1. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-depended Behavior of Prestressed Concrete Members Prof. Kokalanov Gorgi Asist. Markovski Goran Asist. Mihajlov Vikotr Faculty of Civil Engineering, Skopje, Macedonia

2. 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.

3. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

4. 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

5. 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

6. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

7. CAD BUREAU Computer Added Bureau, Skopje, Macedonia Material concrete FC = maximum uniaxial pressure FCT = average tensile strength fuer tension stiffening FCTK = 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

8. 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 : Tension is limited in both principal stress directions to beta-z: Uniaxial stress-strain-relation for tension Uniaxial stress-strain-relation in case of compression Time-dependent behavior of prestressed concrete members

9. 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 w k,cal : w k,cal = 1.7  a m   sm Time-dependent behavior of prestressed concrete members

10. 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

11. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia TEST SPECIMENS NUMBER OF TEST SPECIMENS PROPERTY AGE OF CONCRETE AT TESTING CUBE 20 9 COMPRESS IVE STRENGTH OF CONCRETE t=40 9 t=400 CYLINDER 15/30 6+3 MODULUS OF ELASTICITY t=40 6+3t=400 PRISM 10/10/ 50 6 FLEXURAL TENSILE STRENGTH OF CONCRETE t=40 t=400 6 PRISM 12/12/36 3SHRINKAGEt=400 PRISM 12/12/36 3+3CREEPt=400 Time-dependent behavior of prestressed concrete members

12. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia TensionBending PAB/87 CEB-FIP MC90 Tensile strength Time-dependent behavior of prestressed concrete members

13. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Experimentally: Prof. D. Ivanov, Faculty of Civil Engineering, Skopje Reference: Concrete Society Technical Report N 0 23 Partially prestressing Report of a Concrete Society Working 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. Tensile strength Time-dependent behavior of prestressed concrete members

14. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

15. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

16. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

17. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

18. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Bridge Zdunje L=358m, H=63.89 Time-dependent behavior of prestressed concrete members

19. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Cross Sections Midspan Support Column Time-dependent behavior of prestressed concrete members

20. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Construction Stage 1 Time-dependent behavior of prestressed concrete members

21. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Construction Stage 9 Time-dependent behavior of prestressed concrete members

22. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members

23. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members Dead Load

24. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members Prestresses forces

25. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members Equipment

26. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members Additional Load

27. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members D. Displacement – dead load

28. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members P. Displacement – prestressed forces

29. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members E. Displacement – equipment

30. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members A. Displacement – additional loads

31. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members C. Displacement - creep

32. CAD BUREAU – Computer Added Bureau, Skopje, Macedonia Time-dependent behavior of prestressed concrete members Displacement (D+P+E+A) / (D+P+E+A+C)