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Concrete Solutions 09 Predicting the Deflection of Concrete Structures in Practice Doug Jenkins - Interactive Design Services Introduction Everything should be made as simple as possible, ... but not simpler. Albert Einstein Introduction Are the simplified provisions for the calculation of deflections in AS3600 “too simple” It depends When are Deflections Important? Second order effects Client expectations Contract conditions Code compliance Aesthetics Clearances When are Deflections Important? 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. 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 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 Effect of Shrinkage Symmetrical Reinforcement – No Load Effect of Shrinkage Concrete Shrinkage – de-bonded steel Effect of Shrinkage Apply compression to steel Effect of Shrinkage Re-bond steel and release compression Effect of Shrinkage Apply bending below cracking moment Effect of Shrinkage Apply bending greater than cracking moment Calculation of Shrinkage Curvature Apply “negative” prestress to reinforcement Effect of Shrinkage Moment-Curvature, without and with shrinkage 180 160 Bending Moment, Knm 140 120 100 80 60 40 20 0 0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 Curvature; m^-1 Bending Only Bending + Shrinkage 5.00E-03 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 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 Case Study Case Study 1. 2. 3. 4. 5. 6. 7. 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. Moment-Curvature (long term) 160 Bending Moment, kNm 140 120 100 80 60 40 20 0 0 0.001 0.002 0.003 0.004 Curvature, m^-1 0.005 0.006 0.007 Crown Deflection, mm 0 -20 Crown Deflection, mm -40 Run 1 -60 Run 2 -80 Run 3 -100 Run 4 Run 5 -120 Run 6 Run 7 -140 -160 0 0.2 0.4 0.6 Load Factor 0.8 1 Case Study - Conclusions 1. 2. Analysis including all relevant effects matched measured deflections Most significant effects: – – Reduction in cracking moment due to shrinkage and differential temperature Shrinkage curvature General Conclusions Critical cases: – 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 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. Further Information and Software http://newtonexcelbach.wordpress.com/