Concrete Solutions 09 Predicting the Deflection of Concrete Structures in Practice

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

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

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Introduction

• Are the simplified provisions for the calculation
  of deflections in AS3600 too simple
• It depends

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When are Deflections Important?

• Second order effects
• Client expectations
• Contract conditions
• Code compliance
• Aesthetics
• Clearances

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When are Deflections Important?
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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.

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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

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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

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Effect of ShrinkageSymmetrical Reinforcement
No Load
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Effect of ShrinkageConcrete Shrinkage
de-bonded steel
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Effect of ShrinkageApply compression to steel
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Effect of ShrinkageRe-bond steel and release
compression
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Effect of ShrinkageApply bending below cracking
moment
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Effect of ShrinkageApply bending greater than
cracking moment
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Calculation of Shrinkage CurvatureApply
negative prestress to reinforcement
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Effect of ShrinkageMoment-Curvature, without and
with shrinkage
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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

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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

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Case Study
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Case Study

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

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Moment-Curvature (long term)
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Crown Deflection, mm
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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

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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

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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.

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Further Information and Software

• http//newtonexcelbach.wordpress.com/