Domain

Explanation

Speaker CV

Dr Bassam Izzuddin is a Reader in Computational Structural Mechanics at Imperial College. He has worked extensively in the modelling and assessment of structures under blast, fire and other extreme loading conditions. He has also been the main developer of the nonlinear structural analysis program ADAPTIC, which incorporates advanced adaptive analysis techniques as well as unique capabilities for modelling the response of steel and concrete structures under extreme events. Since joining Imperial College in 1990, Dr Izzuddin has been developing ADAPTIC personally and as the supervisor of several PhD and MSc students. Dr Izzuddin has also been active in the development of simplified models for onshore and offshore structures subject to fire and blast conditions, models that can be readily applied in the structural design process. Recently, he has developed new simplified models for the blast assessment of steel members, which have been disseminated by the SCI and currently used in design practice. Finally, in addition to his development work, Dr Izzuddin has been applying computational modelling techniques to real problems, with the aim of understanding structural behaviour under extreme events and generating design guidance. He has collaborated with fellow researchers in the UK and Europe in several application areas, including the fire response of steel buildings, and the failure of composite floors under extreme loads. He has also collaborated with the Building Research Establishment and British Steel on simulating the structural fire tests at Cardington, and has acted as a consultant on several structural problems, including the response of multi-storey buildings to blast loading. Dr Izzuddin has co-authored over 75 journal and conference papers, and has written several industry-related technical reports.

Abstract

A realistic assessment of the response of building structures to extreme events, such as fire, explosion and earthquake, demands sophisticated models which account for geometric and material nonlinearities as well as for the interactions between the various structural components. An important additional requirement, which is specific to nonlinear analysis, is the robustness of the nonlinear solution procedure so as to avoid premature numerical failure and its incorrect association with structural failure.

This seminar addresses the main requirements of nonlinear analysis for extreme loading conditions, considering structural frames with and without floor slabs. Specific issues related to geometric nonlinearity are first highlighted, including the modelling of large displacements and rotations in 3D space and the merits of step-insensitivity. For material nonlinearity, the requirements of fire and explosion loading, in terms of modelling the effects of elevated temperature and rate-sensitivity, are outlined, and the importance of formulating and utilising a consistent tangent modulus towards achieving numerical robustness is emphasised. Finally, an overview of the requirements of integrated explosion/fire structural analysis is provided, considering both the modelling of material nonlinearity and the demands of the nonlinear solution procedure.

The above requirements have been addressed within an integrated nonlinear analysis environment, ADAPTIC, developed at Imperial College for simulating the nonlinear response of offshore and onshore structures under static and dynamic loading. Several illustrative examples are provided using ADAPTIC which demonstrate the key issues related to the modelling of building structures subject to extreme loading conditions, including fire and explosion.

Contents

• Introduction
• Geometric nonlinearity
• Material nonlinearity
• Composite floor slab: new shell elements
• Integrated blast/fire analysis
• Summary
• Q&A

Introduction

• Nonlinear responses to extreme loadings
• Geometric nonlinearity:
• Buckling
• Large displacements
• Large rotations
• Material nonlinearity:
• Yielding
• Concrete cracking & crushing
• Connection nonlinearity
• Need for robust nonlinear solution:
• Otherwise would have numerical failure
• Which is often mistaken for structural failure

Geometric nonlinearity

• Requirement:
• Model large displacements & rotations
• Insensitive to incremental displacements: least sensitive to loading differences à best: always converges & not sensitive to sudden failures due to small changes
• Steps: time steps & iteration steps
• Co-rotational method: for framed structures & floor slabs
• Coupling element between frame elements (Beam-Column element: 6 d.o.f.) & slab elements (Shell element: 5 d.o.f) integration of overall structure [for individual member à ok]

Co-rotational method

• Formulation in local convected system
• For small displacements, increase the nos. of elements
• Use: simple linear/nonlinear strain-displacement relationship: e=Bd
• Transformation from local to global responses à global coord à global responses
• Derivatives of local deformation w.r.t. global freedoms:
• PVW: transform local {forces & tangent stiffnesses} into global ones

Beam-column element

• B-C element: 6 d.o.f.
• Nodal orientation vectors related to nodal rotation
• Local co-ordinate:
• Modelling local nonlinearity using nonlinear strain-displacement relations
• B-C effect: Poisson effect à bending capacity decreases in axial compression & bending capacity increases in axial tension
• Using higher-order shape functions
• Allow fewer elements needed
• E.g.: elastic quartic B-C formulation
• Analysis procedure: (error ~5%)
• Use simplest: 1 element (1e)
• If necessary for accuracy: use more elements
• Increase mesh complexity if needed

Geometric nonlinearity - floor slab

• Applications:
• Flat composite slab
• Composite floor slab: out-of-plane torsion (M_z~0)
• Using improved co-rotation method
• Slab element:
• Only 5 d.o.f.
• Local deformation defined by 4 nodes (20 basic degrees of freedoms)
• Rotations are relative to local axes (x-y)
• Local co-ord. System (with standard 4 nodes): x-y axes always bisects the element (4 nodes) diagonals à always derive symmetric tangent stiffness matrix
• Composite slab modelling procedure:
• Choice of global rotation freedoms
• Definition of local co-rotation system
• Determination of local deformations
• With the above definition & procedure, findings indicate geometric analysis is step-size insensitive

Material nonlinearity

• More complex material with cubic formulation for fibre-type materials
• Necessity: use several (>1, ~6 for steel) elements per member to model
• Implies: use adaptive analysis technique à use 1e à add more elements if needed to improve analysis quality
• Fire modeling:
• Must involve material elevated temperature
• Deterioration of properties
• Thermal strain
• Stress-strain: bilinear or multi-linear (piecewise linear) E_I
• Explosion / blast modeling:
• Must involve strain-rate effects
• Superimpose otherwise bilinear model with increased stresses (overstress: induced plastic deformation stresses)
• Explicit integration scheme: faster, but convergence problems & errors due to inconsistent tangent stiffness
• Implicit integration: slower, but converged & accurate
• Dynamic stress-strain relations affected by strain-rate effects
• Strain change à strain-rate changes à changes in dynamic stress-strain
• Convergence of solution:
• Use consistent tangent stiffness matrix
• consistent
• In practice, often miss out the consistency à approximate solution à convergence failure (numerical) but not actual structural failure
• Consistency also allows large time steps @ same solution quality

Composite floor slab

• Shell element: slab element 5 d.o.f. per node
• Geometric orthotropy
• BRE test
• Often used: linear à conventional shell element with material orthotropy
• Nonlinear à shell variation using a new customisable shell element
• Modify Reissner-Mindlin (RM) hypothesis in the following ways to derive the new shell element variant:
• Add rib displacement field
• Different orientation of the normals of cover & rib
• Effectively: u_new=u_RM+u_changes

Integrated explosion-fire analysis

• Sequential process:
• First, blast load:
• Fast
• More time steps (shorter intervals)
• Structure becomes partially damaged
• Material model: rate sensitivity
• Explicit integration: can suffice
• Second, fire spread
• Slower
• Fewer time steps (longer intervals)
• Structure burnt down, softens, failure collapse mechanism)
• Material model: elevated temperature
• Explicit integration: problem to suffice à errors in tangent stiffness
• Solution approach:
• Implicit integration with consistent tangent stiffness modulus employed
• Ensures accurate convergence without failure

Summary

• Analytical requirements of nonlinear elastic analysis
• Geometric nonlinearity:
• Step-insensitivity
• Role of co-rotation
• Material nonlinearity:
• Consistent tangent stiffness modulus
• Composite floor slab:
• Geometric orthotropy
• New shell element
• Integration explosion & fire:
• Nonlinear modelling
• Blast only: high deformations
• Fire only: burn down failure mechanism & temperature ~900C
• Blast & then fire: blast reduces collapse temperature ~600C & collapse speed with the ~same collapse mechanism as for fire only

Q&A

• Coupling element:
• "Bridge" between 5d.o.f. shell element (slab) & 6d.o.f. B-C element (frame)
• How?: using co-rotation deformation of B-C & shells to reduce the nodes
• Reference to rigid offsets
• Models:
• Deformation using coupled implicit integration scheme
• Rate-sensitive: Melbourne strain-rate relationship
• Material relationships
• Types:

1. Experiment à formulation
2. Absence of experiments: fit suitable relationships into experimentation

• Stainless steel à components à first, fire à then, blast
• FEM:
• Most concerned when running FEM:
• Simplest solution to be workable: in problems with suitable methods
• Efficiency of FEM
• Frontal solver à slot special elements à 1) elements à d.o.f. à solver
• Scheme:
• Static: use time-history analysis (no need integration for fire)
• Dynamic: use implicit integration with consistent tangent stiffness modulus à more steps, less speed, more accuracy à iterations @ both global level & member level