Prestress PE1

_________________________________________________________________________________Structural I PE Exam Review, FIU, Spring 2009 Luis M. Vargas, PhD, PE

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Structural I PE Exam Review

Luis M. Vargas, PhD, [email protected]

Florida International UniversityDepartment of Civil and

Environmental EngineeringMiami, FL 33174

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Prestress DesignDesignSpecifications

ACI 318-05 Building Code requirements for Structural Concrete PCI Handbook, 6th Ed., 2004

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Prestress DesignDesignPrestress conceptsMaterialPrestress lossesServiceabilityStrength designShear designComposite sections

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Prestress ConceptsConcepts

R/C crack under loads

Prestress beam before loading

Prestress beam after loading

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Prestress BenefitsBenefitsPrestress members are shallowerPrestress precast members require less maintenancePrestress permits longer spans

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Pretension/PostPretension/Post--tensiontension

Pre-tensioning: prestress is applied before member is cast. Member is cast and after f’ci is reached, PS force is released and transfer to concrete (thru bond).Post-tensioning: member is cast leaving tendon ducts, and then concrete is cast. PT is applied after member reaches f’ci .

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PrestressPrestress Types: InternalTypes: Internal

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PrestressPrestress Types: Internal Types: Internal Ft. Lauderdale ICFt. Lauderdale IC

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PrestressPrestress Type: ExternalType: External

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PrestressPrestress Type: External Type: External Long keyLong key

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TendonsTendonsBonded

Pretensioning: bonding thru concrete; in Post-tensioning: bonding thru grout

Unbonded: Generally greased and wrapped w/ paper or plastic (corrosion protection)

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P/T Anchorages P/T Anchorages

Flat anchorage

Multiplane anchorage

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Concrete PropertiesConcrete Properties

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Concrete PropertiesConcrete PropertiesModulus of Elasticity(normal wt concrete)

Ec = 57000 √ f’c

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Steel PropertiesSteel PropertiesReinforcing steel

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PrestressingPrestressing SteelSteelPrestressing Strands: 7 wires

Post-tension Bars: High tensile stress alloy, Grade 150 ksi

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PrestressingPrestressing SteelSteel

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PrestressPrestress RelaxationRelaxation

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ServiceabilityServiceabilityTransfer of prestressing

At Service

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Serviceability RequirementsServiceability Requirements

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At prestress transfer(At beam ends)

At service conditionsTotal load = DL + SDL +LL

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Stresses in PS SteelStresses in PS Steel

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Design Approach for FlexureDesign Approach for FlexureSatisfy serviceability

At transferAt service load conditionsDeflections

Satisfy strength and ductility

M M Compressive stress (-)

Tensile stress (+)

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Serviceability at transfer (Serviceability at transfer (FFoo))

)('6.0

)('3

ncompressiobottomfSM

SeF

AF

tensiontopfSM

SeF

AF

cibot

G

bot

oo

citop

G

top

oo

−≤+−−

≤−+−

'6.0

'6

cibot

oo

citop

oo

fS

eFAF

fS

eFAF

−≤−−

≤+−This can be resolved by drapping

or debonding strands @ ends

At Midspan:

At Supports:

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Service Load Conditions (F)Service Load Conditions (F)

[ ]

[ ]

)('5.7

)('6.0

)('45.0

tensionbottomfSM

SeF

AF

loadTotalPScomptopfS

MS

eFAF

loadSustainedPScomptopfS

MS

eFAF

cbot

T

bot

ctop

Total

top

ctop

Sustained

top

≤+−−

+−≤−+−

+−≤−+−

After All losses, F ≤ Fo

MT = MG + MSuperimposed

Applications: Problems 1, 2 and 3

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PrestressPrestress LossesLossesElastic shorteningConcrete shrinkageConcrete creepSteel relaxationFriction lossesAnchorage setting

Time-dependent losses

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PrestressPrestress Losses: ModelsLosses: ModelsLump-sum approaches:

ACI-ASCE Committee 423AASHTO

Time dependent:CEB-FIP (Comite Eurointernationale du Beton/Federation Internationale de la Precontrainte)

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Type of Type of PrestressPrestress LossLoss

Pretensioned Post-tensionedElastic Shortening (ES) At transfer At sequential jackingShrinkage (SH) At transfer At transferCreep (CR) At transfer At transferRelaxation (RE) Before/After transfer At transferFriction (Fr) --- At jackingAnchorage setting (As) --- At transfer

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Elastic shorteningElastic shorteningPS is transferred to concrete, member and PS steel shorten

cir

G

circir

circi

sescirs

SM

SeF

AFf

fEEKfnfES

+−−=

==Δ=

''

cs

cir

o

oes

EEnsteeloflevelateIS

steeloflevelStress

FFmembersTPFFmembersPSK

//

@

'&/,5.09.0'&,1

==

===

P/T members: jacking is against concrete; depends on jacking sequence. Ex. Tendons jacked in 2 stages. 1st stage: ½ tendons, no ES2nd stage: no ES on 2nd ½, but 1st ½ would experience ES

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Concrete ShrinkageConcrete ShrinkagePS is transferred to concrete, member and PS steel shorten

( )RHSVEKSH ssh −−×=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛− 1006.01102.8 6

Ksh = 1.0 Pretension members= Table 1 of ACI-ASCE Committee for P/T membersKsh considers that P/T members benefit from Shr, whichoccurs prior to P/T

V/S =volume/surface ratio

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Concrete CreepConcrete CreepPS is transferred to concrete, member and PS steel shorten

⎟⎠⎞⎜

⎝⎛ −= cdscir

c

scr ff

EEKCR

Kcr = 2 Pretension members= 1.6 P/T members

fcds = stress in concrete @ cgs of tendons due to all super-imposed DL after member is prestress: Ms/Scir

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Steel relaxationSteel relaxation[ ]CESCRSHJKRE re ⎟

⎠⎞⎜

⎝⎛ ++−=

Kre , J and C from Tables 2 & 3 o ACI-ASCE 423 Committee

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Friction lossesFriction lossesCurvature: change in angle

Px = Po e –µ α α = x/R

Wobble: imperfections in alignment

Px = Po e –k x

Total Px = Po e –(µ α+k x)

µ = .15~.25 rigid metal ductk = 0.0002

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Anchorage settingAnchorage setting

Review Problem: Prestress losses

Only for P/T members, due to seating of wedges in Only for P/T members, due to seating of wedges in anchors, where the jacking force is transferred to the anchors, where the jacking force is transferred to the anchorage deviceanchorage device

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PrestressPrestress Losses Losses

Applications: Problems 4 and 5

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Design Approach for Flexure Design Approach for Flexure --Strength DesignStrength Design

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Strength DesignStrength Design

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Bending StrengthBending Strength

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Bending StrengthBending Strength

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Flexural StrengthFlexural Strength

n

psn

MM

adfAM

u

pps

φ=

−= )2

( fps

fps ?

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Strength Reduction Factor, Strength Reduction Factor, φφ

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ffpsps

'c

psp

ffρω =

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MMminmin = 1.2 = 1.2 MMcrcr

( )

botpe

botperCR

botrbotCR

bot

CR

botrbot

SeF

AFf

SffM

SfeFSAFM

SM

SeF

AFff

fiberbottomtheAt

+=

+=

++=

+−−==

:

Applications: Problems 6, 7, 8 and 9

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Shear in Shear in PrestressPrestress MembersMembers

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Shear of Shear of PrestressPrestress MembersMembers

Web shear: regions w. High shear and Low moment

Capacity controlled by web cracking, Vcw

Flexural/shear cracking: High shear and high moment

Strength controlled by Vci

Vc = min (Vcw, Vci)

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Shear of Shear of PrestressPrestress MembersMembers

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Transfer LengthTransfer Length

Applications: Problems 10, 11 and 12

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Composite ConstructionComposite Construction

Shored constructionUnshored construction

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Precast section: precasting plant

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Precast section: transported & erected into final position

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Cast deck in-place: make section composite

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Prestress PE1