1. Concrete Solutions 09 Predicting the Deflection of Concrete Structures in Practice
Doug Jenkins - Interactive Design Services

2. Introduction Everything should be made as simple as possible,
... but not simpler. Albert Einstein

3. Introduction
Are the simplified provisions for the calculation of deflections in AS3600 “too simple”
It depends

4. When are Deflections Important?
Second order effects
Client expectations
Contract conditions
Code compliance
Aesthetics
Clearances

5. When are Deflections Important?

6. Sources of Deflection
Short term stress-strain and bond behaviour of the concrete and reinforcement.
Time dependent behaviour of the concrete.
Differential strain effects.
Construction sequence and other load sequence effects.

7. Sources of Deflection Short term stress-strain behaviour:
Concrete flexural tensile strength.
Concrete tension-stiffening effect.
Time dependent behaviour of the concrete
Concrete creep
Concrete shrinkage
Loss of tension stiffening
Loss of flexural tensile strength

8. Sources of Deflection Differential strain effects.
Differential shrinkage
Differential temperature
Load sequence effects.
Handling, transport and erection
Propping loads
Change in stiffness after overload.
Construction loads on buried structures.
Timing of composite connections.
Effect of varying axial load

9. Effect of Shrinkage Symmetrical Reinforcement – No Load

10. Effect of Shrinkage Concrete Shrinkage – de-bonded steel

11. Effect of Shrinkage Apply compression to steel

12. Effect of Shrinkage Re-bond steel and release compression

13. Effect of Shrinkage Apply bending below cracking moment

14. Effect of Shrinkage Apply bending greater than cracking moment

15. Calculation of Shrinkage Curvature Apply “negative” prestress to reinforcement

16. Effect of Shrinkage Moment-Curvature, without and with shrinkage

17. Effect of Shrinkage
Shrinkage stresses in the concrete will significantly reduce the cracking moment
Shrinkage will cause significant rotations in any asymmetrical section:
Asymmetrical reinforcement
Cracked section

18. Case Study
Large span pre-cast concrete arch in the UK (approx. 20 m span)
Short term crown deflections under self weight estimated to be about 30 mm
Initial deflections consistent with predictions
Deflections after 6 month delay to backfill increased to 150 mm

19. Case Study

20. Case Study Short term stiffness, gross concrete section
As 1, but age adjusted concrete modulus
As 2, but using Branson equation
As 3, but EC2, β = 1
As 4, but with Mcr reduced due to effect of shrinkage and differential temperature.
As 5, but with β = 0.5
As 6, but with curvature due to shrinkage included.

21. Moment-Curvature (long term)

22. Crown Deflection, mm

23. Case Study - Conclusions
Analysis including all relevant effects matched measured deflections
Most significant effects:
Reduction in cracking moment due to shrinkage and differential temperature
Shrinkage curvature

24. General Conclusions Critical cases: If so:
Will much larger than expected deflections have a significant effect on the design?
If so:
Use conservative estimate of concrete flexural tensile strength, reduced by shrinkage and tensile differential temperature stresses.
Allow for section curvature due to shrinkage
Consider possible differential shrinkage
Allow for cumulative second order effects at ULS

25. General Conclusions Structures requiring particular attention:
Where the maximum bending moment is approximately equal to the concrete cracking moment.
Asymmetric beams (e.g. Super-T), especially those subject to hot dry conditions.
Construction sequence effects.

26. Further Information and Software