## 331 Deflections Of Statically Determinate Trusses

In Art. 3.23, the basic concepts of virtual work and specifically the unit-load method are presented. Employing these concepts, this method may be adapted readily to computing the deflection at any panel point (joint) in a truss.

Specifically, Eq. (3.113), which equates external virtual work done by a virtual unit load to the corresponding internal virtual work, may be written for a truss as n PI

where A = displacement component to be calculated (also the displacement at and in the direction of an applied unit load) n = total number of members f = axial force in member i due to unit load applied at and in the direction of the desired A—horizontal or vertical unit load for horizontal or vertical displacement, moment for rotation Pi = axial force in member i due to the given loads Ii = length of member i Ei = modulus of elasticity for member i Ai = cross-sectional area of member i

To find the deflection A at any joint in a truss, each member force Pi resulting from the given loads is first calculated. Then each member force f resulting from a unit load being applied at the joint where A occurs and in the direction of A is calculated. If the structure is statically determinate, both sets of member forces may be calculated from the method of joints (Sec. 3.30.2). Substituting each member's forces Pi and f and properties Li, Ei, and Ai, into Eq. (3.127) yields the desired deflection A.

As an example, the midspan downward deflection for the truss shown in Fig. 3.68a will be calculated. The member forces due to the 8-kip loads are shown in Fig. 3.69a. A unit load acting downward is applied at midspan (Fig. 3.69b). The member forces due to the unit r . FIGURE 3.69 (a) Loaded truss with stresses in members shown in parentheses. (b) Stresses in truss due to

7 a unit load applied for calculation of midspan deflection.

load are shown in Fig. 3.69b. On the assumption that all members have area Ai = 2 in2 and modulus of elasticity Ei = 29,000 ksi, Table 3.3 presents the computations for the midspan deflection A. Members not stressed by either the given loads, Pt = 0, or the unit load, f = 0, are not included in the table. The resulting midspan deflection is calculated as 0.31 in. ## Renewable Energy 101

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