TABLE OF CONTENTS The flexibility method may be applied to the analysis of portal frames although, as we shall see, in all but simple cases the degree of statical indeterminacy is high so that the number of compatibility equations requiring solution becomes too large for hand computation.
Consider the portal frame shown in Fig. 16.23(a). From Section 16.2 we see that the frame, together with its foundation, form a single two-dimensional ring and is therefore three times statically indeterminate. Therefore we require 3 releases to obtain the statically determinate primary structure. These may be obtained by removing the foundation at the foot of one of the vertical legs as shown in Fig. 16.23(b); we then have two releases of force and one of moment and the primary structure is, in effect, a cranked cantilever. In this example there would be three compatibility equations requiring solution, two of translation and one of rotation. Clearly, for a plane, two-bay portal frame we would have six compatibility equations so that the solution would then become laborious; further additions to the frame would make a hand method of solution impracticable. Furthermore, as we shall see in Section 16.10, the moment distribution method produces a rapid solution for frames although it should be noted that using this method requires that the sway of the frame, that is its lateral movement, is considered separately whereas, in the flexibility method, sway is automatically included.
Determine the distribution of...
