Structural analysis is simple, really. Can your structure carry its loads or not? All you’re doing is comparing two numbers: the capacity and the demand. Capacity is how much the structure can possibly carry. Demand is how much force the structure actually carries.
As we’ve seen, a structure can carry loads in lots of different ways. But they can be split into two main categories: axial loads (pushing or pulling on the ends of a member, like an elevator cable) and transverse loads (pushing or pulling on the side of a member, like a rower’s oar). Almost every load you’ll ever encounter is either axial or transverse, or a little of both. A diagonal load on a beam can be split into an axial component and a transverse component.
One load that’s neither axial nor transverse is torsion, also known as torque. This load occurs when you rotate something about its axis, like a screw. Torsion is common in mechanical engineering but rare in structural engineering.
Every load creates internal forces or stresses inside the structure. (Stress is force divided by area. Engineers sometimes compare force required to force provided, and they sometimes compare stress required to stress provided. Whichever is more convenient.) We already know how to figure out the internal stresses. Axial loads create tension and compression stress, while transverse loads create shear and flexure stress. Whatever internal stresses you calculate – that’s your demand.
The capacity is a function of the size of the beam/column/cable/plate and what material it’s made of. Here’s the key: you need to compare capacity to demand for EVERY type of stress. Sometimes the stress required is zero, and the calculation is easy. For example, a floor joist usually carries no axial loads, so it’s trivial to say it’s OK in tension and compression. But a floor joist does carry transverse loads, so for shear and flexure you must figure out the capacity and the demand. Then you compare them to determine if the joist is adequate.