Explanation Given information: Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below. For summation of forces along x -direction is equal to zero ( ∑ F x = 0 ) , consider the forces acting towards right side as positive ( → + ) and the forces acting towards left side as negative ( ← − ) . For summation of forces along y -direction is equal to zero ( ∑ F y = 0 ) , consider the upward force as positive ( ↑ + ) and the downward force as negative ( ↓ − ) . For summation of moment about a point is equal to zero ( ∑ M at a point = 0 ) , consider the clockwise moment as negative and the counter clockwise moment as positive. The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates Tension (T). Calculation: Show the free body diagram of the truss as shown in Figure 1. Refer Figure 1. Consider the horizontal and vertical reactions at A are A x and A y . Consider the vertical reaction at F is F y . Calculate the value of the angle θ , α as follows: tan θ = 40 60 θ = tan − 1 ( 40 60 ) θ = 33.69 ° α = 90 ° − θ = 90 ° − 33.69 ° = 56.31 ° Take the sum of the forces in the horizontal direction as zero. ∑ F x = 0 A x = − [ 3 × 15 cos α + 2 × 15 cos α + 2 × 30 cos α ] = − [ 3 × 15 cos 56.31 ° + 2 × 15 cos 56.31 ° + 2 × 30 cos 56.31 ° ] = − 74.88 k Find the length of the members IC, HB, KE, and LF using the relation. I C C A = H B B A = 40 60 I C 40 = H B 20 = 40 60 Solve the above relation. I C = 26.6 ft H B = 13.33 ft By symmetry of the truss. K E = I C = 26.6 ft L F = H B = 13.33 ft Take the sum of the moment about A as zero. ∑ M A = 0 [ F y × 100 + 15 ( 120 + 60 − 60 − 40 − 20 ) sin 56.31 ° − 15 ( 40 + 40 + 26.66 + 13.33 ) cos 56.31 ° + 30 ( 100 + 80 ) sin 56.31 ° − 30 ( 13.33 + 26.66 ) cos 56.31 ° ] = 0 100 F y + 748.845 − 998.375 + 4493.07 − 665.472 = 0 F y = − 35.78 k Take the sum of the forces in the vertical direction as zero. ∑ F y = 0 A y + F y = 3 × 15 sin α − 2 × 15 sin α − 2 × 30 sin α A y + F y = 3 × 15 sin 56

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Author: KASSIMALI, Aslam.

Publisher: Cengage,

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Civil engineers primarily deal with beams in their day-to-day applications. A beam is a structural member that resists shear loadings. There are various types of beams such as cantilever beam, simply supported beam, and over the hanging beam. All these b…

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Chapter 4, Problem 39P

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Find the forces in the members IH, IC, and CD of the truss.

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