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

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 assessment • Principles of structural analysis • Benefits for managing substandard structures • Examples • Yield line analysis – achieving confidence • Conclusion 2

Introduction 3

Introduction 27% 4

Introduction 5

Introduction 6

Introduction • Increasing levels of assessment (from BD79/13) • Level 1 - simple • Level 2 - refined • (Level 3 – bridge specific) • (Reliability-based methods) 7

Benefits for assessment Design Assessment Actions Actions Materials Geometry Structural Structural Analysis Geometry Materials Analysis Reinforcement Reinforcement design design 8

Benefits for assessment Design Assessment Optimisation of structural analysis Big reduction in Small reduction in structure management cost costs 9

Principles of structural analysis 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 10

Principles of structural analysis 11

Principles of structural analysis 12

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

Principles of structural analysis • 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 14

Principles of structural analysis • Two important and useful theorems: Resistance • Upper Bound Theorem optimise • Compatible failure mechanism Upper • Energy dissipated = work done by loads bound • Upper bound estimates • Optimise to find worst case Lower • Lower Bound Theorem bound • Equilibrium estimates • Yield optimise • Safe lower bound • Optimise to find best case 15

Benefits for managing substandard structures • 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? 16

Examples of plastic analysis for assessment • 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 17

Example 1 • Concrete structure with vulnerable half joints • Some deterioration and corrosion 18

R10 4 No. R20 8 No. R20 Very light reinforcement in this zone 19

• Our approach: • Optimised strut and tie modelling (lower bound plasticity) • Optimised upper bound mechanism analysis • Non-linear FE 20

Compressive struts Nodes Tension ties 21

Yielding Yielding 22

F v F v H T H T end end V T V T end end A A d d (a) (b) F v F v F v H T H T H T end end end q V T V T q V T end end end A A d (c) (d) 23

• 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 24

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How useful were the 3 approaches? 2 UB analysis 3 NLFE 1 LB strut and tie F v F v H T H T end end q V T V T end end A Safe result Useful for predicting cracking Necessary to find the correct mechanism – otherwise and load deflection Approach entirely defined behaviour unsafe within Eurocodes Convergence issues Very useful for quickly Could be rather conservative identifying substandard if not optimised Could be unsafe if tensile structures strength is relied on Optimised approach works Useful for predicting very well Use of interface elements mechanisms of failure helps reduce this problem 26

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. 27

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

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

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

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.

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

Jon Shave shavej@pbworld.com 33