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PRESTRESSED CONCRETE

DESIGN GUIDE

2013 v2

Prepared by:

Prof. CLIPII Tudor, PhDNAGY-GYRGY Tams, Lecturer, PhDFLORUCodru, PhD student

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The numbering of the tables and formulas is according to SR EN 1992-1-1:2004 (EC2).

1. Initial data

- Element type

- Element length

- Support width

- Prestressing stand length

- Number of tendons

- Type of tendons

- Permanent loads (rest)

- Live loads

- Humidity

- Exposure class

- Life cycle

- Type of the technological curve

- Concrete class

- Cement type

- Steel grade- Modulus of elasticity of the tendons

- Steel class

- Relaxation losses

- Slip in anchorage

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1.1 Characteristics of the cross-section

For the element given in the project theme, the following characteristics of the section will

be computed:

Ac area of the concrete section

Ap area of the prestressed reinforcement

Ic second moment of area of concrete section

Wi the modulus of resistance for the bottom fibre;

i

ci

xIW

Ws the modulus of resistance for the top fibre;

s

c

sx

IW

In ACAD:

- create region REGION

- search the centre of gravityMASSPROP

- move the global axis in the centre of gravityUCS

- list the characteristics of the cross section MASSPROP

x

X

s

i

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2. Heat curing (Thermal treatment)

Heat curing (thermal treatment) is applied according to the following graph:

3...4 h

Pretensionare

Turnare

Transfer

Transfer la 16...22 h

10

20

30

40

50

60

70

4 h 7 h 5 h3...4 h

Ora 10 14 17 21 04 08 09

timp de relaxare (t )

Ore

C

relaxare

Hours

hour

Pre-stressing

Casting

Release

Force Transfer at

Relaxation time (trelax)

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3. Characteristics of the concrete

fck - Characteristic compressive cylinder strength of concrete at 28 days

C X/Y fck= X MPa (N/mm2)

fcm - mean value of concrete cylinder compressive strength (obtained from table 3.1 infunction of the concrete class)

fctm - mean value of axial tensile strength of concrete (obtained from table 3.1 in functionof the concrete class)

fctm(t) - The compressive strength of concrete at an age t.

In formula (3.1) and (3.2) twill be replaced with tT, computed based on the technologicalgraph using formula (B.10).

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Ecm(t) - Secant modulus of elasticity of concrete at an age t

In formula (3.5) twill be replaced with tT, computed based on the technological graph usingformula (B.10).

3.1. Calculation of the total shrinkage strain

0,, cdhcd k

kh is a coefficient depending on the notional size h0 according to Table 3.3

h0 is the notional size (mm) of the cross-section

h0 = 2Ac/u

where:

Ac is the concrete cross-sectional areau is the perimeter of that part of the cross section which is exposed to drying

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0,cd - Nominal unrestrained drying shrinkage, which may be taken from Table 3.2 or

based on formulas given below (B.11 and B.12 from Annex B)

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)(ca - phenomenon is due to water migration in concrete mass; is given by the formula

(3.12)

3.2 Computation of the creep

),( 0t - is the final creep coefficient, obtained using graphics from Figure 3.1.

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4. Characteristics of the prestressing reinforcement

The 0,1% proof stress (fp0,1k) and the specified value of the tensile strength (fpk) are definedas the characteristic value of the 0,1% proof load and the characteristic maximum load inaxial tension respectively, divided by the nominal cross sectional area. Generally, thesevalues are given by the producers. In this case:

15.11.01.0 kp

s

kppd fff

The characteristic strength of the steel (fp0,1k) is given in the theme of the project.

The relaxation of the reinforcement, given in the project theme, can be assumed:

1000=8% - for Class 11000=2.5% - for Class 2

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1000=4% - for Class 3

Ep - Design value of modulus of elasticity of prestressing steel, given in the projecttheme.

Reinforcement types and their denotations used in this project:0,6 TBP15=75 => Ap=137 mm

2

1/2 TBP12=74 => Ap=88 mm2

3/8 TBP9=73 => Ap=49 mm2

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5. Prestressing force during tensioning

5.1. Maximum stressing force

fp0.1k - characteristic 0,1% proof-stress of prestressing steel. This value is given by theproducer.

In this project, the following formula will be used:

kpkpp ffk 1.01.02max 9.0

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6. Immediate losses of prestress for pre-tensioning

6.1. Losses at the anchorage

Account should be taken of the losses due to wedge draw-in of the anchorage devices,during the operation of anchoring after tensioning, and due to the deformation of theanchorage itself. Values of the wedge draw-in are given in the European Technical

Approval.An average value used in calculation can be 4...6 mm, as given in the theme of the project.

Loss of the prestressing stresses and the prestressing loads, caused by the wedge draw-in(slipping), can be asses according to the following relation:

p

p

sl EL

21

where

sl - loss of prestressing stresses due to anchorage slip.

21; - slipping in the anchorage ends. If the pretensioning is done just from one edge

(side) 2= 0.

In this project is considered, that the pretensioning is done just from one edge (side).

pL - length of the prestressing stand (track)

pE - design value of modulus of elasticity of prestressing steel

slpsl AP

where

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slP - losses due to anchorage slip

pA - cross sectional area of the prestressing tendons

6.2. Relaxation of the prestressing steel

The relaxation of the prestressing steel is producing between the moments from thestressing of steel up to the transfer.

where

slppi max

In the formulas 3.28, 3.29 and 3.30, time t represents time of the prestressing steelrelaxation, from the moment of prestressing to the moment of the transfer.

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The equivalent time (teq) is calculated and it is given in the technological graph theme.

Loss of prestressing force caused by the relaxation of the steel can be evaluated as:

prpr AP

where:

rP - loss of prestressing force caused by the steel relaxation

pA - cross sectional area of the prestressing tendons.

6.3. Heat cur ing (Thermal t reatment)

In order to reach faster the required initial strength for concrete, a heat curing process(thermal treatment) is necessary, usually by using hot steam of hot water.

3.1.3

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7. Elastic deformation of the concrete at the transfer

In the moment of the transfer the value of the prestressing force can be computed as:

PPPPP rslerm maxint

where:

maxP - force applied to prestressing steel

slP - losses due to anchorage slip

rP - loss of prestressing force caused by the steel relaxation

P - loss of prestressing force due to heat curing

x

X

s

i

Ape

cpPinterm

To calculate the unit stress in concrete at the level of prestressing steel (cp) a simplified oran exact procedure can be assumed.

The simplified calculation method

eI

eP

A

P

c

erm

c

erm

cp

intint

where:

Ac - area of the concrete cross sectione - distance between the gravity centres of the prestressing steel and concrete cross

sectionIc - second moment area of the concrete cross section

The exact calculation method

)1(2

2

int

r

eA

A

p

c

e

ermp

cp

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where:

p

erm

ermpA

Pintint

)( 0tE

E

cm

p

e

Ep - modulus of elasticity of the prestressing steelEcm(t0) - secant modulus of elasticity of concrete at an age t0. In the case of this project t0

will be replaced with tT , as was computed before.Ac - area of the concrete cross sectionAp - area of the prestressing steele - distance between the gravity centres of the prestressing steel and concrete cross

sectionr - radius of gyration of the concrete cross section, computed as

cAIcr

Loss of prestressing stress ( el ) and loss of prestressing force ( elP ) caused by the

elastic deformation (shortening) of the concrete at transfer can be evaluated according tofollowing relations:

cpeel

elpelAP

In the moment immediately after the transfer, the stress and force in prestressing steel canbe evaluated using the following relations:

el

p

erm

pmA

P int0

00 pmpm AP

In this stage, the stress in the prestressing steel must satisfy the following conditions:

kppkpm

ff ,1.00 85,0;75,0min

If it is not satisfied, maxp must be reduced.

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8. Static design

2

2

1

1

Combination of actions:

SLS

- characteristic Gk+Qk

- frequent Gk+1Qk

- quasi-permanent Gk+2Qk

ULS

- fundamental 1,35*Gk+1,5Qk

Load Characteristic values Bending moment in section 1-1

Self weigth gself,k8

2

,

,

lgM

kself

kself

Rest of the permanent grest,k8

2

,

,

lgM

krest

krest

1 2

Roof 0,5 0,4

Intermediary slab 0,7 0,4

ldisp

lcalcltransf

lsupp lsupp

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Variable qk

Combination Mod of combination Bending moment in section 1-1

Characteristic Gk+Qk8

)(

2

,, lqggM kkrestkselfEk

Frequent Gk+1Qk8

)( 21,, lqggM

kkrestkself

Ef

Quasi-permanent Gk+2Qk8

)( 22,, lqggM

kkrestkself

Eqp

Fundamental 1,35*Gk+1,5Qk8

)5,135,135,1( 2,, lqggM

kkrestkself

Ed

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x

X

s

i

Ape

cpPm0

ct

cb

Mself,k

9. Verif ication of stresses at transfer

9.1. Design of normal stresses in the section 1-1

i

kselfm

c

m

cbW

MeP

A

P ,00 (bottom)

s

kselfm

c

mct

W

MeP

A

P ,00 (top)

eI

MeP

A

P

c

kselfm

c

m

cp

,00 (at the level of the prestressing steel)

9.2. Design of normal stresses in the section 2-2 (at ldisp)

9.2.1. Determination of the position of the section 2-2 (at ldisp)along the element axis

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x

X

s

i Ap e cpPm0

ct

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s

kselfm

c

mct

W

MeP

A

P22

,00

i

kselfm

c

mcb

W

MeP

A

P22

,00

(1)P Local concrete crushing or splitting at the end of pre- and post-tensioned membersshall be avoided.

(3) The strength of concrete at application of or transfer of prestress should not be lessthan the minimum value defined in the relevant European Technical Approval.

)( 0tfctmct - condition to remain the entire section uncracked

In the case when in section 2-2 the relation )(6,0 0tfckcb is not satisfied, the solution to

decrease the stress in concrete consists in disposal of one or more (plastic) sheets to theone or more tendons. In this way, the wrapped tendon(s) is considered not anchored (nuconlucreaza) in concrete, the section being verified with this new (reduced) stress. If the

relation continues to be unsatisfied (false), another tendon is considered to be wrapped insheet, followed by the re-verification of the section. The procedure is continued up to thestage when the relation is satisfied (becomes true).

In the above formula t0will be replaced with tT, computed based on the technological graphusing formula (B.10).

- condition to avoid longitudinal cracking

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In the case that disposal of one or more sheets is necessary, verification in another cross-

section (2-2), situated at distance ofldisp measured from the sheets end will be done.

ldisp 2

2

2'

2'ldisp

lteaca ldisp

teaca

teaca

123

sheet

sheet

sheet

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10. Final losses of prestress

In the case of this project ezcp .

eI

M

c

Eqp

cpQPc ,

eI

MeP

A

P

c

kselfm

c

m

cp

,00

pr - can be evaluated based on the relations 3.28, 3.29 or3.30, considering t

being the life-cycle of the element

and

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QPcepmpi ,0

)( 0tE

E

cm

p

e

where t0 is 28days, thus Ecm(t0) became Ecm.

The final force of prestressing, considering the rheological losses can be determined with:

rscmm PPP 0

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11. Verification of the stresses in service stage in section 1-1

e

ct

cb

Pk=nPm8

M

n=1

11.1. Verifications for ct

For exposure classes XD, XF, XS

ct will be computed considering M = MEkand will be verified the relation

ckct f 6,0

For the rest of the exposure classes

ct will be computed considering M = MEQPand will be verified the relation

ckctf 45,0

11.2. Verifications for cb

For exposure classes X0, XC1, XS

cb will be computed considering M = MEfand will be verified the relation

ctmcbf

For exposure classes XD1, XD2, XD3, XS2, XS3

cb will be computed considering M = MEfand will be verified the relation

0cb

For exposure classes XC2, XC3, XC4

cb will be computed considering M = MEqp and will be verified the relation

0cb