Loss of Prestress

SECTION 4

LOSS OF PRESTRESS

EMPHASIS ON ITEMS SPECIFIC TO POST-TENSIONED SYSTEMS

DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEELEAD AUTHOR: BRIAN SWARTZ

LOSS OF PRESTRESS Friction Elastic shortening Anchor set Shrinkage Creep Relaxation

Initial losses Specific to post-tensioning

Time dependent losses (Long term losses)Similar to pre-tensioning

STRESSING OF PT STRANDS

The stressing jack bears against the concrete Concrete is compressed gradually as the

strand is tensioned Many things occur simultaneously

• Stressing, friction, elastic shortening

FRICTION LOSSESFriction between strand and duct

Live End (Jacking) Force

Dead End (Restraint) Force

Dead End Force < Live End Force

Strand

Duct

Idealized Reality

“Wobble” and “Curvature Effects”

Duct/Strand Cross-Section

DuctStrand

FRICTION LOSSES Monitor elongation in addition to

pressure during stressing

Overcoming friction: Over-tensioning (limited) Stressing from both ends

FRICTION LOSSES Calculating losses

Function of:• Curvature friction coefficient• Angular change over length of strand• Wobble friction coefficient• Length from jack to point of interest

Reference:• Post-Tensioning Manual, Appendix A

ELASTIC SHORTENING LOSSES

fpy

Strain

Stre

ss

fjack

fpu

Elastic Response of Concrete To Compression

Elastic Response of Concrete To Load

“Elastic Shortening Loss”

Jacking (Exact Magnitude Affected by Friction)

Effective Stress after Jacking/Elastic Shortening

For Post-Tensioning, All Occur Simultaneously

ELASTIC SHORTENING LOSSES Shortening of concrete compressed during

stressing as the two occur simultaneously If only one strand (tendon) – no ES losses If multiple strands (tendons)

Tendons stressed early in the sequence will suffer losses as subsequent tendons are stressed

The first strand stressed will suffer the most total loss

The last strand stressed has zero loss Reasonable to take the average of first and

last

ELASTIC SHORTENING LOSSESΔ 𝑓 𝑝𝐸𝑆=𝐸𝑝𝜖𝑝

Strain in strandSteel elastic modulus

Hooke’s Law

Change in strand stress due to elastic shortening loss

Assume: Perfect bond between steel and concrete 𝜖𝑝=𝜖𝑐

Strain in the concrete, due to compressive stress applied:

𝜖𝑐=𝑓 𝑐𝑔𝑝𝐸𝑐𝑖

Concrete stress at prestressing centroidConcrete elastic modulus at time of stressing

Δ 𝑓 𝑝𝐸𝑆=𝑁−12𝑁 ( 𝐸𝑝

𝐸𝑐𝑖) 𝑓 𝑐𝑔𝑝

Substitution through previous steps

Average of first and last strand that experience loss; the last strand tensioned has zero loss, hence the (N-1) term.

ANCHORAGE DEVICESSTANDARD ANCHORSENCAPSULATED

ANCHOR

WEDGES

ENCAPSULATEDANCHOR

Source: PTI

ANCHORAGE DEVICES: WEDGE

Source: PTI

HOW ARE STRANDS ANCHORED?

Concrete

Duct

Strand

Anchor cast in concrete

ANCHORAGE SEATING LOSS

fpy

Strain

Stre

ss

fjack

fpu

Elastic Shortening

Anchor Seating

Effective Stress after Anchor Seating

Jacking

Anchorage Seating Loss

ANCHORAGE SEATING LOSS

Calculating losses Some of the imposed strain on the

strand is lost when the wedge seats in the plate

• Function of:– Hardware used– Type of stressing jack (Power seating, etc.)

Reference: Post-Tensioning Manual, Appendix A

FRICTION AND ANCHORAGE LOSSES

Jack

ing

Stre

ss1

Jacking1

Forc

e in

Ten

don

Jack

ing

Stre

ss1

Jacking1

Forc

e in

Ten

don


Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Release Jack [Transfer force to

anchor]

Forc

e in

Ten

don

Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1


anchor]

Forc

e in

Ten

don


Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Jack

ing

Stre

ss2

Increased PT due to jacking2

Effect of live end jacking2

Jacking2

Forc

e in

Ten

don

Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Jack

ing

Stre

ss2



Jacking2

Forc

e in

Ten

don


Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Jack

ing

Stre

ss2

Anc

. Sea

ting

Loss

2



Forc

e in

Ten

don


anchor]

Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Jack

ing

Stre

ss2

Anc

. Sea

ting

Loss

2



Forc

e in

Ten

don


anchor]


Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Jack

ing

Stre

ss2

Anc

. Sea

ting

Loss

2



Jacking1 Jacking2

Forc

e in

Ten

don

Jack

ing

Stre

ss1

Anc

. Sea

ting

Loss

1

Jack

ing

Stre

ss2

Anc

. Sea

ting

Loss

2



Jacking1 Jacking2

Forc

e in

Ten

don


The variable prestress force in the previous slide is negligible for: Strands less than 100 feet (single-end

stressed) Strands less than 200 feet (both ends

stressed)

Reference: Bondy, K.B., “Variable Prestress Force in Unbonded Post-Tensioned Members,” Concrete International, January 1992, pp. 27-33.

SHRINKAGE, CREEP, AND RELAXATION

fpy

Strain

Stre

ss

fjack

fpu

Elastic Shortening

Concrete Shrinkage and Creep

Effective Stress for Service

Jacking

Anchor Seating

Time Dependent Losses Due to Concrete Shrinkage and Creep[Relaxation also considered in this stage]

CONCRETE SHRINKAGE

Moisture

L L’ LLL

LL

sh

'

CONCRETE SHRINKAGE

Time

Con

cret

e Sh

rinka

ge S

train

(εsh

)

Linetype Key:Model BaselineEffect of Decreasing f’cEffect of Decreasing HEffect of Decreasing V/S

Ultimate Shrinkage (Baseline Condition)

Start of drying

CONCRETE CREEPL L 1’

Shrinkage Specimen

L

Creep Specimen

L 2’

P

ε1ε2

Concrete shortening due to sustained compression

CONCRETE CREEPSpecimen 2

Specimen 1

Cas

t C

oncr

ete

End

Cur

ing

(Sta

rt D

ryin

g)

App

ly

Load

Stra

in

Time

Shrinkage

Elastic

Creep

CONCRETE CREEP

Time, t

Con

cret

e St

rain

(S

um o

f Ela

stic

and

Cre

ep R

espo

nse)

Instantaneous application of stress, fc

Elastic Strain

c

cel E

f

Creep Strain

c

cicr Eftt,

tiLinetype Key:

Model BaselineEffect of Decreasing f’c

Effect of Decreasing HEffect of Decreasing V/S

Effect of the same applied stress, fc, at a later time

Total Strain

ic

ctotal tt

Ef ,1

Creep strain is calculated by a creep coefficient, , that expresses creep strain as a function of elastic strain.

STEEL RELAXATION A loss of stress in the steel after being

held at a constant elongation (sustained tension)

For low-relaxation steel (industry standard) relaxation losses are very small compared to other loss components (~1-3 ksi)

Loss of Prestress

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