10 Sample Problem 1.2 For the truss shown in Fig. (a), calculate the normal stresses in (1) member AC; and (2) member BD. The cross-sectional area of each member is 900 mm². D E 30KN G 70 KN 4 panels at 4 m 16m (a) Pa A, 40KN (b) FBD of pin A Solution Equilibrium analysis using the FBD of the entire truss in Fig. (a) gives the following values for the external reactions: 4, 40 kN, H, 60 kN, and H, -0. Part 1 Recall that according to the assumptions used in truss analysis, each member of the truss is an axially loaded bar. To find the force in member AC, we draw the FBD of pin A, as shown in Fig. (b). In this (FBD). Pas and Pac are the forces in members AB and AC, respectively. Note that we have assumed both of these forces to be tensile. Because the force system is concurrent and coplanar, there are two independent equilibrium equations. From the FBD in Fig. (b), we get Σ0+140+P-0 3m Pa C A, 40 AN 30KN 4m (c) FBD Pac+ 0 Solving the equations gives Pac 53.33 kN (tension). Thus, the normal stress in member AC is Pac Ac 53.33 kN 900 mm 53.33 x 10' N 900 x 10 m² 59.3 x 10 N/m² 59.3 MPa (T) Answer Part 2 To determine the force in member BD, we see that section in Fig. (a) cuts through members BD, BE, and CE. Because three equilibrium equations are available for a portion of the truss separated by this section, we can find the forces in all three members, if needed. The FBD of the portion of the truss lying to the left of section is shown in Fig. (c) (the portion lying to the right could also be used). We have again assumed that the forces in the members are tensile. To calculate the force in member BD, we use the equilibrium equation M-0 +0-40(8)+30(4)- Pas(3) = 0 Copyright 2000 Compage Leaming All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to dextronic rights, some third party content may be supposed from the clock and which yields Pao -66.67 kN 66.67 kN (C) Therefore, the normal stress in member BD is Pap -66.67 kN 900 mm -66.67 x 10' N 900 x 10-6 m² -74.1 x 10 N/m2 -74.1 MPa (C) Answer