Use of pin-jointed structures in teaching frame analysis

In the flexibility-based method of frame analysis described in this paper, the principle of superposition is used to combine (a) the effect of applied loads and actions with the unknown end moments equated to zero and (b) the effect of the unknown end moments in an otherwise unloaded structure. The first stage of this superposition process, in which the unknown end moments are equated to zero, corresponds to a pin-jointed structure in which loads and actions are applied to simply supported elements. This pin-jointed structure is demonstrated in this paper to provide a simple and consistent model for teaching independent modes of sway and the associated compatibility expressions relating sway translations to element sway rotations and joint translations. It also simplifies derivation of the sway equilibrium equations and consideration of the effects of temperature and settlement. More importantly it provides a useful basis for sketching bending moment diagrams and deflected shapes. As the pin-jointed structure represents a compatible set of virtual displacements it may also be applied to similar processes in stiffness-based methods of analysis. This helpful teaching model is illustrated using examples of a continuous beam and a pair of sway frames.