less than or equal to 0.15dp.

The term [ρp (fpu /fc′ ) + (d/dp)(ω _ ω′)] in Eq. (18-3) may

also be written [ρp (fpu /fc′ ) + As fy /(bdp fc′) _ As′fy /(bdp fc′)].

This form may be more convenient, such as when there is no

unprestressed tension reinforcement.

Equation (18-5) reflects results of tests on members with

unbonded tendons and span-to-depth ratios greater than 35

(one-way slabs, flat plates, and flat slabs).18.10 These tests also

indicate that Eq. (18-4), formerly used for all span-depth ratios,

overestimates the amount of stress increase in such members.

Although these same tests indicate that the moment strength of

those shallow members designed using Eq. (18-4) meets the

factored load strength requirements, this reflects the effect of

the Code requirements for minimum bonded reinforcement, as

well as the limitation on concrete tensile stress that often

controls the amount of prestressing force provided.

18.7.3 — Nonprestressed reinforcement conforming to

3.5.3, 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 fy . Other nonprestressed reinforcement

shall be permitted to be included in strength computations only if a strain compatibility analysis is performed

to determine stresses in such reinforcement.


18.8 — Limits for reinforcement of flexural


R18.8 — Limits for reinforcement of flexural


18.8.1 — Prestressed concrete sections shall be

classified as either tension-controlled, transition, or

compression-controlled sections, in accordance with

10.3.3 and 10.3.4. The appropriate strength reduction

factors, φ, from 9.3.2 shall apply.

R18.8.1 — The net tensile strain limits for compression- and

tension-controlled sections given in 10.3.3 and 10.3.4 apply

to prestressed sections. These provisions take the place of

maximum reinforcement limits used in the 1999 Code.

The net tensile strain limits for tension-controlled sections

given in 10.3.4 may also be stated in terms of ωp as defined

in the 1999 and earlier editions of the Code. The net tensile

strain limit of 0.005 corresponds to ωp = 0.32β1 for

prestressed rectangular sections.

18.8.2 — Total amount of prestressed and nonprestressed 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

fr specified in This provision shall be permitted

to be waived for flexural members with shear and

flexural strength at least twice that required by 9.2.

R18.8.2 — This provision is a precaution against abrupt flexural failure developing immediately after cracking. A flexural

member designed according to Code provisions requires

considerable additional load beyond cracking to reach its

flexural strength. Thus, considerable deflection would warn

that the member strength is approaching. If the flexural

strength were reached shortly after cracking, the warning

deflection would not occur. Transfer of force between the

concrete and the prestressing steel, and abrupt flexural failure

immediately after cracking, does not occur when the

prestressing steel is unbonded18.11; therefore, this requirement does not apply to members with unbonded tendons.

ACI 318 Building Code and Commentary





18.8.3 — Part or all of the bonded reinforcement

consisting of bars or tendons shall be provided as

close as practicable to the tension face in prestressed

flexural members. In members prestressed with

unbonded tendons, the minimum bonded reinforcement consisting of bars or tendons shall be as

required by 18.9.

R18.8.3 — Some bonded steel is required to be placed near

the tension face of prestressed flexural members. The

purpose of this bonded steel is to control cracking under full

service loads or overloads.

18.9 — Minimum bonded reinforcement

R18.9 — Minimum bonded reinforcement

18.9.1 — A minimum area of bonded reinforcement

shall be provided in all flexural members with unbonded

tendons as required by 18.9.2 and 18.9.3.

R18.9.1 — Some bonded reinforcement is required by the

Code in members prestressed with unbonded tendons to ensure

flexural performance at ultimate member strength, rather than

as a tied arch, and to limit crack width and spacing at service

load when concrete tensile stresses exceed the modulus of

rupture. Providing the minimum bonded reinforcement as

stipulated in 18.9 helps to ensure adequate performance.

Research has shown that unbonded post-tensioned members

do not inherently provide large capacity for energy dissipation

under severe earthquake loadings because the member

response is primarily elastic. For this reason, unbonded

post-tensioned structural elements reinforced in accordance

with the provisions of this section should be assumed to

carry only vertical loads and to act as horizontal diaphragms

between energy dissipating elements under earthquake loadings of the magnitude defined in 21.1.1. The minimum

bonded reinforcement areas required by Eq. (18-6) and (18-8)

are absolute minimum areas independent of grade of steel or

design yield strength.

18.9.2 — Except as provided in 18.9.3, minimum area

of bonded reinforcement shall be computed by

As = 0.004Act


where Act is area of that part of cross section between

the flexural tension face and center of gravity of gross


R18.9.2 — The minimum amount of bonded reinforcement

for members other than two-way flat slab systems is based

on research comparing the behavior of bonded and

unbonded post-tensioned beams.18.12 Based on this

research, it is advisable to apply the provisions of 18.9.2

also to one-way slab systems. — Bonded reinforcement required by Eq. (186) shall be uniformly distributed over precompressed

tensile zone as close as practicable to extreme tension

fiber. — Bonded reinforcement shall be required

regardless of service load stress conditions.

18.9.3 — For two-way flat slab systems, minimum area

and distribution of bonded reinforcement shall be as

required in,, and

R18.9.3 — The minimum amount of bonded reinforcement

in two-way flat slab systems is based on reports by Joint

ACI-ASCE Committee 423.18.6,18.11 Limited research available for two-way flat slabs with drop panels18.13 indicates

that behavior of these particular systems is similar to the

behavior of flat plates. Reference 18.11 was revised by

Committee 423 in 1983 to clarify that Section 18.9.3 applies

to two-way flat slab systems.

ACI 318 Building Code and Commentary


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