Loading Conditions

The loading arrangement simulated in the numerical model follows the experimental setup. The loads are assumed to be applied on a rigid steel plate. The plate was not included in the thermal analysis, and it was considered to be at room temperature for the duration of the simulations.

The load was applied to the top surface of the steel plate as a pressure. The applied forces were transferred to the timber surface through rigid ties between the plate and the slab surface.

The load is applied gradually during the initial stage of the analysis. This is implemented in a number of separate steps in ABAQUS for the simulations shown in this chapter. The final step is the heating step where the results of the transient thermal analysis are used as input for the fire duration modelled.

5.5.5 Boundary Conditions

In order to avoid element distortion and stress concentrations at the support points of the beam, the bearing area of the pinned roller supports was spread over two rows of nodes at the ends of

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the floor beams. The simulated span of the beam was adjusted to accommodate this so that the interior nodes were considered to be at the location of the pinned base connection.

The axes of symmetry shown in Figure 4-3 were maintained in the structural modelling. At these planes of symmetry the rotation and translation was fixed to ensure that a full floor was simulated in the model. For example, a plane of symmetry cutting through the length of the floor simulates fixed translational motion transverse to the span direction (the reaction force), and fixed rotation in both directions of that plane (the reaction moments). Hence the floor is ideally simulating a mirror image of each boundary.

5.5.6 Time-step and Solver Technique

In the structural analysis the direct sparse solver technique in ABAQUS was used, using Newton’s technique to solve the nonlinear equations with linear extrapolation. The model allowed for geometric nonlinearity. This is important for analyses where relatively large displacements in one plane may affect stresses in a perpendicular plane. Automatic time-steps were used to optimise the modelling procedure, and to ensure numerical stability in solution convergence.

5.5.7 Element Type

The element type used in the three-dimensional structural analysis is an eight node solid continuum linear brick with reduced integration and hourglass control. These elements have temperature and displacement degrees of freedom activated at each node which allow for the thermal input to be modified over a specified step time while conducting a stress analysis.

A study by Fragiacomo et al. (2010) found that for sequentially coupled thermo-stress analyses modelling timber in tension, the twenty node linear brick elements showed no noticeable improvement in results obtained with a significant increase in computational time required to run simulations. Due to the similarities between that study and the current research, the eight node linear brick element has been specified to economise the available resources. Figure 5-7 shows both the linear and quadratic solid continuum elements for stress analysis.

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Figure 5-7: Solid continuum 3D elements

In ABAQUS reduced integration is used to economise run time by using a lower-order integration to form the element stiffness matrix. This results in reduced run times, and usually provides more accurate results in three-dimensions as long as element distortion is limited.

Reduced integration also avoids issues with shear and volumetric locking.

Hourglass control is required with first-order reduced integration elements as the elements can distort in such a way that strain calculations at the integration points are zero, leading to further mesh distortion and instability. This is known as hourglassing, referring to the shape of the distorted elements.

5.5.8 Material Model

The concrete damaged plasticity model was used due to its functionality in allowing for different strength curves to be defined in tension and compression, which is a key aspect required for timber modelling. Further information on the material model and a detailed description of the model development is given in Section 5.6.

5.5.9 Thermal Expansion

Thermal expansion is extremely important to consider in structural analyses, as when the structure is restrained a change in temperature will cause a change in the stress state of the elements. In the case of modelling a floor in three dimensions, restraining the floor in any direction results in an increase in the stresses with an increase in temperature, hence proper definition of support conditions are paramount to ensure appropriate analysis.

Although the floor assemblies under study are simply-supported and free to move at one end, any additional expansion or contraction effects will influence the vertical displacement of the floor assemblies. The coefficient of thermal expansion is highly dependent on the moisture content, grain direction and temperature of the timber. Common values for softwoods parallel to the grain range from 3.0 − 4.5 × 10⁻⁶ m/mK (Glass and Zelinka, 2010; Weatherwax and

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Stamm, 1956), with both radial and transverse directions being approximately 8 and 13 times greater than the parallel to grain value respectively. Due to the lack of available data to determine the actual variation of the coefficient of thermal expansion for LVL, a set value of 3.5 × 10⁻⁶ m/mK was specified in the analysis. A parametric study into the effect of the thermal expansion coefficient is presented in Section 5.8.4.

As discussed in Section 2.7.2, the char which forms on the outside of timber as it burns tends to shrink, while a normally moist timber member exposed to a thermal gradient will also expand initially but would tend to shrink at higher temperatures as the moisture is driven off. In terms of a large timber member exposed to fire, some moisture is driven off while some is driven deeper into the section increasing the remaining moisture content of that section, and it is important to appropriately quantify how the entire member will behave and whether to incorporate thermal expansion effects. As the heated section of the timber is very small compared with the residual section for the majority of any fire duration, the effects of thermal expansion are likely to be relatively small on the global system when compared with a material such as steel.

For a timber floor assembly, the uneven expansion of the floor in the cross-section will be crucial in the concentration of stresses on that cross-section. This effect will increase as the heated portion of the floor increases, in other words during the latter stages of burning.

However, both radially and transversely the effects of thermal expansion will also be nullified by the presence of the shrinking char layer as the fire progresses. Hence for the following analyses an isotropic coefficient of thermal expansion of 3.5 × 10⁻⁶m/mK is specified.