Explanation The figure 1 represents the free body of the truss. Write the expression for the sum of all the forces acting along x direction. ∑ F x = 0 A x = 0 From the symmetry of loading, A y = I = 1 2 total load A y = I = 6 kN Considering the Joint A , This joint is subjected to only two unknown forces, the forces exerted by A B and those by A C . Use a force triangle to determine F A B and F A C . Figure 1 represents the force triangle. the member A B pushes on the joint so A B is in compression and the member A C pulls the joint so A C is in Tension. Write the expression for the forces in proportion form from the force triangle. F A B 9.849 = F A C 9 = 5 kN 4 (I) Here, F A B is the force acting along A B , F A C is the force acting along A C . Consider the joint B This joint is subjected to only two unknown force, the force exerted by B D and those by B C . Use a force triangle to determine F B C and F B D . Figure 3 represents the force triangle. the member B D and B C pushes the joint so B D and B C are in Compression. Write the expression for the sum of all forces acting along x direction. 9 9.849 ( F A B + F B D + F D C ) = 0 (II) Write the expression for the sum of all forces acting along y direction. 4 9.849 ( 12.31 kN+ F B D − F B C ) − 2 kN = 0 (III) Considering the joint C , This joint is subjected to two unknown forces, the forces exerted by C E and those by C G and. Use a force polygon to determine F C E and F C G .in the Figure 5. the member C E and C G pulls on the joint so C D and C G are in Tension. Considering the joint D , This joint is subjected to two unknown forces, the forces exerted by C D and those by D E and. Use a force polygon to determine F C D and F D E .in the Figure 3. the member C D and D E pushes on the joint so C D and D E are in compression. Write the expression for the sum of all forces acting along y direction. 4 5 F C E − 4 9.849 F B C − F C D = 0 (IV) Write the expression for the sum of all forces acting along x direction. F C G + 3 5 ( 3.75 kN ) + 9 9.849 ( F B C ) − F C D = 0 (V) Conclusion: For the joint A , Solve equation I to find F A B and F A C . F A B 9.849 = F A C 9 = 5 kN 4 F A B = 12.31 kN F A C = 11.25 kN For the joint B , Substitute 12

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ISBN: 9781260912814

Author: BEER

Publisher: MCG

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Chapter 6.1, Problem 6.14P

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Determine the force in each member of the truss and state whether each member is in tension or compression.

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Determine the force in each member of the truss and state whether each member is in tension or compression.

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Determine the force in each member of the truss and state whether each member is in tension or compression.

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