Explanation Concept Used: In approximate method of analysis the following assumptions are used. The girder does not support any axial force. At a distance of 0.1 L from the left support, the moment in the girder is zero. At a distance of 0.1 L from the right support, the moment in the girder is zero. Calculation: Calculate the length of the cantilever span supporting the part of girder H G by considering the assumptions. Figure-(1) a = 0.1 L ...... (I) Here, the distance from the left and right end of the girder is a , and the span of the girder is L . Substitute, 3 m for L in Equation (I) a = 0.1 × 3 m =0 .3 m Draw the free body diagram of the part of the girder H ' G ' as shown in Figure-(2) Figure-(2) Write the equilibrium equation for the forces acting in the vertical direction. ∑ F Y = 0 5 kN / m × 2.4 m − F HG − F HG = 0 12 kN − 2 F HG = 0 F HG = 6 kN Here, summation of all vertical forces is ∑ F Y , and the force in the member H G is F HG . The following figure shows the free body diagram of the cantilever portion H H ' . Figure-(3) Write the equilibrium equation for net moment at point H . ∑ M H = 0 5 kN / m × 0.3 m × 0.3 m 2 + F HG × 0.3 m − M H = 0 0.225 kN-m + 0.3 F HG − M H = 0 M H = 0.225 kN-m + 0.3 F HG ...... (II) Here, net moment about point H is ∑ M H , moment at point H is M H . Substitute, 6 kN for F HG in Equation (II) M H = 0.225 kN-m + 0.3 m × 6 kN = 0.225 kN-m + 1.8 kN-m = 2.025 kNm Calculate the length of the cantilever span supporting the part of girder I J by considering the assumptions. Figure-(4) a = 0.1 L ...... (III) Here, the distance from the left and right end of the girder is a , and the span of the girder is L . Substitute, 3 m for L in Equation (III) a = 0.1 × 3 m =0 .3 m Draw the free body diagram of the part of the girder I ' J ' as shown in Figure-(5) Figure-(5) Write the equilibrium equation for the forces acting in the vertical direction. ∑ F Y = 0 5 kN / m × 2.4 m − F IJ − F IJ = 0 12 kN − 2 F IJ = 0 F IJ = 6 kN Here, summation of all vertical forces is ∑ F Y , and the force in the member I J is F IJ . The following figure shows the free body diagram of the cantilever portion J ' J

Structural Analysis, Student Value Edition

10th Edition

ISBN: 9780134622088

Author: HIBBELER, Russell C.

Publisher: PEARSON

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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 12, Problem 12.17P

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The internal moment at joint H form HG and at joint J from JI and JK.

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Chapter 12, Problem 12.16P

Chapter 12, Problem 12.18P

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Chapter 12 Solutions

Structural Analysis, Student Value Edition

Ch. 12 - Prob. 12.1P Ch. 12 - Prob. 12.2P Ch. 12 - Prob. 12.3P Ch. 12 - Prob. 12.4P Ch. 12 - Prob. 12.5P Ch. 12 - Prob. 12.6P Ch. 12 - Prob. 12.7P Ch. 12 - Prob. 12.8P Ch. 12 - Prob. 12.9P Ch. 12 - Prob. 12.10P

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