Loading Arrangement

To appropriately investigate structural modelling requires that the loading method is scrutinised to ensure different methods of applying a load give the results expected. This also enables any unforeseen model behaviour to be checked, such as element distortion and stress concentrations under concentrated loads.

The first method of applying loads was through steel plates designed to be identical to those used in the experiments, as discussed in Section 5.5.4. A separate method of applying a uniformly distributed load across the entire surface of the timber slab was used as a check to ensure any unreasonable element distortion did not occur in the steel plates or timber slab, and the contact pairs worked properly. This was simulated as a pressure across the entire upper

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surface, calculated to achieve the same bending moment as the point loads in the test conditions. In this way comparisons could be made between the results, as the displacement response should be relatively similar for these conditions, but not identical. The displacement response for Test B is shown in Figure 5-15 for both loading types.

Figure 5-15: Comparison between loading arrangement for 3D structural analysis

It can be seen from the figure that changing the loading arrangement had a small impact on the results. A greater displacement response is seen through much of the test duration, with almost identical failure times predicted for both loading arrangements. Considering the moment demand through the span of the floor and hence the deflected shape, this behaviour is as expected for comparisons between uniformly distributed loading and four point loading scenarios.

This proves that for this type of analysis a simplification of the loading arrangement to be a pressure across the entire top slab is therefore appropriate as the differences in displacement response are small.

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During the course of the structural modelling, a number of material models in ABAQUS were used and compared to determine which was the most appropriate for defining the mechanical properties of timber. As there are no predefined properties pertaining to timber as a material, and the creation of separate subroutines to do this requires an advanced programming knowledge of ABAQUS, the material models available were adapted to suit this purpose. This provides a unique challenge in that each material model has been derived for separate purposes, and applying these to timber in the fire state requires that many assumptions need to be made to adapt their use to timber appropriately. The different mechanisms of each of these material models need to be understood, adjusted for and in some cases manipulated to produce the behaviour desired.

The major material models investigated and described in this section are:

 Engineering constants – elastic. separate directions, hence orthotropic behaviour can be easily implemented, and a vast number of materials can be simulated using this model in ambient conditions. Once the thermal loads are introduced however, the model has no appropriate method of implementing plasticity but for defining a yield stress and a corresponding plastic strain. The stress-strain curve in this material model is used for both tension and compression which in turn limits its applicability to thermal problems in timber, or any material which exhibits significantly different tension and compression behaviour.

The steel model, as the name suggests, is primarily designed for use in modelling steel materials. The definition of linear elastic properties requires the assumption of elastic isotropy for the material. The model only allows for the definition of a modulus of elasticity and a Poisson’s ratio, and the modulus of rigidity is calculated from this using the generic relation

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shown in Equation 5-1. Hence as with the concrete damaged plasticity model, the calculated modulus of rigidity is much larger than is preferable for timber which impacts on the results.

Figure 5-16 shows the results of the four models plotted together with the original concrete

Figure 5-16: Comparison between material models for 3D structural analysis

It can be seen from Figure 5-16 that the variation in results for the material models is large.

Considering the elastic engineering constants analysis, the model shows a constant large over-prediction of displacement response throughout the test, and does not give meaningful results when identifying failure behaviour. Focussing on the plastic analysis, the improvement of the engineering constants model is questionable. The modelled displacement response became greater, hence this could be argued as worse as it was now further away from the experimental

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results. However a failure trend is now more discernible, and is seen from the figure to be very near to the concrete damaged plasticity model output.

The elastic steel model provides a much better approximation to the concrete damaged plasticity model output, with an over-prediction of stiffness occurring at approximately 37 minutes. It is clear that the elastic analyses cannot capture any failure behaviour, and the displacement results do not runaway at any stage.

Incorporating plasticity into the steel model has improved it from the elastic analysis, and is identical to the concrete damaged plasticity record with the exception of a very small deviation at 40 minutes. This is completely expected, as both the elastic and plastic inputs used are identical, although implemented in a slightly different manner. The downfall of the steel plasticity model is apparent when a larger range of analyses are conducted, as only a compression or tension stress-strain curve can be defined for general plasticity. Hence when a structure is analysed which fails in compression, with these inputs defined only for tension, unrealistic behaviour may result.

As previously discussed, a complete record of strain behaviour is required in order to properly characterise the behaviour of timber as a material. Inputs of properties such as strain can differ between material models, so much so that careful consideration of the model mechanics must be undertaken before simple analysis in order to obtain meaningful results.

The wide spread of results reinforces the importance in choosing an appropriate material model which can incorporate the desired behaviour of a real assembly. For any research considering timber assemblies, it is highly recommended that the concrete damaged plasticity model is used as a starting point, moving to other material models depending on the model behaviour desired.

5.8.4 Thermal Expansion

To determine the influence of the coefficient of thermal expansion on modelling, a parametric study is conducted varying the value of the coefficient parallel to the grain direction of the timber. Values of 0, 3.5 and 7.0 × 10⁻⁶ m/mK are compared in Figure 5-17 for Test B, where the value used in the numerical model is represented by a solid red line.

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Figure 5-17: Comparison between thermal expansion coefficient for 3D structural analysis

As the elements expand they tend to cause a build-up of stresses throughout the section, due to the uneven nature of the heating profile. This in turn causes the displacement response to be adversely affected from a structural sense as the section cannot support the same stresses it could if the thermal expansion was not present. It can be seen from the figure that the variation in displacement response is relatively low for the range of parameters modelled, with a higher coefficient of thermal expansion corresponding to a greater level of displacement throughout much of the test duration. The major impact of this parameter is seen during the latter stages of the simulation, where a larger proportion of the cross-sectional area of the floor is heated.

Ignoring the coefficient of thermal expansion completely results in a stiffer deflection response and a less conservative model. As a product of the modelling process the failure time predicted by the model is very similar regardless of what coefficient is specified (within a reasonable range as shown here). When the floor undergoes large displacements the effect of thermal expansion through the section becomes almost negligible due to the scale of the strains caused by the thermal expansion being nullified by the very large strains due to load displacement.

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