What the solve is, and isn't
We've worked our way through nine steps so far in this learning pathway, and there are several things they all have in common: every analysis assumed
- that linearly elastic material behaviour was maintained,
- that the resulting deformations of the structure are small by comparison to the size of the structure,
- that all loads were applied statically. This last assumption means that we can safely assume static behaviour since the magnitudes of any inertia forces are negligible.
In this final step, we'll make sure these limiting assumptions are understood and that we have a clear picture of where we might expect them to break down and invalidate our analysis.
1.0 Linear, static, elastic
Linearly elastic material behaviour means the material response is proportional to the load. Consider one of our truss members in tension. If we double the axial load, we double the member elongation. Scaled up to a full structure where each member maintains linear elastic behaviour, all of the results that capture the structure's response obey this linearity between applied load and structural response. Another way to describe this behaviour is to say that we never observe plastic behaviour in the structure.
Static means the loads are applied slowly and remain constant (their magnitude doesn't change once fully applied). This means we do not consider inertia forces, and as a result, common dynamic effects such as vibration or impact are not captured. A wind load, for example, is approximated as a constant wind pressure.
Small deflections - all loads are assumed to act on the undeflected shape. This may at first glance appear obvious if you haven't come across the concept of geometric non-linearity before. We cover this topic in some detail in . All structures deflect under load; this means that those loads are no longer applied to the same points in space once the structure has finished deflecting. The consequence of this is that we can generate in the structure. The classic example of this is the P- effect observed in an axially loaded column undergoing lateral sway. We cover this example in . But the basic idea is as follows.