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 Structural Analysis Introduction Basic Principles Simple Calculation Methods Steel Members Composite Members Concrete Members Timber Members Masonry Members Finite Element Models General Principles Conceptural Models Assessment of Failure Sensitivity Assessment Validation

### Structural Analysis

 Model Simple element models Sub-models Advanced computer finite-element models Complexity Simple Intermediate Advanced Input parameters Temperature through the cross-section Material strength and stiffness reduction Applied static load Simplified boundary conditions Temperature through cross-section and along member Material strength and stiffness reduction Applied static load Boundary conditions Detailed temperature distribution Full material stress-strain-temperature relationship Thermal expansion properties Applied static load Boundary conditions Element type and density Accuracy Ignore real behaviour but assumed to be conservative Ultimate strength calculation Begin to consider actual load paths and restraint Ultimate strength calculation Predict strains and stresses, displacements and rotations for all members throughout the fire duration Localised behaviour may not be modelled accurately in whole building modelling Design tools Simple equations for hand calculations Simple equations for hand calculations Plastic design, redistribution of moments Simple computer models Commercially available or purpose written computer software

The simplest method for predicting the structural response of buildings in fire is to analyse individual members at the fire limit state using partial load and material safety factors, which take into account realistic loads at the time of the fire and actual material strengths. These methods are given in the codes and design guides and take into account the reduction in strength and stiffness of materials during a fire. Simple design methods, which are based on fundamental engineering principles, can be used irrespective of the fire model used. However, some empirical structural design methods can only be used with the standard time-temperature fire model, which were used to derive the methods.

Simple plastic design methods exist to consider frame behaviour in a fire. In the Eurocodes, frame behaviour is utilised to allow the effective lengths of continuous steel, composite and concrete columns to be reduced from ambient temperature values.

Following the Cardington full-scale fire tests a simple sub-structure design model for steel framed buildings with a composite floor slab was developed. The model is based on membrane action of floor slabs and allows the beneficial effect of the grillage of beams and floor slab, acting as a unit, to be included within the structural design. The approach can be used with any fire model.

The simple design models for individual members and sub-frames are assumed to be conservative but do ignore some aspects of the actual behaviour of real buildings. A possible design approach to predict more accurately the behaviour of buildings in fire is to use finite element modelling. The approach incorporates the stress-strain-temperature relationship of materials and can predict stresses and deformations throughout the whole structure. Expertise is required to use these advanced models and special care is required in defining the types of elements used, boundary conditions, localised behaviour and interpretation of the results. Although finite element modelling of whole building behaviour can provide a more accurate estimation of the structural response, over the full duration of the defined fire, they can be poor at predicting localised behaviour such as reinforcement fracture and connection failure due to the need to refine the element type and mesh density to adequately identify localised behaviour. All designs carried out using finite element modelling should consider the possibility, and consequence, of localised behaviour.

A radical finite element modelling could include the modelling of whole building to understand the global structural behaviour and locate any localised weak links, followed by refined modelling of the weak links to investigate any critical localised failure.

It is worth emphasising that the analysis of the structure will only be as accurate as the fire modelling and thermal analysis. Therefore the accuracy of all three components of the design should be considered when assessing the final analysis.

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