J. M. Rotter

Fundamental principles of structural behaviour under thermal effects

Abstract This paper presents theoretical descriptions of the key phenomena that govern the behaviour of composite framed structures in fire. These descriptions have been developed in parallel with large scale computational work undertaken as a part of a research project (The DETR-PIT Project, Behaviour of steel framed structures under fire conditions) to model the full-scale fire tests on a composite steel framed structure at Cardington (UK). Behaviour of composite structures in fire has long been understood to be dominated by the effects of strength loss caused by thermal degradation, and that large deflections and runaway resulting from the action of imposed loading on a ‘weakened’ structure. Thus ‘strength’ and ‘loads’ are quite generally believed to be the key factors determining structural response (fundamentally no different from ambient behaviour). The new understanding produced from the aforementioned project is that, composite framed structures of the type tested at Cardington possess enormous reserves of strength through adopting large displacement configurations. Furthermore, it is the thermally induced forces and displacements, and not material degradation that govern the structural response in fire. Degradation (such as steel yielding and buckling) can even be helpful in developing the large displacement load carrying modes safely. This, of course, is only true until just before failure when material degradation and loads begin to dominate the behaviour once again. However, because no clear failures of composite structures such as the Cardington frame have been seen, it is not clear how far these structures are from failure in a given fire. This paper attempts to lay down some of the most important and fundamental principles that govern the behaviour of composite frame structures in fire in a simple and comprehensible manner. This is based upon the analysis of the response of single structural elements under a combination of thermal actions and end restraints representing the surrounding structure.

A structural analysis of the Cardington British Steel corner test

This paper presents a structural analysis of the Cardington British Steel Corner Test. The test is analysed using ABAQUS, the commercial finite element program. The results of the analysis indicate that the response of the structure is dominated by the effects of thermal expansion and that material degradation and gravity loading are of secondary importance until very late in the test. It is noted however that at extreme temperatures a significant load carrying mechanism is tensile action in the reinforcement mesh and that gravity loading can effect the magnitude of the tensile forces produced. The results suggest that one method of helping maintain structural integrity in composite structures during extreme fires is to ensure that a sufficient amount of ductile reinforcement is present in the concrete floor slabs.

Composite beams in large buildings under fire -- numerical modelling and structural behaviour

A good engineering assessment of the fire safety of a building structure should be based on a sound understanding of the mechanics of its behaviour under fire. Existing standards and methods of design for fire assume that the structural behaviour is effectively the same as that at ambient temperature, allowing for the reduced material properties. This simple assumption is valid for statically determinate structures, but is in serious error for highly redundant structures, and may be unconservative in certain cases. In particular, the effect of thermal expansion is generally ignored, even though it may swamp the effects of all other phenomena in a large highly redundant building under a local fire. This paper presents some of the results of an extensive investigation (Usmani et al., DETR-PIT project, final report (draft), March 2000) in which the structural action in a two-way slab and composite beam structure subjected to a compartment fire has been explored. These results show that thermal expansion dominates the response of highly redundant structures under local fires, and that local yielding and large deflections can be beneficial in reducing damage to the complete structure. However, it is now clear that explicit cognisance should be taken of thermal expansions in design calculations, but this can only be done when a thorough understanding of the behaviour, appropriately generalised, is in place. This is the main motivation behind the results presented in this paper.

The Behaviour of Locally-Supported Cylindrical Shells: Unstiffened Shells

Abstract Many metal silos and tanks are locally supported on columns or other discrete supports to permit easy access beneath the vessel. The discrete supports introduce local forces into the cylindrical shell, which in turn produces zones of local high axial compression. The strength of compressed cylindrical shells has long been known to be governed by buckling considerations, but the buckling strength of discretely supported cylinders has only been investigated in recent years. Design rules which pre-date this study were empirical in nature and not based on rigorous buckling calculations or tests. In the present study, the theoretical buckling behaviour in the elastic–plastic range has been found to be so complicated that much work is needed to define the buckling strength for the purposes of structural design. This paper presents a description of the linear and nonlinear behaviour of isotropic unstiffened cylinders which are discretely supported at the lower edge. Much of the information given here is vital to the development of a more reliable design rule for shells under these loading conditions.

Structural behaviour in fire compartment under different heating regimes — Part 1 (slab thermal gradients)

Modelling the full-scale Fire Tests at Cardington has led to new understanding of the behaviour of structures under fire conditions. Much of this understanding has come from parametric explorations using models verified against the tests. The structural phenomena observed in highly redundant, composite structures, during a compartment fire are dominated by restrained thermal expansion. The large deflections experienced in the structural elements in the region of the fire are almost entirely attributable to thermally induced strains. The mechanisms responsible for producing these large deflections are restrained thermal expansion and thermal bowing. Material degradation and loading are secondary influences. A clear understanding of the response of the structure to an average temperature increase and through depth temperature gradients is essential. This paper discusses the structural response when subjected to different heating regimes obtained by changing the mean temperature and temperature gradient applied in the concrete slab of the composite floor slab system to a computer model of the British Steel restrained beam test.

Plastic buckling of rings at steel silo transition junctions

Abstract Elevated steel bins and tanks typically consist of a cylindrical vessel, a conical hopper and a skirt. The intersection of these three shell segments is termed the transition junction and is subject to a large circumferential compression. A ring is often required at this junction. The high circumferential compression at the intersection may lead to a buckling failure of the ring. Elastic buckling of the ring at the transition junction has been studied recently, but very little is currently known about the plastic buckling of such a ring. This paper presents a theoretical investigation into the plastic buckling of the transition ring using a finite element analysis. Simple annular plate rings are studied first, and the results are compared with the few known predictions from an earlier study. The plastic buckling of T-section rings is then explored.

Structural behaviour in fire compartment under different heating regimes - Part 2 (slab mean temperatures)

The effect of varying the thermal regime in a highly restrained composite beam in a steel frame structure is studied using a finite element model. The variation of through depth thermal gradients in both directions of the orthotropic slab was studied in the first part of this paper. In this part the effect of varying the mean temperature increase in the slab is investigated using the same model of the British Steel restrained beam test.

Recent research on the behaviour and design of steel silo hoppers and transition junctions

Abstract This paper presents a summary of recent research on the behaviour and design of conical steel hoppers and transition junctions in both uniformly supported and column-supported circular steel silos. The hopper in a steel silo supports the majority of the weight of the stored bulk solid and can fail in several different modes including membrane yielding and meridional rupture. The junction between the hopper, the cylinder and the skirt is termed the transition junction. It is subject to a large circumferential compression which arises from the meridional tension in the hopper and is therefore often strengthened by a ring. The transition junction can fail by elastic or plastic buckling of the ring or by plastic collapse of the hopper/cylinder/skirt/ring junction. A comprehensive picture of the behaviour and design of hoppers and transition junctions in a uniformly supported silo is presented, and several important design aspects of hoppers and transition junctions in column-supported silos are discussed.

Plastic collapse of restrained steel silo hoppers

Abstract Elevated steel silos and tanks commonly consist of a cylindrical shell, a conical hopper and a skirt. Much of the total weight of the stored material is supported by the hopper, which is in biaxial tension and may fail by forming a plastic collapse mechanism. This paper examines the plastic collapse of hoppers which are sufficiently restrained by a ring at the hopper/cylinder junction for the collapse mode to be entirely confined to the hopper. The hopper joints are assumed to be stronger than the shell plate. An elastic-plastic finite-element program is used to study the plastic collapse behaviour of these hoppers. It is found that the plastic collapse mode is usually a local mechanism near the top of the hopper. Collapse strengths are determined for hoppers of both uniform thickness and varying thickness subject to internal pressure with and without frictional shear. Most of the calculations are performed using elastic-plastic small deflection theory, because this leads to well-defined collapse strengths and relates to classical limit analysis. Calculations made using large deflection theory show that the non-linear changes of geometry have a significant stiffening and strengthening effect. The parametric study presented in this paper defines a simple lower bound to the strength of the hopper.