Explanation Given information: The Figure of the truss is shown. The members identified by “x” are AE, CD, and BF . Consider the forces in the members AE, CD, and BF are denoted by F A E , F C D , and F B F . 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). Calculation: Show the truss as shown in Figure 1. Refer Figure 1. Find the slope of the member CD as follows: Consider the slope of the member CD with the horizontal is ( θ ) . Then, tan θ = 3 4 θ = tan − 1 ( 3 4 ) θ = 36.869 ° Consider a horizontal section passing through the members AE, CD, and BF denoted by a-a . Show the portion of the truss just above the section as shown in Figure 2. Refer Figure 2. For Equilibrium of forces, Take the sum of all horizontal forces in x direction as zero. ∑ F x = 0 100 − F C D cos θ = 0 100 − F C D cos ( 36.869 ° ) = 0 F C D = 100 cos ( 36.869 ° ) F C D = 125 kN ( T ) Take sum of moments about F as zero. ∑ M F = 0 F A E × 16 + 50 × 6 + F C D sin θ × 6 − F C D cos θ × 2 = 0 F A E × 16 + 50 × 6 + 125 sin ( 36

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Load on Structures

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 44P

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Find the forces in the members AE, CD, and BF 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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