B.A. Izzuddin

An integrated adaptive environment for fire and explosion analysis of steel frames - Part I: analytical models

Abstract This paper presents a new method for the nonlinear analysis of steel frames subject to fire and explosion loading conditions. The proposed method subsumes conventional nonlinear analysis in that it can be applied to the two cases of fire and explosion loading in isolation and, more significantly, within the same analysis. The resulting integrated approach can therefore be used to study the behaviour of steel members and frames subject to scenarios of explosion loading followed by fire, effectively enabling the influence of explosion on the fire resistance to be evaluated. The paper describes the component beam-column formulations and discusses their incorporation within an adaptive analysis framework, which is largely responsible for the considerable efficiency of the proposed method. Details of the required elasto-plastic material models are finally presented, including the adopted models for steel subject to elevated temperatures, creep and high strain-rates. The companion paper provides several verification and application examples, using the nonlinear analysis program adaptic , which demonstrate the accuracy and efficiency of the proposed method, and which investigate the influence of explosion on the fire resistance of steel members and frames.

An integrated adaptive environment for fire and explosion analysis of steel frames - Part II: verification and application

Abstract The companion paper presents a new adaptive method for integrated fire and explosion analysis of steel frames. This paper verifies the new developments, implemented within the nonlinear analysis program ADAPTIC, particularly against the results of experiments on steel members and frames subjected to fire. The benefits of adaptive nonlinear analysis are then highlighted by means of an example which demonstrates its computational superiority over conventional nonlinear analysis. Finally, parametric studies on column and frame configurations subject to the successive actions of explosion and fire are undertaken using the developed integrated analysis tool. The results of these preliminary studies indicate that the damage induced by moderate explosion loading can significantly influence the fire resistance of steel structures. Collectively, the capabilities and efficiency of the developed environment emphasise the important role that it can play in further studies aimed at generating design guidance.

Analytical assessment of the structural performance of composite floors subject to compartment fires

The behaviour of composite steel-concrete building floors exposed to fire conditions is examined in this paper. The work represents part of a large project dealing with the numerical modelling and assessment of structural behaviour based on the fire experiments undertaken on a full-scale multi-storey steel-framed building at Cardington, UK. After providing brief details on the analytical tools and modelling approaches adopted in this investigation, the structural models constructed to simulate the fire tests are described and salient findings are highlighted. Although the detailed models provide some insight into key behavioural aspects such as the paramount influence of restraint to thermal expansion, the complex structural interactions that occur under fire conditions may not be readily demonstrated. In order to illustrate a number of underlying response mechanisms, the analytical results obtained from an idealised structural system, in which a single compartment is subjected to fire, are summarised. Assessment of the structural response using such simplified models provides a clear interpretation of the behaviour and, with further refinements, may be employed for undertaking detailed studies aimed at developing improved design recommendations.

Conceptual issues in geometrically nonlinear analysis of 3D framed structures

This paper aims to clarify some of the conceptual issues which are related to the geometrically nonlinear analysis of 3D framed structures, and which have been a source of previous confusion. In particular, the paper discusses the symmetry of the tangent stiffness matrix and the nature of the element end moments. It is shown that a symmetric tangent stiffness matrix can always be achieved for a conservative system if the nodal equilibrium equations, including the equations which describe moment equilibrium, are identical to those derived from a variational energy approach. With regard to the element end moments, it is suggested that any definition can be adopted in formulating the geometrically nonlinear element response. Furthermore, it is proposed that any definition for nodal rotations expressing a unique vector transformation may be adopted without compromising modelling accuracy. The argument of this paper is validated with reference to three variants of a large displacement analysis method for 3D frames, where several illustrative examples are utilised.

An efficient beam-column formulation for 3D reinforced concrete frames

Abstract This paper presents a new beam–column formulation which can be used for the accurate, yet efficient, modelling of 3D reinforced concrete (R/C) frames. The formulation is intended for modelling the nonlinear elastic behaviour of a whole R/C beam–column with only one element, which is an essential ingredient of adaptive elasto-plastic analysis. On the longitudinal axis level, quartic shape functions are used to represent the two transverse displacements. A constant axial force criterion is employed instead of shape functions for the axial displacement, which is largely responsible for the accuracy of the proposed formulation. For concrete, the formulation assumes a nonlinear compressive stress–strain relationship and no tensile resistance; whereas for steel, a linear stress–strain relationship is utilised. On the cross-sectional level, the formulation is capable of modelling the interaction between the axial force and the biaxial moments for a general R/C cross-section, with explicit expressions obtained using a novel approach based on integration over triangular subdomains. The paper provides the details of the proposed formulation, and presents several verification examples to demonstrate the accuracy of this formulation and its ability to model the nonlinear elastic response of reinforced concrete beam–columns with only one element per member.

Numerical modelling of the structural fire behaviour of composite buildings

This paper describes numerical models constructed to simulate the response of composite steel/concrete building floors under fire conditions. In particular, this study deals with two of the fire tests recently undertaken on a full-scale multi-storey building at Cardington, UK. The analysis is carried out using a structural analysis program which accounts for both geometric and material nonlinearities, and which includes temperature-dependent constitutive models for steel and concrete materials. The approaches used to represent the various structural details are discussed, and the procedure employed for incorporating the experimentally measured temperature profiles and histories is outlined. For the two tests considered in this investigation, the numerical results are in general agreement with the experimental data, particularly in terms of the magnitude of vertical deformations induced in the floors at elevated temperatures. Close examination of the numerical and experimental findings provides an insight into the complex interactions that occur in the structure at elevated temperatures. Most significantly, the influence of the restraint to thermal expansion of the heated floor area, which is provided by the surrounding parts of the structure, is shown to be of paramount importance. The increasing confidence that can be placed in numerical models as well as the improved understanding of the structural fire response may be used in developing more realistic and cost-effective design methods which are based on the actual structural response rather than that of isolated members.

Response of idealised composite beam–slab systems under fire conditions

Abstract This paper presents a numerical model for beam–slab floor systems in which a single compartment is subjected to fire. The system consists of a composite steel–concrete slab and a bare steel beam. Several idealisations are made in order to illustrate important behavioural patterns which occur under fire conditions. Nonlinear analyses are undertaken using an advanced yet computationally efficient computer program which accounts for the large displacement behaviour at elevated temperatures. The model is shown to capture the main parameters influencing the performance of the system under fire. In particular, the significance of axial restraint and thermal expansion on the overall deformation and capacity of the system is demonstrated. It is indicated that thermal expansion may have beneficial as well as detrimental consequences on the performance, depending on the particular structural configuration under consideration. The paper also closely examines the level of dependency of the response on the sequence of application of loading and elevated temperature as well as the assessment of the overall system response from consideration of the respective responses of individual components. It is shown that such concepts may be effectively employed in undertaking detailed studies for improved quantification of the fire resistance of beam–slab systems with a view to the development of more rational performance-based design procedures.

Efficient nonlinear analysis of elasto-plastic 3D R/C frames using adaptive techniques

Abstract This paper presents a new nonlinear analysis method for three-dimensional reinforced concrete (R/C) frames employing adaptive analysis concepts. The first two components of the proposed adaptive method, namely the elastic and elasto-plastic beam–column formulations, are described. The details of automatic mesh refinement, which is the third component of the adaptive method, are then presented. These include the construction of an effective interaction surface representing generalised stress states at the elastic limit, the determination and checking of generalised stresses for exceeding the elastic limit along an elastic element, and the refinement of an elastic element into an appropriate number of elastic and elasto-plastic elements. Examples are finally presented to illustrate the accuracy and efficiency of the proposed analysis method.

Nonlinear analysis of masonry structures using mesoscale partitioned modelling

This paper presents an effective and accurate computational strategy for unreinforced brick masonry structures. Mesoscale descriptions allow a realistic representation of the nonlinear structural behaviour of URM, but can pose prohibitive computational demands for large-scale problems. To overcome this drawback, the computational strategy presented in the paper employs the domain partitioning approach, which is coupled with an accurate mesoscale finite element model. This allows the effective parallelisation of the nonlinear structural analysis simulation, where significant speed-up can be achieved in the nonlinear analysis of large masonry structures. The potential and effectiveness of the proposed computational strategy are shown through numerical examples, where full-scale masonry structures are considered.

ADAPTIVE SPACE FRAME ANALYSIS. PART I: A PLASTIC HINGE APPROACH.

This is one of two companion papers presenting new procedures for the efficient largedisplacement analysis of steel frames in the elasto-plastic range. Emphasis is given in this paper to the development and improvement of a plastic hinge approach utilizing the concept of adaptive mesh refinement. In the companion paper, such a concept is discussed in the context of a more accurate approach accounting for the spread of plasticity. The proposed plastic hinge approach is formulated through the extension of an earlier 3D elastic quartic element into the inelastic domain, where a general surface is suggested for representing plastic interaction between the axial force and the biaxial moments. The numerical problems associated with the formation of adjacent plastic hinges as well as the case of pure axial plasticity are highlighted, and methods for dealing with such problems are discussed. The efficiency of the proposed approach derives partly from the ability of the quartic formulation to represent beam-columns using only one element per member, but more significantly from the utilization of adaptive mesh refinement. The latter consideration is shown to have particular advantages in elasto-plastic analysis of braced structures. The methodology presented in this paper and implemented in the nonlinear analysis program ADAPTIC, is verified in terms of robustness, accuracy and efficiency using a number of examples including geometric as well as material nonlinearity effects.