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. Method of sections: The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates Tension (T). The Figure of the truss is shown. The members identified by “x” are FG , FC , and BC . Calculation: Show the free body diagram of the truss as shown in Figure 1. Refer Figure 1. Consider the horizontal and vertical reaction at A are denoted by A x and A y . Consider the vertical reaction at D is denoted by D y . Take the sum of the moment about A and Equate to zero. ∑ M A = 0 D y × 24 − ( 100 × 8 ) − ( 100 × 12 ) − ( 50 × 16 ) − ( 60 × 6 ) = 0 D y × 24 − 3160 = 0 D y = 3160 24 D y = 131.67 kN Take the sum of the forces in the vertical direction as zero. D y + A y = 100 + 100 + 50 D y + A y = 250 131.67 + A y = 250 A y = 250 − 131.67 A y = 118.33 kN Find the angle ( θ ) made by the member CF with the horizontal as follows: tan θ = 6 4 θ = tan − 1 ( 6 4 ) θ = 56.30 ° Consider a vertical section a-a passing through the members FG , FC , and BC . Show the portion of the truss to the right of the section as shown in Figure 2. Refer Figure 1 and Figure 2. Consider the forces in the members FG , CF , and BC as F F G , F C F , F B C

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ISBN: 9781337630931

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 34P

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Find the forces in the members FG, FC, and BC of the truss by the method of sections.

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Structural Analysis

Ch. 4 - Prob. 1P Ch. 4 - Prob. 2P Ch. 4 - Prob. 3P Ch. 4 - Prob. 4P Ch. 4 - Prob. 5P Ch. 4 - Prob. 6P Ch. 4 - Prob. 7P Ch. 4 - Prob. 8P Ch. 4 - Prob. 9P Ch. 4 - Prob. 10P

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Find the forces in the members FG , FC , and BC of the truss by the method of sections.

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Find the forces in the members FG, FC, and BC of the truss by the method of sections.

Chapter 4 Solutions