Civil and Structural Engineering Computing: 2001
Chapter 16 A. Nadjai, D. Laverty and M. O'Gara
School of the Built Environment, University of Ulster, Belfast, United Kingdom Keywords: masonry, walls, fire, thermal bowing, deflection, load, strain
A mathematical model is developed to simulate the lateral deflection response of axially loaded masonry walls subjected to elevated temperatures. The developed model is based on the method of slice approach dividing the wall into a series of discrete slices and generates 'through the thickness' changes in material properties and stress strain relationships. The transient nature of the fire process is modelled using a time step analysis applying thermal profiles derived from Lagrangian shape functions acting on temperatures at specific node points, the latter determined experimentally. To verify the model an experimental programme was conducted on scale model walls of different height and subjected to different loads. Use of theoretically based methods has gathered momentum in the last two decades, especially with the advances in computer technology. Computing power enables detailed evaluation of a dynamic transient process. The aim is to generate the fire process and develop a representative computer model. With sound knowledge of material properties and the effects of temperature, then computer models are capable of recreating the effects of material degradation and subsequent thermo-structural response. Analysis can be very complex and specialised, and designers may be unable to understand the intricacies of tools such as finite element. Unless thermal effects on material properties are thoroughly understood then computer models will be flawed. For example before Anderberg [1] no one understood the significant influence of transient strain on concrete response, theoretical models prior to this time therefore did not truly represent total strain response. Even today there is still very limited data available on material property response with temperature. One must also understand the effects of interaction of various parameters. The simultaneous combined effects of load and temperature acting in concrete specimens produces significantly different response than the additive effects applied separately.
The present work describes the development of one such approach, a mathematical
model to predict the deflection response of axially loaded concrete masonry walls in
fire situations. To validate the theoretical model a comprehensive suite of
experimental tests was conducted on walls of varying slenderness ratio and different
load. The methodology used for the experimental testing was unique in that
In fire separating elements such as firewalls, heat is usually exposed to one face. This is particularly important in the case of masonry materials due to its generally low thermal conductivity, producing high thermal gradients over the cross section [2]. If the wall is unrestrained this leads to differential thermal expansion of the material. With the hot face expanding more rapidly than the cool one, the unrestrained wall will tend to bow towards the fire. It has been the experience of may experimental programs [1,4] that in cases of high slenderness ratio thermal displacements may be of a magnitude to cause instability buckling. There has been little attempt to mathematically describe the thermo-structural behaviour of masonry walls. Free thermal bowing equations have been derived based on simplified conditions, which will be discussed herein. The present work attempts to develop these equations to situations of fixed end conditions, and applied axial loading.
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scale
walls were used, requiring an enhanced fire curve to generate thermal similitude in
model and prototype. The theoretical model considers internal equilibrium of axial
forces and moments and generates an equivalent linear strain and associated strain
gradient (curvature) from total strains through the wall cross section. The effect of
load and load eccentricity are incorporated by computing linear stress distribution
though the section using conventional structural mechanics. The combined effects of
temperature and stress are considered at discrete points through the wall and are
integrated through the section to compute the resultant wall curvature and
subsequent deflection. The model under pins the significant influence of Load
Induced Thermal Strain (LITS) on deflection response.