Introduction and Reference Case

With the developed FE modelling process, it is now possible to explore the effects of various parameters within the system. This allows further analysis to take place and the quantification of the impacts of various changes to the setup of the system.

The study considers the following aspects:

a. Bay dimensions – beam length, slab span, aspect ratio

b. Panel position – above the top flange of the beam or sitting on bottom flange c. Shear connection

d. Inter-panel connection

e. CLT panel make up and layout – standard panels vs. designed panels

The remainder of this chapter will cover the findings of the parametric study analysed with a focus on different subject areas.

6.2.2 Further Model Development – Implementation Process

Following on from the preliminary models described in section 4.3.3, and the validation and

development that is discussed through the remainder of Chapter 4 and Chapter 5, a modelling approach has been developed to explore the quantification of composite action. The key changes from the models used in Chapter 4 are:

• Modelling individual laths in CLT

• Modelling of the glue layers in the CLT panels, represented as shell elements (see Figure 6.1) • Inclusion of yield points in the material model to make material failure visible

The type of shear connection (nail plate and the hypothetical helix connector) as well as the panel to panel connection have been incorporated into the model for use and comparison in investigations.

As the complexity of the models increases in order to take into account a variety of features of the system, the analysis times increase exponentially. Inclusion of the glue layers, the plasticity of timber and the shear interface, the discrete modelling of the panel slats, and the large number of associated

frictional contacts that must be modelled all increase the solution time significantly. To counter this, it is advantageous, from a computational cost perspective, to use symmetry in order to halve or quarter the required number of elements and contacts. This was done during the modelling of the CLT-ASB system. In the system being analysed, symmetry is utilised at the centre of the beam (both along the centre of its cross-section and at the midspan point), and the centre of the span of the CLT panel. At these positions, the equivalently behaving system has a restraint on the rotation of the elements and the translation of the element along one of the horizontal axes, but allows vertical deflections to occur, i.e. a roller- moment support (see Figure 6.2)

Within ANSY there are a number of potential methods of restraining parts of the model, and one such method, the “Remote Displacement” constraint, appears to allow these rotations and translations to be defined exactly as necessary. However, the experience of the author is that whilst the nature of the definitions suggests it will behave as desired, in actual fact the rotations are not constrained as expected; deformation in other axes are affected which can lead to the solution not converging and plasticity to develop in unusual locations and in an erratic manner. A more effective option is to use the

"Frictionless Support” constraint, which behaves in a more predictable manner, though horizontal movements of the overall system must be controlled by other constraints.

6.2.3 Reference Case - Effective Width Determination

To provide a comparison point against which the effect of changes and variations in the system characteristics can be measured, a reference case setup was selected, and is outlined here. Each subsequent model created for the study of the effect of different parameters will have the same

characteristics as this case, save for the parameter under consideration. The one exception to this is the study of slab position, where the shear connection was assumed as bonded instead of the nailplate, and compared to the reference case with a bonded shear connection.

The response is sought against an imposed load of 2kN/m2 _{applied as an area load in the model, whilst} the effect of gravity is omitted to limit the number of variables – the large deflection option (which allows for 2nd _{order effects in ANSYS) is utilised, meaning the inclusion of gravity loads may obscure} deflection relationships by enhancing deflections. This will allow repeats of the finite element study to be performed with larger or smaller imposed loads and comparison to be made without needing to compensate for the gravity induced deflections and stresses.

The beam ends were modelled as simply supported, with fixity in the horizontal plane of its mid-span (due to the symmetry constraints, as detailed in section 6.2.2), and freedom to move longitudinally at the end. This was to prevent further stresses being induced or the deflection (taken at mid-span) being reduced because of restricting the curvature and movement of the beam.

The “reference case”, as it will from hereon be referred to, is of the following configuration: • Beam span: 6m

• CLT panel: KLH 230ss, spanning 9m, one-way • Shear Connection: nail plate

• Inter-Panel Connection: Assumed infinitely strong/stiff bond between panels in tensile zone

The nailplate shear connection was assumed, included as a single part at the interface of the ASB bottom flange and the CLT panel. A 280ASB74 section was modelled, in conjunction with a series of 7ss230 KLH CLT panels. Between the panels, an inter-panel connection was modelled as a perfectly bonded tensile zone only connection – in practice this means the bottom two layers of the 5-layer panels were joined together using a bonded contact, as shown in Figure 6.3.

The concept of an effective width is a means of simplifying the design and analysis of a composite beam section. It helps quantify how much of the floor slab contributes stiffness to the composite section, and therefore is a key part of addressing Research Question 3. As described in detail in section 2.2.2, the effective width is derived from the distribution of longitudinal stress (or strain) in the floor slab. The set-up of ASB and CLT panels was replicated in a finite element model (shown in Figure 6.4) from which the response of the system in terms of stress distribution could be extracted.

To extract the stress trace from the finite element model results in ANSYS, a linearized stress output was utilised. The trace gives evidence of the actual effective width computed by the simulation, with sampling points taken from equally spaced locations along a defined path. The magnitude of the stresses should be related to the ability of the shear connection.

The laminar nature of CLT combines with the anisotropic character of the parent timber to the result that the only layers giving meaningful contribution to the composite section are those with planks running parallel to the beams. These layers have their stiff axis in the correct orientation to contribute. The position of sampling was selected as just below the extreme fibre of the CLT layer in the

compression zone with its longitudinal axis running parallel to the beam – if the layers in a CLT panel are numbered consecutively from bottom to top, then layers 1, 3, and 5 are orientated perpendicular to the beam, whilst layers 2 and 4 run parallel to the beam and contribute to the composite section.

The extreme fibre of layer 4 was selected so the largest stress the CLT was subjected to could be extracted. However, the stress result is affected by the edge effects, meaning it was more

representative to take measurements at an offset from both the top faces of the longitudinal oriented CLT layers (by 1mm) and the centre of the beam span (the boundary of the model as formulated). These characteristics are the same for all effective width outputs detailed in this section

Figure 6.5 shows an example ANSYS output of longitudinal stress when taken across the CLT panel at the midpoint of the beam span, whilst Figure 6.6 shows the same output at an offset of 100mm from the model edge. Comparing the two figures one can see that end effects are playing some role, as both the shape of the stress curve and the magnitude of the maximum stress measured are different, with the larger stress occurring in the trace taken at an offset. Further, the maximum stress in the trace taken at the model edge does not occur at the first sampling position (denoted by a white tag containing the number “1”) which is the value used to compute the effective width approximation. As such, these two factors have a distorting effect on the calculated effective width and the effect is not consistent, meaning sampling at an offset is a more appropriate data set for calculating effective widths. This methodology is followed for the remainder of the parametric study.

Figure 6.4 - Components of finite element model, with false colour highlighting: ASB (red), shear connection (green) and CLT panels (yellow)

The output trace of stresses for the reference case is given in Figure 6.7 as the blue circles. Also shown is the derived effective width, computed as detailed in section 1.4.4. For this, case the effective width has been calculated as 2.99m (noting that the trace only displays one side of the beam, whilst

symmetrical stress distribution is present). This result set will be used as a reference for comparison to determine the impact of various design changed. Deflection was found to be 12.39mm under the defined loading. This compares to 13.12mm that was found when the shear connection was removed and replaced with frictional contacts to represent the non-composite case. In these results, “composite benefit” is defined as the reduction of beam midspan deflection when compared to this non-composite case, expressed as a percentage of the non-composite deflection. For example, the result for the

reference case represents a composite benefit of 5.6% using a nail-plate shear connection, rather than a non-composite connection.

A maximum stress was found at the edge of the CLT panel closest to the beam, with a value of

1.06N/mm2_.

Concrete-Steel composite sections show a complex relationship between effective width, the beam span, and the position at which the measurement is taken. This appears to also hold true for CLT-ASB composite floors. Figure 6.8 shows a plot of the longitudinal stress in the CLT layer subject to mostly compressive loads, and demonstrates how the level compressive stress is at its maximum at the centre of the beam span (disregarding the visible end effects), and reduces towards the supports. However, the situation is more complex as can be seen in Figure 6.9.

Figure 6.9 displays the same data as regions of longitudinal compression and tension, and what is clear is that large portions of the CLT layer that are in the “compression zone” of a composite section are experiencing tension. The equivalent plot of layer 2, the contributing layer in the tensile region shows a corresponding compression in the same region which demonstrates that the panel is hogging in those areas rather than sagging under the distributed imposed load. The plate is deforming into a saddle shape that is characteristic of an elastic plate that is supported on two opposing sides only.

0.00 0.20 0.40 0.60 0.80 1.00 1.20 -0.5 0.5 1.5 2.5 3.5 4.5 C O M P R E S S IO N S T R E S S ( N /M M 2) POSITION (M)

Longitudinal Compression Stress

6x9m Nail-Plate connection (Reference) Eff. Width

Whilst this deformation is reasonable, it has the effect of obscuring the measurement needed to determine the effective width closer to the supports – the tensile stresses when included in the calculation will disrupt the summation, and it is not possible to separate the stresses due to composite action from those due to the edge support conditions. A further complication is that, rather than matching the standard result from plate theory of a plate simply supported on two sides, the supports (steel beams) are in fact flexible, and have variable stiffness (from the perspective of the floor plate) along the sides.

Figure 6.8 -Plan view of longitudinal stress plot in layer 4 (parallel to the beam)