A short reflection on the model so far

So far we've set up or model based on a simply implementation of the Bernoulli - Euler beam equation.

We're only considering bending due to moments created by forces applied in the vertical direction and have ignored bending due to shear forces acting on the board (which in most cases is reasonable). The model is a small deflection model (and we need to keep our eye on this) and is a based on linear elasticity ( i.e it assumes that the elastic properties can be modelled by simple springs).

According to the wikipedia source ( I have not confirmed ) the large diflection considerations only need to be applied when the radius of curvature at any point is less than 10 times the baord thickness. In our case this is going to less than 15 cm which obviously we would never reach.

Thinking about stiffness in terms of E,I and L, gives quite a usable way of thinking about designing flex. Although the model is (necessarily) simple you canhopefully see that it has already provides some great insights into the relationship between many of the board parameters that we play with when designing boards: E captures the contribution of the core materials, I the geometry including concave and channels, width thickness and L the length.

One glaring omission from this list is the laminate and layup schedule ( i.e how many layers, what orientation the fibres have, the type of resin and reinforcement etc). The answer fairly obviously lies in the the values and way you use E.


Unfortunately, its not quite as straightforward as constructing the value of 'I' by building up more complex shapes by adding and subtracting various pieces. While we do build up a piecemeal model of the 'E' structure of the core the laminate itself needs a simplifying model to make dealing with the complexities of the load transfer between the resin and reinforcement. We are of course going to choose the simplest model ( good old engineers approach!) called the Slab Model which will yield an 'effective' E for the composite material that we will be able to make use of in building up our 'jigsaw' of different 'E' materials.