To determine The force in the member DF , DG, and EG . 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 horizontal and vertical reaction at A are denoted by A x and A y . Consider the vertical reaction at L is denoted by L y . The truss is symmetric about the center vertical line FG . Calculate the vertical reaction at A and E . A y = L y = ( Total load 2 ) A y = L y = ( 1.2 kN + 1.2 kN + 1.2 kN + 1.2 kN + 1.2 kN 2 ) A y = L y = 3 kN ( ↑ ) Consider a section passing through the DF , DG , and EG . Draw the free body diagram of the truss to the left of the section as in Figure (1). Refer to Figure (1). Consider the forces in the member DF, DG, and EG are denoted by F D G , F E G , F D F . Consider the sum of the moment about the point G is zero. ∑ M G = 0 8 m × 1 .2 kN + 4 m × 1 .2 kN − 10.25 m × 3 kN − 3 m × F D F = 0 − 16.35 kN ⋅ m − 3 m × F D F = 0 F D F = − 16.35 kN ⋅ m 3 m F D F = − 5

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 6.2, Problem 6.43P

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The force in the member DF, DG, and EG.

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Vector Mechanics for Engineers: Statics and Dynamics

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 - Prob. 6.3P Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.5P 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 - Prob. 6.10P

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