structural assessments Jon Shave Head of Specialist Civil - - PowerPoint PPT Presentation

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structural assessments Jon Shave Head of Specialist Civil - - PowerPoint PPT Presentation

Apr 10, 2024 233 likes •576 views

Plastic analysis for practical structural assessments Jon Shave Head of Specialist Civil Engineering Consultancy Services Parsons Brinckerhoff 1 Plastic analysis for practical structural assessments Introduction Benefits for

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Plastic analysis for practical structural assessments

Jon Shave Head of Specialist Civil Engineering Consultancy Services Parsons Brinckerhoff

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Plastic analysis for practical structural assessments

  • Introduction
  • Benefits for assessment
  • Principles of structural analysis
  • Benefits for managing substandard structures
  • Examples
  • Yield line analysis – achieving confidence
  • Conclusion

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Introduction

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Introduction

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27%

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Introduction

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Introduction

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Introduction

  • Increasing levels of assessment (from BD79/13)
  • Level 1 - simple
  • Level 2 - refined
  • (Level 3 – bridge specific)
  • (Reliability-based methods)

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Benefits for assessment

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Structural Analysis

Geometry Actions Materials Reinforcement design

Structural Analysis

Geometry Actions Materials Reinforcement design

Design Assessment

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Benefits for assessment

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Design Assessment

Optimisation

  • f structural

analysis

Small reduction in structure cost

Big reduction in management costs

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Principles of structural analysis

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Most level 1 structural assessments (like designs) are based around a model that assumes elastic behaviour. But in many cases this does not reflect the way the structure would behave at the ultimate limit state. Cracking Yielding

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Principles of structural analysis

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Principles of structural analysis

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Principles of structural analysis

  • Two important and useful theorems:
  • Lower Bound Theorem
  • Equilibrium
  • Yield
  • Safe lower bound
  • Optimise to find best case
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Principles of structural analysis

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  • Two important and useful theorems:
  • Upper Bound Theorem
  • Compatible failure mechanism
  • Energy dissipated = work done by loads
  • Upper bound
  • Optimise to find worst case
  • Lower Bound Theorem
  • Equilibrium
  • Yield
  • Safe lower bound
  • Optimise to find best case
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Principles of structural analysis

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  • Two important and useful theorems:
  • Upper Bound Theorem
  • Compatible failure mechanism
  • Energy dissipated = work done by loads
  • Upper bound
  • Optimise to find worst case
  • Lower Bound Theorem
  • Equilibrium
  • Yield
  • Safe lower bound
  • Optimise to find best case

Lower bound estimates

  • ptimise

Upper bound estimates

  • ptimise

Resistance

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Benefits for managing substandard structures

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  • Upper bound methods particularly useful for understanding

structural risk

  • “Substandard structures” – how to manage the structure?
  • Load mitigation
  • Monitoring
  • How would it fail?
  • How could you strengthen it?
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Examples of plastic analysis for assessment

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  • Structural assessment “failures” often
  • Flexural – eg bending in slabs
  • Shear – eg half joints and hinges

Examples for each case where LB + UB plastic methods have been used

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Example 1

  • Concrete structure with vulnerable half joints
  • Some deterioration and corrosion

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Very light reinforcement in this zone 4 No. R20 8 No. R20 R10

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  • Our approach:
  • Optimised strut and tie modelling (lower bound plasticity)
  • Optimised upper bound mechanism analysis
  • Non-linear FE

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Tension ties Compressive struts Nodes

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Yielding Yielding

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A Fv HT

end

VT

end

Fv HT

end

VT

end

q A Fv HT

end

VT

end

d q A Fv HT

end

VT

end

d

(d) (c) (a) (b)

A Fv HT

end

VT

end

d

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  • Strut and tie (Lower bound)
  • Required a plastic approach using

a statically indeterminate system

  • 40T ALL pass
  • Upper bound
  • Critical mechanism predicted to

be a rotation of the nib

  • Pretty good agreement regarding

ULS resistance

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1 LB strut and tie 2 UB analysis 3 NLFE

Safe result Approach entirely defined within Eurocodes Could be rather conservative if not optimised Optimised approach works very well

A Fv HT

end

VT

end

Fv HT

end

VT

end

q

Necessary to find the correct mechanism – otherwise unsafe Very useful for quickly identifying substandard structures Useful for predicting mechanisms of failure Useful for predicting cracking and load deflection behaviour Convergence issues Could be unsafe if tensile strength is relied on Use of interface elements helps reduce this problem

How useful were the 3 approaches?

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Example 2

  • Flexure in a subway slab
  • Light transverse reinforcement
  • Heavy longitudinal reinforcement
  • Elastic analysis:
  • Shear ok
  • Transverse bending problem?
  • Yield line analysis
  • Range of simple mechanisms investigated
  • Suggested that fan mechanism likely to be critical
  • Increased resistance to 40T.

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Yield line analysis – achieving confidence

  • Ductility issues
  • Ductility is needed
  • Watch out for low ductility rebar (in old structures)
  • And over-reinforced sections
  • If reinforcement is stronger than estimated, it might not yield
  • Important that shear is not critical at any stage
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Yield line analysis – achieving confidence

  • Finding the right mechanism
  • Necessary to optimise over a wide range of mechanisms
  • Previously software was based around looking for typical “simple”

mechanism types

  • Previously some judgement may have been needed regarding the need to

consider other mechanisms eg fans

  • Could usually get close to minimum resistance by considering “simple”

mechanisms

  • With full optimisation comes better confidence that critical mechanism has

been found

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Yield line analysis – achieving confidence

  • Particular issues with estimating

bending resistance

  • Highly skewed, heavy reinforcement – more

complex behaviour – caution

  • Anticlastic bending (hog+sag)
  • Ref “Design of concrete slabs in biaxial

bending” Denton/Shave/Bennetts/Hendy 2010

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Yield line analysis – achieving confidence

  • Beneficial effect of membrane action
  • There will be a significant amount of beneficial membrane action

associated with the development of yield-line mechanisms

  • Combination with lower bound achieves further confidence
  • If there is any doubt – can complement with an associated lower bound

analysis

  • If lower bound and upper bound are close together - confidence
  • Optimisation of LB may be needed.
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Conclusions

  • Yield line analysis a useful way of using plastic analysis
  • Particularly useful for assessment of existing structures
  • Useful for managing substandard structure risk
  • Optimisation is essential
  • Presence of beneficial membrane action gives further

confidence

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Jon Shave shavej@pbworld.com

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