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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 .
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Concrete Solutions 09Predicting 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
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 ShrinkageApply bending greater than cracking moment
Calculation of Shrinkage CurvatureApply “negative” prestress to reinforcement
Effect of ShrinkageMoment-Curvature, without and with shrinkage
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 • 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.
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
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/