04.07 Panel Bending
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Introduction
Panels as two-dimensional thin elements may, from a structural analysis point of view, be considered as plates. Analytical procedures for the detailed response of plate elements can become very complex. Timoshenko produced a series of complex equations providing solutions for standard cases, otherwise specific solutions need to be developed from first principles. Alternatively, testing could be utilised to assess a particular panel’s performance. However, from a practical analytical viewpoint a simplified approach based on the likely load paths and load distribution should enable an initial qualitative assessment of the panel response. From this a simplified quantitative solution can be found that may be considered a suitable basis for design bearing in mind the limiting assumptions.
Load Distribution
The manner in which a panel distributes load will depend upon the nature of the applied load, the size and shape of the panel, the panel thickness, the build up of the panel cross-section, and the nature of the supports. Most panels within the cladding envelope are loaded orthogonal to the panel surface, e.g. Wind loading, and the panel thickness is small in relation to its span. image. Such panels act predominantly in bending. The presumption here will be that the cross-section may be considered as contiguous, the response of composite sections is dealt with in detail elsewhere.
Wind loading applies a uniformly distributed pressure over the whole panel surface and the panel will deform in response. It is the nature and form of this deformation that distributes the load on the panel to any adjacent supporting elements. The nature of particular fixing details can have a significant influence upon localised stresses and strains. The manner in which a panel will deform in response to a uniformly distributed loading will depend upon whether the panel is considered to be ‘one-way’ or ‘two-way’ spanning. In terms of support conditions these two situations are analogous to ‘2 edge’ and ‘4 edge’ supports. However, care needs to be exercised with regard to the support criteria, because depending upon the panel dimensions, even though the panel may be supported on 4 edges, the panel may still act principally as a one way spanning beam.
When a panel is supported on two opposing edges the panel will simply deflect, distributing any applied load to the supports, as a normal beam element spanning in only one direction, image. When four edge support is provided the panel bends in two directions, distributing load to all four edges, which causes the panel to attempt to ‘dish’, image. Load is distributed to all four edges and for a square panel equal load is carried at each edge, image. The nature of this ‘dishing’ (two-way curvature), is influenced by the dimensions of the panel. When the panel is square a uniformly distributed load is shed evenly to all four edges, but as the panel becomes more oblong less and less load is transferred across the longer dimension the panel becomes predominantly single spanning across the shorter span, image. Once the panel dimensions exceed the ratio 3:1 it will normally be appropriate to consider the panel as one-way spanning, regardless of any support along the shorter edges.
The structural design of the panel will then follow from the presumed load distribution. With the spanning arrangement determined, the analysis follows that for a normal beam, which can utilise simple bending theory. Due care and attention will need to be paid with respect to load reversal in terms of any composite panel cross-section.
As with any beam component, the nature and type of edge fixing detail will impact upon how the panel can deform and thus influence load distribution. A ‘pinned’ support will allow rotation, whereas a ‘fixed’ support will provide rotational restraint. Most practical fixing details will lie somewhere between these two extremes, but for design purposes a decision will need to be taken as to that most applicable to the situation being considered. Load reversal will need attention to ensure any fixing detail is adequate under both positive and suction wind pressures.