cad bureau – computer added bureau, skopje, macedonia time-depended behavior of prestressed...

CAD BUREAU – Computer Added Bureau, Skopje, Macedonia

Time-depended Behavior of Prestressed Concrete MembersProf. Kokalanov Gorgi

Asist. 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

SPECIMENS

PROPERTY

AGE OF CONCRETE AT TESTING

CUBE 20

9COMPRESS

IVE 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

A

Zf nbz

W

LP

f

n

bzs4

15.115.1

28.0

0.1)4.0

6.0(4

bzsbz

bz

bzs

bz

bzs

ff

f

f

cmd

df

f

PAB/87

24.124.1

28.0

08.0

08.017.0

7.0

bzsbz

bz

bzs

bz

bzs

ff

f

f

cmd

d

d

f

f

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

f

f

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

Fo

rce

[kN

]

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



MODULUS OF ELASTICITY

0

5

10

15

20

25

30

35

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

RESS

ES 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


Fo

rce

Experimental

SOFiSTiK



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 5


Fo

rces

Sofistik A4 beams

Sofistik A3 beams

Experiment A4 beams

Experiment A3 beams



Lonigudinal Section M=1:500

Bridge Zdunje L=358m, H=63.89



Cross Sections

Midspan

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)

cad bureau – computer added bureau, skopje, macedonia time-depended behavior of prestressed...

Documents

cad bureau computer

macedonia slide

pure concrete

macedonia material concrete

biaxial behavior

time steps

short time load

tension uniaxial stressstrain