By E. W. Parkes
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Additional info for Braced Frameworks. An Introduction to the Theory of Structures
1-3 are very satisfactory when it is desired to find the forces in all the bars of the framework. Jf the forces in only a few of the bars are required, however, a more economical solution may be possible. Consider the plane truss shown in Fig. 26(a). Suppose we wish to find the force in member AB. The reactions at the supports can readily be found to be lOkN at the left-hand end and 20kN at the right-hand end. Now cut the truss through members AB, AD and 37 BRACED FRAMEWORKS CD, and consider the left-hand portion (Fig.
2) The number of bars (b), reactive forces (r) and joints (j) must be related by the equation b + r = 2j (plane frame) 3/ (three-dimensional frame) (3) The bars must be properly arranged. It is important to notice that these conditions make no mention of the applied load system. Whether a framework is statically determinate depends only upon the geometry of the framework and its supports: provided condition (1) is satisfied, statical determinacy is in no way dependent on the loads applied to the structure.
We must clearly add a further condition to equation (19)—for statical determinacy equation (19) must be satisfied and the bars must be properly arranged. It is not possible to give a simple definition of "proper arrangement", nor is it necessary to try to do so : the reader will quickly learn with experience to recognise parts of a structure which have been over-braced or inadequately braced. In cases of doubt the difficulty can always be resolved by sketching the process of erection of the frame: indeed, the reader is urged to use this method of determining whether a structure is statically determinate in preference to the use of equation (19), since by considering the geometrical problem of fitting the bars together he will learn far more about the behaviour of frameworks than he will do by blindly applying a formula.