TABLE OF CONTENTS A truss may be internally and/or externally statically indeterminate. For a truss that is externally statically indeterminate, the support reactions may be found by the methods described in Section 16.4. For a truss that is internally statically indeterminate the flexibility method may be employed as illustrated in the following examples.
Determine the forces in the members of the truss shown in Fig. 16.18(a); the cross-sectional area, A, and Young's modulus, E, are the same for all members.
The truss in Fig. 16.18(a) is clearly externally statically determinate but, from Eq. (16.5), has a degree of internal statical indeterminacy equal to 1 ( M = 6, N = 4). We therefore release the truss so that it becomes statically determinate by cutting one of the members, say BD, as shown in Fig. 16.18(b). Due to the actual loads ( P in this case) the cut ends of the member BD will separate or come together, depending on whether the force in the member (before it was cut) was tensile or compressive; we shall assume that it was tensile.
We are assuming that the truss is linearly elastic so that the relative displacement of the cut ends of the member BD (in effect the movement of B and D away from or towards each other along the diagonal BD) may be found using, say, the unit load method as illustrated in Ex. 15.6...
