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Chapter 10

Q. 10.10

Determine the member end forces of the frame shown in Fig. 10.21(a).

Step-by-Step

Verified Solution

Symmetry The frame is symmetric with respect to the vertical s axis passing through the hinge at D, as shown in Fig. 10.21(b). The left half of the frame, ACD, will be used for analysis.

Symmetric and Antisymmetric Components of Loading See Fig. 10.21(b)
and (c).

Member Forces Due to the Symmetric Loading Component The substructure with symmetric boundary conditions is shown in Fig. 10.21(d). The reactions and the member end forces of the substructure, as determined from equilibrium considerations, are shown in Fig. 10.21(d) and to the left of the s axis in Fig. 10.21(e), respectively. The member end forces to the right of the s axis are then obtained by reflection (see Fig. 10.21(e)).

Member Forces Due to the Antisymmetric Loading Component The substructure with antisymmetric boundary conditions is shown in Fig. 10.21(f ). The member forces are determined by analyzing the substructure and by reflecting the negatives of the computed forces and moments about the axis of symmetry (see Fig. 10.21(g)).

Total Member Forces The total member end forces, obtained by superimposing the member forces due to the symmetric and antisymmetric components of the loading, are shown in Fig. 10.21(h).            Ans.