Explanation 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. Calculation: Consider the members ABC and CDE to get the forces in each link. Draw the free body diagram of the member CDE as 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) 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 − M 0 = 0 4 C y a + 2 C x a − M 0 = 0 Substitute − 2 C x for C y . 4 × ( − 2 C x ) a + 2 C x a − M 0 = 0 − 6 C x a = M 0 C x = − 1 6 a M 0 Calculate the vertical reaction at C ( C y ) as shown below. Substitute − M 0 6 a for C x in Equation (1). C y = − 2 × ( − M 0 6 a ) = M 0 3 a 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 − M 0 6 a for C x . 1 2 F B G − M 0 6 a = 0 F B G = 2 M 0 6 a Hence, the force in link BG is F B G = 2 M 0 6 a ( T ) _ . Apply the Equilibrium equation along the vertical forces and equate to zero for equilibrium. ∑ F y = 0 − F A F − 1 2 F B G + C y = 0 Substitute 2 M 0 6 a for F B G and M 0 3 a for C y

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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Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

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Chapter 6.3, Problem 6.116P

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The force in each link.

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Chapter 6 Solutions

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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