time-depended behavior of prestressed concrete members

CAD BUREAU – Computer Added Bureau, Skopje, Macedonia

Time-depended Behavior of Prestressed Concrete MembersProf. Kokalanov GorgiAsist. Markovski Goran

Asist. Mihajlov Vikotr Faculty of Civil Engineering, Skopje, Macedonia

CAD BUREAU Computer Added Bureau, Skopje, Macedonia

An influence of live load under time-dependent behavior of prestressed concrete members is considered.

The experimental program includes 3 series ( A, B ,V) of prestressed concrete simple beams with dimensions 15/28 cm and L=2,80 m span. There are 4 groups of beams in each

series.


Time-dependent behavior of prestressed concrete members


• First group beams were testing at short - time load until breaking at t=40 days.

• Second group will be tested until breaking at t=400 days.

• Third group after 10 days of prestressing two concentrated forces are applied. There is no cracking. These beams are under sustained load for 360 days.

• Fourth group beams with same sustained load as third plus cyclic live load (two concentrated forces). These forces act at time steps of 12 hours (12 hours Fg+Fp, another 12 hours only Fg). The load ( Fg+Fp) is sufficient to produce cracking.

prestressed at t=30days



Mathematical Model

• The beam is divided into 30 shell (QUAD) elements.• The elements are divided into 20 layers. For each layer, the

allowable stresses are obtained from the strain-distribution of the pure concrete with the lower value value of tensile strength FCTK. The compression stresses is limited as well due the relation of the principle stresses. The steel forces include tension stiffening effect.



Material concrete FC = maximum uniaxial pressureFCT = average tensile strength fuer tension stiffeningFCTK = lower value of tensile strength for pure concrete The biaxial compression stress is limited due to the relation of the principal stresses:

Biaxial behavior acc. Kupfer-Hilsdorf-Rüsch acc. to the relation of the principal stresses



With the obtained max. value of beta-ic a uniaxial stress-strain-relation is built for each layer and each element:

beta-ic

-eps

Verlauf nach [2]

Verlauf nach [1]

linear

Verlauf nach [2]

Tension is limited in both principal stress directions to beta-z:beta-z

eps

GF

sigma

epslin

Uniaxial stress-strain-relation for tension

Uniaxial stress-strain-relation in case of compression



Material steel Standard is a bilinear stress-strain-relation with yield limitation. Trilinear relation is possible within a manual input:

The tension stiffening effect is included according Eurocode 2 and results in a crack-width wk,cal:

wk,cal = 1.7 am sm



Creep and shrincage

• Concrete creep-strains are calculated with a rough method of decreasing the concrete modulus of elasticity

E-creep = E-linear * 1/(1+phi) with a total creep value phi.

• The modulus of elasticity of the steel is not changed. • Shrincage is analized with a strain-load that acts only on the

concrete and not on the reinforcement.



TEST SPECIMENS

NUMBER OF TEST

SPECIMENSPROPERTY

AGE OF CONCRETE AT TESTING

CUBE 209

COMPRESSIVE

STRENGTH OF

CONCRETE

t=40

9 t=400

CYLINDER 15/30

6+3 MODULUS OF

ELASTICITY

t=40

6+3 t=400

PRISM 10/10/ 50

6FLEXURAL TENSILE

STRENGTH OF

CONCRETE

t=40

t=4006

PRISM 12/12/36 3 SHRINKAGE t=400

PRISM 12/12/36 3+3 CREEP t=400



Tension Bending

AZf n

bz W

LP

fn

bzs4

15.115.1

28.0

0.1)4.06.0(4

bzsbz

bz

bzs

bz

bzs

ffff

cmddf

f

PAB/87

24.124.1

28.008.008.01

7.0

7.0

bzsbz

bz

bzs

bz

bzs

ffff

cmddd

ff

CEB-FIP MC90

Tensile strength



Experimentally:Prof. D. Ivanov, Faculty of Civil Engineering, Skopje

Reference:Concrete Society Technical Report N0 23Partially prestressingReport of a Concrete SocietyWorking Party.

The stress of which cracking becomes visible corresponds approximately to the modules of rupture (normal tensile strength due to bending of unreinforcement concrete)It is about twice the tensile strength of the concrete.

2bz

bzs

ff

Tensile strength



0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Midspan displacement

Forc

e [k

N]

Sofistik fct=5.2 E=24000Experiment, Average resultExperimant Beam A1.1Experiment Beam A1.2Sofistik fct=2.6 E=24000



MODULUS OF ELASTICITY

05

1015

2025

3035

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1

STRAINSST

RES

SES EXPERIM

EC-2

s - exper s - EC2 e0 0 0.00

5.15 6.45 0.207.98 9.71 0.31

10.81 12.50 0.4113.64 15.62 0.5316.48 18.49 0.6519.31 21.74 0.8022.14 24.78 0.9624.97 27.69 1.1427.80 30.27 1.3430.63 32.67 1.6133.46 33.93 1.93



0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

Midspan displacement

Forc

e

ExperimentalSOFiSTiK



Long Time Effect - Cycle Loading

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Midspan displacement

Forc

es

Sofistik A4 beamsSofistik A3 beamsExperiment A4 beamsExperiment A3 beams



Lonigudinal Section M=1:500

Bridge Zdunje L=358m, H=63.89



Cross SectionsMidspan

Support

Column



Construction Stage 1



Construction Stage 9




Dead Load



Prestresses forces



Equipment



Additional Load



D. Displacement – dead load



P. Displacement – prestressed forces



E. Displacement – equipment



A. Displacement – additional loads



C. Displacement - creep



Displacement (D+P+E+A) / (D+P+E+A+C)

time-depended behavior of prestressed concrete members

Documents

biaxial behavior

tension uniaxial stressstrain

short time load

trilinear relation

sustained load

bilinear stressstrain

time steps

load fg fp