Explanation Assumption: Apply the sign convention for calculating the equations of equilibrium as below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Calculation: Consider the vertical reaction at A and I are denoted by A y and I y Calculate the end reactions at A and I as follows: Taking moment about A , ∑ M A = 0 − 2 ( 2.4 ) − 2 ( 4.8 ) − 2 ( 7.2 ) − 1 ( 9.6 ) + A y ( 9.6 ) = 0 − 4.8 − 9.6 − 14.4 − 9.6 + 9.6 A y = 0 − 38.4 + 9.6 A y = 0 9.6 A y = 38.4 A y = 4 kN Consider the equilibrium of forces along horizontal direction. ∑ F x = 0 A x = 0 Pass a section through member CD , DE, and DF . Sketch the free body diagram of roof truss as shown in Figure 1. Refer to Figure 1. Calculate the distance BJ and DE . B J = 2.16 9.6 = 9 40 D E = − 1 2.4 = − 5 12 Find the a value as shown in below: a = 0.46 slope BJ Substitute 9 40 for BJ

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 6.2, Problem 6.55P

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Find the force in member CE,DE, and DF.

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Chapter 6 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.2P Ch. 6.1 - Prob. 6.3P Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Using the method of joints, determine the force in...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.8P Ch. 6.1 - 6.9 and 6.10 Determine the force in each member of...Ch. 6.1 - 6.9 and 6.10 Determine the force in each member of...

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Find the force in member CE , DE , and DF .

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