Explanation Calculation: Assumption: Apply the sign convention for calculating the equations of equilibrium as shown 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 the downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counterclockwise moment as positive. Consider the members ABC and CDE to get the forces in each link. Sketch the Free Body Diagram of member CDE as shown in Figure 1. Refer to Figure 1. Apply the Equations of Equilibrium as shown below. Apply the equilibrium equation for moment at point J and equate to zero for equilibrium. ∑ M J = 0 C x × 4 a + C y × 2 a = 0 C y = − 2 C x (1) Refer to Figure 1. Apply the Equations of Equilibrium as shown below. Apply the equilibrium equation for moment at point K and equate to zero for equilibrium. ∑ M K = 0 C y × 4 a + C x × 2 a − P × 3 a = 0 4 C y + 2 C x − 3 P = 0 Substitute − 2 C x for C y . 4 × ( − 2 C x ) + 2 C x − 3 P = 0 − 6 C x = 3 P C x = − 1 2 P Calculate the vertical reaction at C ( C y ) as shown below. Substitute − 1 2 P for C x in Equation (1). C y = − 2 × ( − 1 2 P ) = P Apply the Equilibrium equation along the horizontal forces and equate to zero for equilibrium. ∑ F x = 0 1 2 F B G + C x = 0 Substitute − 1 2 P for C x . 1 2 F B G − 1 2 P = 0 F B G = 1 2 P Hence, the force in link BG is F B G = 1 2 P ( T ) _

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 6.3, Problem 6.114P

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Find the force in each link.

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Chapter 6.3, Problem 6.113P

Chapter 6.3, Problem 6.115P

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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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