By E. W. Parkes
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Extra resources for Braced Frameworks. An Introduction to the Theory of Structures
To draw the influence line we need only determine the value of P A B when the unit load is at each panel point. The points on the graph so obtained can then be connected by straight lines. In fact it is not usually necessary to calculate P AB for each panel point, but only for the points on either side of the panel containing the member concerned. The influence line usually falls linearly to zero at the ends of the truss from these two panel points (see Fig. 33). *-8m**| FIG. 35 not discuss the derivation of an influence line further; the reader is, however, advised to check the diagram of Fig.
A oT 'ST -4ΐ :&—f I FIG. 34 they are also known). An influence line is, however, a continuous graph, and we must now consider the effect of applying load in between panel points. Suppose we have a unit load applied at distance x from end S of a bar ST of length / (Fig. 34(a)). Let the value of the force in bar AB when the unit load is at S be (PAB)S and when the unit load is at T let it be (PAB)T. Now consider the equilibrium of bar ST (Fig. 34(b)). By taking moments about S and T the end reactions can be found to have the values (l-x)/l and x/l, as shown.
Figure 39(d) is re-drawn with the usual notation in Fig. ) We shall now construct the displacement diagram for the cantilever truss shown in Fig. 40(a). The extensions of the members are tabulated. We begin at the fixed point a,f. Bar AB extends by 0O62cm. e. b lies somewhere on a line through b' 56 STATICALLY DETERMINATE TRUSSES perpendicular to ab'. Bar FB extends by 0O41cm. e. b lies somewhere on a line through b" perpendicular to fb". A (e, ' FIG. ,X> 39 The intersection of the line through b' perpendicular to ab' with the line through b" perpendicular to/Z>" gives the position of b.