There are two important concepts in the design of structures to withstand loads. One is stiffness, which relates to the ability of a structure to maintain its shape under load; the other is stress, which relates to the fact that all structural materials can withstand only a certain level of stress without failing. Stiffness is a global structural concept, whereas stress is a local concept.
The stiffness properties of structural members are greatly affected by their cross-sectional properties; this is especially true of thin-walled members. For example, Figure 2.1(a) shows a C-channel fixed at one end with an upward load applied at the other end along the vertical wall. What is interesting is that this load causes a counterclockwise rotation as shown and not a clockwise rotation as might be expected. The reason is because the shear center (the center of twist) is to the left of the wall.
Figure 2.1(b) shows an example of stress distribution in a bar with a hole. Changes in local geometry can cause significant changes in stress, giving rise to what are called stress concentrations. These are clearly visible around the edge of the hole.
The explorations in this chapter consider the stiffness properties of various structures and the stress distributions in some common components. The first and second explorations establish the stiffness properties of basic structural components and some thin-walled 3D structures.