Technically speaking: Understanding strength | 41
FLEXURE MATTERS
Dr Morwenna Spear of the BioComposites Centre asks ‘Why do we subconsciously default to bending to understand strength?’
year or two ago I really enjoyed reading a book by Roland Ennos called The Wood Age: How one material shaped the whole of human history. In it, we see example after example of how the Bronze Age, the Iron Age and right through to the Industrial Revolution and the Modern Age, wood has been the key ingredient that is taken for granted, but should really be the star of the show.
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I’ll let you read it to find out more, but one thing that jumped out to me very early in the book, given that Roland’s background in academia is biology, anthropology and primate behaviour, was his comment about how our earliest ancestors understood wood very well. In fact, the flexibility of green wood, and then the rigidity of dried wood is key to the transition from a forest-based life into a life of early hominids on the plains and savannahs. Now, bear with me here for the connection
to the theme for this edition’s technically speaking article.
What I notice, whether I am talking to students, or to inventors of new products, or business people looking at their innovative wood panels, is that the first thing everyone does when a sample is passed round is try to flex it. It’s like a subconscious response. Maybe this is still hard wired into our psyche – is this wood piece strong enough to stand on? How flexible is it? Will it break easily for me to use? So, the next article in our series about essential tests for wood-based
panels is the three-point bend test. In the photo you can see an improvised
four-point bend test – two thumbs press on one side of the sample and the two hands are creating force in the opposite direction. In our laboratory we use three points of contact instead. Two supports set the required distance apart, and a central point load is applied. This causes the piece to flex and the force required is recorded, along with the deflection at that moment in time. The force and deflection can give a simple graph, usually with a steady gradient initially and eventually decreasing in steepness before breakage occurs. A stress strain curve can also be plotted, and is more useful. Here we use the engineer’s bending equation to take the cross-sectional area of the panel into account. Why? Well, the thickness of the panel will have a strong effect on the stiffness. We need to take into account the cubed value of the thickness (height) but only the linear value of the width of the sample. We can calculate the modulus of elasticity (MOE, or stiffness) using the formula below, with values for load and deflection taken from the straight section of the curve.
MOE = (Load x span3 ) (4 x deflection x width x height3 )
This formula has handily incorporated the second moment of area for a rectangular
beam into the MOE equation, given that any wood-based panel is likely to provide a rectangular cross-section.
If we look at the stiffness of I-beams, the shape, with a wide flange at top and bottom and only a thin central web, would mean the equation needs adjusting. Thinking about I-beams helps you realise that stiffness can be increased by moving the upper and lower faces further apart, while not increasing the area of the centre – the web is essentially transferring tensile and compressive load from the outer faces, and resisting shear. This brings us to the third point, that when we design wood panels, especially particleboard, with three layers, and the outer faces are higher density than the core, we are again tapping into this concept. Putting the strongest material in the outer faces increases the stiffness. As long as the core is sufficiently well bonded to transfer load between the two, then the panel will achieve good stiffness. A final thought in closing. As wood-based panels can be made in many different thicknesses, the span of the EN 310 test needs to be adjusted to suit the thickness of the panel. The aim is to make sure there is an equal chance of avoiding shear behaviour in this central region. Thus, the test piece needs to be long enough to allow a span of 20 times the thickness of the panel. For an intuitive and very straightforward test, there is some clever engineering supporting it. ●
Above: An improvised four-point bend test – two thumbs press on one side of the sample
www.wbpionline.com | February/March 2025 | WBPI
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