automated at last. Afternoon Workshop Thursday 26 February 2015 - - PowerPoint PPT Presentation

The yield-line method for concrete slabs: automated at last.

Afternoon Workshop Thursday 26 February 2015 IStructE HQ, Bastwick Street, London

Programme

14:00 - 14:15 Arrival / tea and coffee 14:15 - 14:55 Event welcome / How the new automated method works Matthew Gilbert University of Sheffield 14:55 - 15:05 Complementary technology: lower bound computational analysis Angus Ramsay Ramsay Maunder Associates 15:05 - 15:35 Tea / coffee break 15:35 - 15:50 Benefits of plastic analysis methods in practical structural assessment Jon Shave Parsons Brinkerhoff 15:50 - 16:30 Application of the LimitState:SLAB software to slab analysis problems Tom Pritchard LimitState 16:30 - 17:00 Panel discussion. Panel: John Morrison (Buro Happold) and workshop speakers.

Welcome!

• Dept. of Civil & Structural Engineering
• One of the largest civil engineering

departments in the UK

• Alma mater to many prominent

engineers (incl. many past IStructE presidents)

• Long history of undertaking ‘useful’

research

• Dept. of Civil & Structural Engineering
• Research highly rated in recent ‘REF

2014’ quality audit (e.g. 2nd in the UK for ‘research intensity’)

• £81M new building will provide

state-of-the-art teaching space:

Ensuring research is usable

‘Valley of death’ Academic research Industry uptake

Increasing technology readiness Availability of resource

Ensuring research is usable

‘Valley of death’ Academic research Industry uptake

Increasing technology readiness Availability of resource

Spinout companies

LimitState Ltd

• Spun-out from University in 2006
• Commercialising academic research:
• Providing engineers with powerful

software for ultimate limit state analysis & design

• Taking advantage of state-of-the-art

algorithms & optimization technology

• Ensuring software is robust and well

validated

• Adding value:
• Ensuring applications are fully

supported and are easy to use

Existing LimitState products

Masonry arch bridge analysis software: Geotechnical analysis software: Now used by most major UK consultants and contractors, and in over 30 countries worldwide

How the new automated method works

Matthew Gilbert University of Sheffield (and founding Director of LimitState Ltd)

Background & motivation

Background & motivation

Rigid-plastic Linear elastic Deflection Load

Background & motivation

Rigid-plastic Linear elastic Deflection Load

Background & motivation

• The finite element method has made

linear-elastic analysis convenient and mainstream But to assess collapse rigid-plastic analysis tools are much less well developed

Rigid-plastic (‘limit’) analysis

• Used to estimate the maximum load sustainable by a

body or structure

• Benefits (cf. elastic methods for ultimate analysis):
• Tend to lead to more economic solutions when used in design
• Can reveal hidden reserves of strength when used in assessment

collapse / ‘limit’ load Deflection Load typical actual response

Collapse analysis: existing tools

More:

• complex
• time consuming
• input parameters
• expertise required
• accurate [potentially at least!]

‘Traditional’: based on hand analysis solutions etc. ‘Advanced’: based on non- linear finite elements etc.

(potentially embedded in simple programs / spreadsheets etc.)

GAP!

Collapse analysis: existing tools

More:

• complex
• time consuming
• input parameters
• expertise required
• accurate [potentially at least!]

‘Traditional’: based on hand analysis solutions etc. ‘Advanced’: based on non- linear finite elements etc.

(potentially embedded in simple programs / spreadsheets etc.)

‘Mainstream’: using numerical rigid-plastic analysis?

Collapse analysis: existing tools

More:

• complex
• time consuming
• input parameters
• expertise required
• accurate [potentially at least!]

‘Traditional’: based on hand analysis solutions etc. ‘Advanced’: based on non- linear finite elements etc.

(potentially embedded in simple programs / spreadsheets etc.)

‘Mainstream’: using numerical rigid-plastic analysis?

Collapse analysis: existing tools

More:

• complex
• time consuming
• input parameters
• expertise required
• accurate [potentially at least!]

‘Traditional’: based on hand analysis solutions etc. ‘Advanced’: based on non- linear finite elements etc.

(potentially embedded in simple programs / spreadsheets etc.)

‘Mainstream’: using numerical rigid-plastic analysis?

The yield-line method

The ‘yield-line’ method of analysis

• The term ‘yield-line’ was first coined by

Ingerslev, in the first ever paper to appear in The Structural Engineer

• Johansen then developed the theory

underpinning the method

• Later shown that the yield-line method is

an ‘upper bound plastic analysis’ method

Calculations (work method)

• Equate internal and

external work (for chosen yield-line pattern)

(from Kennedy & Goodchild, 2004)

Pros and cons of the yield-line method

• Pros:
• Simple, direct, estimate of the collapse load
• Leads to economical designs (and/or realistic

assessments of capacity of existing slabs)

• Cons:
• Non-conservative (unsafe) if incorrect

mechanism chosen

• Only considers flexural failure

Renewed interest in the 1990s & 2000s

• Middleton and co-workers showed many

concrete bridges appeared to have ‘hidden reserves’ of strength:

5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Capacity (tonnes) Elastic assessment Plastic assessment

Renewed interest in the 1990s & 2000s

• The Cardington European Concrete Building Project indicated that

yield-line design brought benefits when used in design

‘Yield line design is so easy…. …once you know what you are doing!’

Foreward, Practical Yield Line Design, Kennedy & Goodchild, 2004

‘Yield line design is so easy…. …once you know what you are doing!’

Foreward, Practical Yield Line Design, Kennedy & Goodchild, 2004

Automating the yield-line method

Automating the yield-line method

• Element based formulations have been tried:
• But solutions highly dependent on element topology!
• Better solutions via geometry optimization (moving nodes), but e.g.

‘fan’ mechanisms could still not be identified (e.g. Johnson 1994)

e.g. H.S.L. Chan, 1972

But another method can identify ‘fans’…

• Truss ‘layout optimization’ (Dorn et al, 1964):

But another method can identify ‘fans’…

• Modified ‘self-stress’ truss layout optimization:

Truss layout optimization: formulation

volum ume nodal al equili ilibrium rium bar ar force rce length gth/y /yie ield ld stress ss

f

externa nal l force ce

Similarity of formulations

Truss (‘layout optimization’ with self-stress): Slab (‘discontinuity layout

• ptimization’, DLO):

Similarity of formulations

Truss (‘layout optimization’ with self-stress): Slab (‘discontinuity layout

• ptimization’, DLO):

volum ume nodal al equili ilibrium rium bar ar force rce impose posed d self-st stre ress ss length gth/y /yie ield ld stress ss

Similarity of formulations

Truss (‘layout optimization’ with self-stress): Both are simple linear optimization problems Slab (‘discontinuity layout

• ptimization’, DLO):

volum ume nodal al equili ilibrium rium bar ar force rce impose posed d self-st stre ress ss length gth/y /yie ield ld stress ss impose posed d unit displaceme lacement nt energy gy rotation ation at yield ld-line line nodal al sompa mpatib ibili ility ty length gth x momen ment t capa pacity city

DLO - nodal compatibility constraint







5 1

cos

i i i

 

1

• Rotations at nodes must

sum to zero:

• Key feature: compatibility is

also implicitly enforced at crossover points







5 1

sin

i i i

 

node no node here!

DLO – treating applied loads

Examples

Example 1: Fixed square slab

• Analytical solution available:  = 42.851

(Fox, Phil. Trans. Roy. Soc, 1974)

• Best DLO solution:  = 42.857, which is

just 0.01% higher (Gilbert et al., Proc. Roy.

Soc, 2014)

Example 1: Fixed square slab (cont.)

Power law extrapolation gives 5 digit agreement with analytical solution

Example 2: Indented slab

• Best literature solution:  = 29.2

(Jackson, PhD Thesis, Cambridge University, 2010)

• Best DLO solution:  = 28.988

(Gilbert et al., Proc. Roy. Soc, 2014)

Example 2: Indented slab (cont.)

Simplified collapse patterns can also be obtained, e.g. to facilitate validation via hand calculations:

Increasing simplification

Example 3: Apartment

Example 3: Apartment

(from Kennedy & Goodchild, 2004)

Example 3: Apartment

Refinements

• 1. ‘Tidying up’ yield-line patterns
• In the automated method, yield-lines must terminate at nodes
• n a predefined grid
• Post-processing the solution using ‘geometry optimization’

gives even clearer yield-line patterns, e.g:

• 2. Lower bound solutions
• The yield-line method provides

upper bound solutions

• The automated yield-line method

provides solutions which are for engineering purposes exact

• However, for completeness, a lower

bound solution can be obtained (e.g. see Ramsay presentation)

• Example problem, from

‘Benchmark’ article (gap = 0.2%):

Conclusions

Conclusions

• The yield-line method provides a powerful means of analysing

the ultimate (collapse) limit state

• However, the lack of a general implementation has limited usage

in recent years

• The yield-line method has been automated via ‘discontinuity

layout optimization’ (DLO) :

• Typically involves linear optimization (easy to solve)
• Fan type mechanisms (and others) identified automatically
• Automated yield-line analysis software is now available for use in

industry (and free for academic use): www.limitstate.com