Determine the force in each member of the Warren truss shown in Fig. 4.19(a) by the method of jo
Solution Static Determinacy The truss has 13 members and 8 joints and is supported by 3 reactions. Because m + r = 2j and the reactions and the members of the truss are properly arranged, it is statically determinate.
Zero-Force Members It can be seen from Fig. 4.19(a) that at joint G, three members, CG; FG, and GH, are connected, of which FG and GH are collinear and CG is not. Since no external load is applied at joint G, member CG is a zero-force member.
FCG = 0 Ans.
From the dimensions of the truss, we find that all inclined members have slopes of 3:4, as shown in Fig. 4.19(a). The free-body diagram of the entire truss is shown in Fig. 4.19(b). As a joint with two or fewer unknowns—which should not be collinear—cannot be found, we calculate the support reactions. (Although joint G has only two unknown forces, FFG and FGH, acting on it, these forces are collinear, so they cannot be determined from the joint equilibrium equation, ∑Fx =0.)
Reactions By using proportions,