Time-depended Behavior of Prestressed Concrete Members
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Transcript of 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.
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
• 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
Time-dependent behavior of prestressed concrete members
CAD BUREAU Computer Added Bureau, Skopje, Macedonia
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.
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
Time-dependent behavior of prestressed concrete members
CAD BUREAU Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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.
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
CAD BUREAU – Computer Added Bureau, Skopje, Macedonia
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
Time-dependent behavior of prestressed concrete members
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0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
Midspan displacement
Forc
e
ExperimentalSOFiSTiK
Time-dependent behavior of prestressed concrete members
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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
Time-dependent behavior of prestressed concrete members
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Lonigudinal Section M=1:500
Bridge Zdunje L=358m, H=63.89
Time-dependent behavior of prestressed concrete members
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Cross SectionsMidspan
Support
Column
Time-dependent behavior of prestressed concrete members
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Construction Stage 1
Time-dependent behavior of prestressed concrete members
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Construction Stage 9
Time-dependent behavior of prestressed concrete members
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Time-dependent behavior of prestressed concrete members
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Time-dependent behavior of prestressed concrete members
Dead Load
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Time-dependent behavior of prestressed concrete members
Prestresses forces
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Time-dependent behavior of prestressed concrete members
Equipment
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Time-dependent behavior of prestressed concrete members
Additional Load
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Time-dependent behavior of prestressed concrete members
D. Displacement – dead load
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Time-dependent behavior of prestressed concrete members
P. Displacement – prestressed forces
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Time-dependent behavior of prestressed concrete members
E. Displacement – equipment
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Time-dependent behavior of prestressed concrete members
A. Displacement – additional loads
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Time-dependent behavior of prestressed concrete members
C. Displacement - creep
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Time-dependent behavior of prestressed concrete members
Displacement (D+P+E+A) / (D+P+E+A+C)