A ‘frame’ resists the action of external loads primarily by bending of its members. Thus the loads V and H applied to the plane rectangular portal frame of fig. 7.1(a) will give rise to certain bending moments. It is the evaluation of this single variable, the bending moment M, that is the objective of the structural analysis of the frame. Further, for the example of fig. 7.1, in which the loads are applied at discrete points and the members are straight between nodes, a knowledge of the values of the bending moment at those nodes (five in number in fig. 7.1) will give a complete description of the state of the frame. In fig. 7.1(b) the general bending-moment diagram has been sketched (with the sign convention that bending moments producing tension on the outside of the frame are positive).

The application of the first of the master equations of the theory of structures, that of statical equilibrium, will give some relations between the values of the bending moments at the nodes, MA to ME in fig. 7.1(b). As usual, a statical analysis may be made straightforwardly by the use of virtual work, and fig. 7.1(c) shows a pattern of deformation involving discontinuities at the five cardinal points. Between these hinges the members of the frame remain straight; the two columns are each inclined at a small angle θ to their original directions, and the two half-beams at an angle φ.