Stress analysis

An analysis gives us the internal actions in every member of a structure: the axial force, shear forces, the bending moments and, in 3D, the torque. Determining these actions is a necessary step to calculating the stresses in the structure which is the information that actually helps us in design. For example, steel doesn't yield because of a bending moment as such. It begins to yield when the stress at a point in the cross-section gets too high, exceeding the yield stress. So turning internal actions into stresses is where a member design check really begins, and that's what this pathway is all about.

The actions we mentioned above, axial force, shear force etc. are stress resultants. This means they are the cumulative effect of stresses acting on the fibres of the structural element. In this Stress analysis pathway, we'll use these stress resultants to determine their corresponding stresses. We'll work out each kind of stress by hand, see Structure Bench calculate and display it for us, and then check both against a finite element analysis of the cross-section. Along the way, we'll cover normal stress from axial force and bending and shear stress from shear force and torsion, how the two can be combined into a single von Mises stress, and how that compares with the yield strength of the material, typically steel.

Structure Bench gives you two tools for visualising the stresses in a structure, and the objective of this pathway is to help you understand how each one works and when to reach for it:

• the member stress view, which paints the stresses along every member using beam theory. It's quick, it covers the whole model at once, and it's exactly the calculation you'd do by hand,
• stress planes, which cut a member at a point of your choosing and solve the stress field across the real cross-section using finite element analysis. They're slower and local to the cut, but they show you, with greater granularity, what is happening throughout a given cross-section.

We'll work through eight steps with eight models. The model for each step can be opened alongside the pathway page, so you can explore the model and its results as you read. If you're a member, you can copy any of the models into one of your own projects and dig a little deeper by modifying and re-solving them yourself. As with every pathway, you'll get far more out of it by poking and prodding the models yourself than by reading about them! By the end of the pathway, you'll be able to: