Structural Analysis

Plane Trusses by the Method of Joints Problems and solutions

Example 4.4

Determine the force in each member of the Warren truss shown in Fig. 4.19(a) by the method of jo

ints.

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,

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