Lecture Lecture 5 5 Losses of Losses of Prestress Prestress - - PDF document

SLIDE 1

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The Hashem ite University Departm ent of Civil Engineering

Lecture Lecture 5 5 – – Losses of Losses of Prestress Prestress

Dr Hazim Dwairi Dr Hazim Dwairi

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• Dr. Hazim Dwairi
• Dr. Hazim Dwairi

Types of Losses Types of Losses

• Initial PS force undergoes force loss over

Initial PS force undergoes force loss over i d f i t l i d f i t l 5 a period of approximately a period of approximately 5 5 years years

Losses of PS Immediate Time-dependent

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• Elastic shortening
• Anchorage losses
• Friction losses
• Concrete Creep
• Concrete Shrinkage
• Steel Relaxation

SLIDE 2

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Types of Losses Types of Losses

Losses of PS Concrete Steel

• Elastic shortening
• Creep
• Relaxation

F i ti

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• Creep
• Shrinkage
• Friction
• Anchorage set

General Notes General Notes

• Early failures in PS structures were due to the

Early failures in PS structures were due to the inaccuracy in predicting losses over time inaccuracy in predicting losses over time inaccuracy in predicting losses over time. inaccuracy in predicting losses over time.

• Losses of PS force may be grouped into:

Losses of PS force may be grouped into:

– Immediate during construction

Immediate during construction

– Time

Time-

• dependent over an extended period of time

dependent over an extended period of time

• The jacking force

The jacking force P Pj

j (largest force applied to a

(largest force applied to a tendon) is immediately reduced due to friction tendon) is immediately reduced due to friction

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tendon) is immediately reduced due to friction, tendon) is immediately reduced due to friction, anchorage and elastic shortening to initial force anchorage and elastic shortening to initial force Pi

i

SLIDE 3

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General Notes General Notes

• As time passes by, the force reduces gradually,

As time passes by, the force reduces gradually, rapidly at first but then more slowly due to rapidly at first but then more slowly due to rapidly at first but then more slowly, due to rapidly at first but then more slowly, due to creep, shrinkage and relaxation. creep, shrinkage and relaxation.

• After many years, the force stabilizes to what is

After many years, the force stabilizes to what is known as effective force known as effective force P Pe.

• For

For pretensioning pretensioning, , P Pj

j never acts on the concrete,

never acts on the concrete, but only on the anchorage of the casting bed but only on the anchorage of the casting bed

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but only on the anchorage of the casting bed, but only on the anchorage of the casting bed,

• For post

For post-

• tensioning,

tensioning, P Pj

j is fully applied to the

is fully applied to the concrete only at the ends. concrete only at the ends.

General Notes General Notes

• An exact determination of the PS losses is not

An exact determination of the PS losses is not feasible all the time sometimes it is reasonable feasible all the time sometimes it is reasonable feasible all the time, sometimes it is reasonable feasible all the time, sometimes it is reasonable to lump to lump-

• sum loss estimates.

sum loss estimates.

• Exact losses affect service load behavior such

Exact losses affect service load behavior such as deflection and crack width. as deflection and crack width.

• Overestimation of losses leads to high PS force

Overestimation of losses leads to high PS force causing excessive camber and tensile stresses causing excessive camber and tensile stresses

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causing excessive camber and tensile stresses. causing excessive camber and tensile stresses.

• Underestimation of losses leads to little PS

Underestimation of losses leads to little PS force, thus not using the system to its full force, thus not using the system to its full capacity. capacity.

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Lum p Lum p-

• sum Estim ate of Losses

sum Estim ate of Losses

• First introduced in the ACI code of

First introduced in the ACI code of 1963

• 1963. The

. The current ACI code doesn’t have lump current ACI code doesn’t have lump sum sum current ACI code doesn t have lump current ACI code doesn t have lump-sum sum

• estimates. However AASHTO and Post
• estimates. However AASHTO and Post-
• tensioning institute (PTI) suggest lump

tensioning institute (PTI) suggest lump-

• sums.

sums.

Type of Steel Total Losses f’c =27.6 MPa Total losses f’c =34.5 MPa Pretensioned Strand 310 MPa AASHTO Lump-sum losses *

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Pretensioned Strand

• 310 MPa

Post-tensioned wire or strand 221 MPa 228 MPa Bars 152 MPa 159 MPa * Losses due to friction are excluded, it should be computed according to sec. 6.5 of AASHTO and added.

Lum p Lum p-

• sum Estim ate of Losses

sum Estim ate of Losses

Type of Steel Total Losses (Slabs) Total losses F(Beams and joists) PTI Lump-sum losses for post-tensioning

• These losses are applied to only routine,

These losses are applied to only routine, standard conditions of loading normal concrete standard conditions of loading normal concrete

(S abs) ( ea s a d jo sts) Stress relieved 270-K strands and stress relieved 240-K wire 207 MPa 241 MPa Low relaxation 270-K strands 103 MPa 138 MPa Bars 138 MPa 172 MPa

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standard conditions of loading, normal concrete, standard conditions of loading, normal concrete, quality control, construction procedure and quality control, construction procedure and normal environmental conditions. normal environmental conditions.

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Type of PS Losses Type of PS Losses

Type Stage Stress Loss Pre Post (ti, tj) Total Elastic shortening At transfer At seq ential Δf Elastic shortening (ES) At transfer At sequential jacking

• ΔfpES

Relaxation (R) Before and after transfer After transfer ΔfpR(ti, tj) ΔfpR Creep (CR) After transfer After transfer ΔfpCR(ti, tj) ΔfpCR Shrinkage (SH) After After stransfer Δf SH(ti tj) Δf SH

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Shrinkage (SH) After transfer After stransfer ΔfpSH(ti, tj) ΔfpSH Friction (F)

• At jacking
• ΔfpF

Anchorage Set (A)

• At transfer
• ΔfpA

Total Life Life ΔfpT(ti, tj) ΔfpT

Total Losses Total Losses

• Pretensioned

Pretensioned Members: Members:

Δf

Δf Δf Δf Δf

ΔfpT

pT =

= ΔfpES

pES+ ΔfpR pR+ ΔfpCR pCR+ ΔfpSH pSH

ΔfpR

pR= ΔfpR pR(t

to

• ,t

,ttr

tr)+

)+ΔfpR

pR(t

ttr

tr,t

,ts) to = time at jacking (usually zero) = time at jacking (usually zero) ttr

tr = time at transfer (usually

= time at transfer (usually 18 18 hours) hours) ts = time at stabilized loss (usually = time at stabilized loss (usually 5 5 years) years)

• Th

Th

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• Thus,

Thus, fpi

pi =

= f fpJ

pJ - ΔfpR pR(t

to,t ,ttr

tr)

) -

• ΔfpES

pES Elastic Shortening Relaxation Jacking stress

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Total Losses Total Losses

• Post

Post-

• tensioned Members:

tensioned Members:

Δf

Δf Δf Δf Δf Δf Δf

ΔfpT

pT =

= ΔfpA

pA+ ΔfpF pF+ ΔfpES pES+ ΔfpR pR+ ΔfpCR pCR+ ΔfpSH pSH

ΔfpR

pR= ΔfpR pR(t

ttr

tr,t

,ts

s)

ΔfpES

pES is applied only when tendons are jacked

is applied only when tendons are jacked sequentially and not simultaneously. sequentially and not simultaneously.

• Thus,

Thus, f f Δf Δf

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fpi

pi =

= fpJ

pJ - ΔfpA pA - ΔfpF pF Tendon Friction Anchorage set Jacking stress

(1 1) Elastic Shortening (ES) ) Elastic Shortening (ES)

• As concrete is compressed, it shortens the PS steel due

As concrete is compressed, it shortens the PS steel due to assumed perfect bond. to assumed perfect bond.

• In post

In post-

• tensioned beams with single tendon, there is no

tensioned beams with single tendon, there is no need to calculate ES since it is compensated by jacking. need to calculate ES since it is compensated by jacking. (same for several tendons jacked simultaneously. (same for several tendons jacked simultaneously.

• Pretensioned

Pretensioned Beams: Beams:

Pi Pi

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ΔES

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= = Δ

c c i c c i ES

A E P A E L P ε : tendon eccentric

• f

case general For the level steel at the concrete in the stress = = Δ ∴ = = = = Δ

cs cs pES cs c i c c i s ES s pES

f nf f nf A nP A E P E E f ε

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moment weight

• Self

. 1

2 2

= + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − =

D c D c i cs

M I e M r e A P f

• Post

Post-

• tensioned Beams:

tensioned Beams:

Δ1 Δ2 Δ3 1 3 2

• Jacking

Jacking 1 1st

st tendon

tendon Δ1 No loss No loss

• Jacking

Jacking 2 2nd

nd tendon

tendon Δ2 loss in loss in 1 1st

st tendon

tendon

• Jacking

Jacking 3 3rd

rd tendon

tendon Δ3 loss in loss in 1 1st

st and

and 2 2nd

nd tendon and

tendon and no loss in no loss in 3 3rd

rd tendon

tendon

Therefore, the

Therefore, the 1 1st

st tendon suffers the maximum amount of

tendon suffers the maximum amount of l l

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losses. losses.

Average f N e I e P A P n f

pES N J j j c j j i c j i J pES

= Δ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = Δ

∑

− = + + +

tendons;

• f

number . . ) (

1 ) 1 ( ) 1 ( ) 1 (

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(2 2) Steel Relaxation (R) ) Steel Relaxation (R)

• Prestressing

Prestressing tendons undergo relaxation under constant tendons undergo relaxation under constant length, depending on steel stress and time interval. The length, depending on steel stress and time interval. The l it d d d th d ti f th t i d l it d d d th d ti f th t i d loss magnitude depends on the duration of the sustained loss magnitude depends on the duration of the sustained PS force, and ratio of PS force, and ratio of f fpi

pi/f

fpy

py

⎧ f 94 : jacking tendon to due stress For (a) : to tendons in the stress tensile the limits 05

• ACI318

The

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⎪ ⎩ ⎪ ⎨ ⎧ = tion recommenda r manufature f f

• f

smaller f

pu py pJ

8 . 94 .

pu py pi

f f

• f

smaller f anchorage at the members tensioned

• post

In (c) 74 . 82 . : sfer after tran y Immediatel (b) ⎩ ⎨ ⎧ =

pu pi

f f 70 . : sfer after tran couplers, and anchorage at the members, tensioned post In (c) =

• For stress

For stress-

• relieved strands:

relieved strands:

⎞ ⎛ ⎞ ⎛ f

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hours in is t' ' 55 . 10 log ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = Δ

py pi pi pR

f f t f f

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• For low

For low-

• relaxation strands:

relaxation strands:

hours in is t' ' 55 . 45 log ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = Δ

py pi pi pR

f f t f f hours in is t

• For step

For step-

• by

by-

• step losses:

step losses:

⎞ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = Δ 55 . 10 log log

1 2 py pi pi pR

f f t t f f

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⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = Δ 55 . 45 log log

1 2 py pi pi pR

f f t t f f

• ACI

ACI-

• ASCE method of accounting for relaxation:

ASCE method of accounting for relaxation:

( ) [ ] C

f f f J K f

pSH pCR pES re pR

× + + Δ − = Δ

Table Table 3 3. .4 4 C values C values

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(3 3) Creep Loss (CR) ) Creep Loss (CR)

• The continuous deformation of concrete over extended

The continuous deformation of concrete over extended periods of time & sustained loads is know as creep. periods of time & sustained loads is know as creep.

• The rate of strains increase rapidly at first, but decreases

The rate of strains increase rapidly at first, but decreases with time until a constant value is reached with time until a constant value is reached

• Creep strains depend on the applied sustained load, mix

Creep strains depend on the applied sustained load, mix ratio, curing conditions, environmental conditions, and ratio, curing conditions, environmental conditions, and the age of concrete when first loaded. the age of concrete when first loaded.

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strain elastic strain creep : t coefficien creep Ultimate = =

EL CR u

C ε ε

• Typical values of the C

Typical values of the Cu ranges between ranges between 2 2 and and 4 4. . recommended value if no information is available is recommended value if no information is available is 2 2 35 35

u t

C t t C

6 . 6 .

10 : t' ' at time t coefficien Creep + =

recommended value if no information is available is recommended value if no information is available is 2 2.35 35

• Prestress loss due to creep at time ‘t’ after

Prestress loss due to creep at time ‘t’ after prestressing prestressing for bonded members is: for bonded members is:

at the concrete in stress the is where

cs cs c ps t pCR

f f E E C f = Δ

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tendon. PS the

• f

centroid the

• f

level

cs

f

• In post

In post-

• tensioned unbonded members, the loss is

tensioned unbonded members, the loss is essentially uniform along the whole span. An average essentially uniform along the whole span. An average values of values of f fcs

cs between the anchorage points can be used.

between the anchorage points can be used.

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( )

members ed pretension for . 2 : is loss creep for expession ASCE

• ACI

The = − = Δ

CR csd cs c ps CR pCR

K f f E E K f

• nly.

load dead ed superimpos all to due steel

• f

level at concret in stress sfer after tran steel

• f

level at concrete in stress members tensioned

• post

for 1.6 ≡ ≡ =

csd cs

f f

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members tensioned

• post

for 1.28 members ed pretension for 6 . 1 concrete t lightweigh for 20% by reduced be should : Note = =

CR CR

K K

(4 4) Shrinkage Loss (SH) ) Shrinkage Loss (SH)

• The free water normal concrete mixes evaporates with

The free water normal concrete mixes evaporates with time, the rate depending on humidity, temperature, and time, the rate depending on humidity, temperature, and i d h f b i d h f b size and shape of members. size and shape of members.

• Drying is accompanied by reduction in volume, the

Drying is accompanied by reduction in volume, the change occurring at higher rate initially. Approximately change occurring at higher rate initially. Approximately 80 80% of shrinkage occur in the first year. % of shrinkage occur in the first year.

• The ACI

The ACI-

• ASCE committee recommends ultimate

ASCE committee recommends ultimate shrinkage strain of ( shrinkage strain of (εSH

SH)u =

= 780 780 x x 10 10-6

6

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• The PCI stipulates a values of (

The PCI stipulates a values of (εSH

SH)u =

= 820 820 x x 10 10-6

6

days 3 to 1 after curing steam ; ) ( 55 ) ( days 7 after curing moist ; ) ( 35 ) (

u SH t SH u SH t SH

t t t t ε ε ε ε + = + =

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• For

For pretensioned pretensioned members: members: ΔfpSH

pSH =

= εSH

SH x

x E Eps

ps

Where, Where, εSH

SH is adjusted for humidity and V/S ratio

is adjusted for humidity and V/S ratio

• For

For pretensioned pretensioned members transfer commonly takes members transfer commonly takes For For pretensioned pretensioned members, transfer commonly takes members, transfer commonly takes place after place after 24 24 hours after casting, and nearly all hours after casting, and nearly all shrinkage takes place after that. shrinkage takes place after that.

• For post

For post-

• tensioned members, stressing may take place

tensioned members, stressing may take place after one day or much later, thus, a large percentage of after one day or much later, thus, a large percentage of shrinkage may already have taken place by then. shrinkage may already have taken place by then.

• ACI corrects shrinkage strain for environmental

ACI corrects shrinkage strain for environmental

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• ACI corrects shrinkage strain for environmental

ACI corrects shrinkage strain for environmental conditions by: conditions by: εSH

SH =

= 780 780 x x 10 10-6

6 x

x γSH

SH

γSH

SH is tabulated in ACI committee report R

is tabulated in ACI committee report R435 435-

• 95

95

( )

Humidity Relative RH : Where 100 0024 . 1 10 2 . 8 : is loss shrinkage for expression PCI

6

≡ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − × =

−

RH S V K Δf

SH pSH

days in PS

• f

n applicatio to curing moist

• f

end the from time to relating factor K mm in ratio surface to volume S V

SH ≡

=

Post-tensioned

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Days 1 3 5 7 10 20 30 60 KSH 0.92 0.85 0.80 0.77 0.73 0.64 0.58 0.45 Pretensioned KSH = 1.0

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(5 5) Friction Losses (F) ) Friction Losses (F)

• For post

For post-

• tensioned members, the tendons are

tensioned members, the tendons are usually anchored at one end & jacked from the usually anchored at one end & jacked from the y j y j

• ther. As the steel slides in the duct during
• ther. As the steel slides in the duct during

jacking, friction losses take place making the jacking, friction losses take place making the tension at the anchored end loss than at the tension at the anchored end loss than at the jacking end. jacking end.

• The total friction is the sum of:

The total friction is the sum of:

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– Curvature friction due to imposed curvature.

Curvature friction due to imposed curvature.

– Wobble friction, due to unintentional misalignment,

Wobble friction, due to unintentional misalignment, even in straight tendons. even in straight tendons.

(5 5) Friction Losses (F) ) Friction Losses (F)

s Tendon Jacking Stres

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Distance along tendon T

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(a) Curvature Effect (a) Curvature Effect

α

F1

L

F1 F2=F1

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1

F2=F1-dF1

dα

dF1 F1 F1dα

d dF dα μF dF α μ μ − = − =

∫ ∫

1 1 1

then effect, curvature to due duct the & ndon between te friction

• f

t coefficien the denotes if F e F F F F d F

μα

μα α μ = = − − =

∫ ∫

2 1 2 1 1

ln ln

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R L

e F e F F R L if F e F F

μ μα μα

α μα

− − −

= = = − = =

1 1 2 1 1 2

/ ; ln

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: similarly then effect, wobble to due concrete g surroundin the & ndon between te friction

• f

t coefficien the denotes K if

(b) Wobble Effect (b) Wobble Effect

( )

: is loss friction the Thus : effects both ing Superimpos : similarly

1 2 1 2 1 2

= = =

− − − − − μα μα

e f f

• r

e F F e F F

KL KL KL

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( )

( )

radians in x 8y try trigonome From 1

1 1 2 1

= − − ≈ − = − = Δ

− −

α μα

μα

kL f e f f f F f

kL p

Tendons Central Angle Tendons Central Angle

x α/2 α/2 y m x/2

1 2 2 2 tan x m x m = = α

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radians in 8 4 2 & 2 1 x y Then x y m y if = = ≈ α α

SLIDE 16

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Wobble and Curvature Wobble and Curvature Coefficients Coefficients

Type of tendon K (1/m) μ T d i fl ibl t l h ti Tendons in flexible metal sheeting 1- wire tendons 0.0033 – 0.0049 0.15 – 0.25 2- 7-wire strands 0.0016 – 0.0066 0.15 – 0.25 3- High-strength bars 0.0003 – 0.0020 0.08 – 0.30 Tendons in rigid metal ducts (7- wire strands) 0.0007 0.15 – 0.25 Mastic-coated tendons (wire 0.0033 – 0.0066 0.05 – 0.15

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( tendons and 7-wire strands) Pre-greased tendons (wire tendons and 7-wire strands) 0.001 - 0.0066 0.05 – 0.15

(6 6) Anchorage Slip or Seating ) Anchorage Slip or Seating Loss (A) Loss (A)

• In post

In post-

• tensioned members, a small amount of

tensioned members, a small amount of force is lost at the anchorage upon transfer, as force is lost at the anchorage upon transfer, as force is lost at the anchorage upon transfer, as force is lost at the anchorage upon transfer, as the wedges seat themselves on the tendons, or the wedges seat themselves on the tendons, or as the hardware deform. This magnitude ranges as the hardware deform. This magnitude ranges between between 6 6. .35 35mm & mm & 9 9. .53 53mm for the two piece mm for the two piece wedges. wedges.

• Similarly, in

Similarly, in pretensioned pretensioned, losses may occur due , losses may occur due

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y, y, p p , y , y to slippage at the permanent casting to slippage at the permanent casting anchorages, the loss may be compensated by anchorages, the loss may be compensated by the overstressing. the overstressing.

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(6 6) Anchorage Slip or Seating ) Anchorage Slip or Seating Loss (A) Loss (A)

Δ Δ

A E

f length tendon L slip

• f

magnitude : ≡ ≡ Δ = Δ

A ps A pA

Where E L f

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• Dr. Hazim Dwairi

The Hashemite University The Hashemite University

tendon ng prestressi

• f

modulus Eps ≡

Pretensioned Members Elastic Shortening Loss Post-tensioned Members Friction Loss Creep Loss Shrinkage Loss Relaxation Loss Anchorage Slip Loss Elastic Shortening Loss Creep Loss

Prestressed Prestressed Concrete Concrete

• Dr. Hazim Dwairi
• Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Shrinkage Loss Relaxation Loss