Explanation The truss is loaded as shown in the figure. The free body diagram for the entire truss is given by Figure 1. The sum of the moments in the counter clockwise direction about A for the entire truss is given as, H ( 36 ft ) − ( 4 kips ) ( 9 ft ) − ( 4 kips ) ( 18 ft ) = 0 (I) Solve for H from (I). H ( 36 ft ) − ( 4 kips ) ( 9 ft ) − ( 4 kips ) ( 18 ft ) = 0 H = 3.00 kips The sum of the forces in the positive x direction for the entire truss is given as, A x = 0 (II) The sum of the forces in the positive y direction for the entire truss is given as, A y + 3 kips − 8 kips = 0 A y = 5.00 kips (III) The member D E and F G are zero force members. This means that force on the member B D and D F will be the same. So will be the force on the members E G and G H . The free body diagram of the joint A is given as, From the diagram the relation between the force on the members A B and A C are given as, F A B 5 = F A C 3 = A y 4 (IV) The free body diagram of the joint C is given as, From the diagram the sum of the forces in the positive x direction is given as, F C E = 3.75 kips (V) From the diagram the sum of the forces in the positive y direction is given as, F B C = 4.00 kips (VI) The free body diagram of the joint B is given as, From the diagram the sum of the forces in the positive y direction is given as, − 4 5 F B E + 4 5 F A B − F B C = 0 (VII) From the diagram the sum of the forces in the positive x direction is given as, 3 5 F A B + 3 5 F B E + F B D = 0 (VIII) The free body diagram of the joint F is given as, From the diagram, the relation between the force on the members are given as, F E F 5 = F F H 5 = F D F 6 (IX) The free body diagram of the joint F is given as, From the diagram, the relation between the force on the members are given as, F G H 3 = H 4 (X) Conclusion: Solve for F A B from (IV) by substituting 5.00 kips for A y . F A B 5 = 5.00 kips 4 F A B = 6

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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Chapter 6.1, Problem 6.20P

To determine

The force in each member of the Pratt bridge.

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Chapter 6.1, Problem 6.19P

Chapter 6.1, Problem 6.21P

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Vector Mechanics for Engineers: Statics and Dynamics

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The force in each member of the Pratt bridge.

Solution Summary: The author explains the force in each member of the Pratt bridge. The free body diagram for the entire truss is given by Figure 1.

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