To determine Find the forces in each member of the truss using the method of joints. Find whether the member is in compression or tension. 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 forces in the member AB , BC , and AC are denoted by F A B , F B C , and F C A . Show the truss as shown in Figure 1. Refer to Figure 1. Consider the horizontal and vertical force at point B is denoted by B x and B y . Consider the horizontal reaction at C is denoted by C x . Apply the equilibrium vertical forces equilibrium condition. The sum of the forces in the vertical direction is equal to zero. ∑ F y = 0 B y = 0 Apply the moment equilibrium condition. The moment about C is equal to zero. ∑ M C = 0 − ( 16 in . ) B x − 36 in . × 240 lb=0 B x = − 36 in . × 240 lb 16 in . B x = − 540 lb B x = 540 lb ( ← ) Apply the equilibrium vertical forces equilibrium condition. The sum of the forces in the horizontal direction is equal to zero. ∑ F x = 0 C x + B x + 240 lb = 0 C x − 540 lb + 240 lb = 0 C x = 300 lb ( → ) Show the free body diagram of Joint B as shown in Figure 2. Refer Figure 2. Show the relation between the force in the member AB and BC as follows: F A B 5 = F B C 4 = B x 3 F A B 5 = F B C 4 = 540 lb 3 (1) Calculate the force in the member AB as follows: Refer Equation (1)

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 6.1, Problem 6.1P

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Find the forces in each member of the truss using the method of joints.

Find whether the member is in compression or tension.

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Chapter 5, Problem 5.148RP

Chapter 6.1, Problem 6.2P

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A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be fixed supports. The beam was originally designed to withstand a triangular distributed load, however, the loading condition has been revised and can be approximated by a cosine function as shown in the figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can assume that the bending rigidity (El) is constant. wwo cos 2L x A B Figure 3: Built in beam with a varying distributed load In order to do this, you will: a. Solve the reaction forces and moments at point A and B. Hint: you may find it convenient to use the principal of superposition. (2%) b. Plot the shear force and bending moment diagrams and identify the maximum shear force and bending moment. (2%) c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x. (1%)

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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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