Explanation Check the determinacy of the truss as shown below. m + r − 2 j = 0 Here, number of members are m , number of reactions are r and number of joints are j . Substitute 21 for m , 3 for r and 10 for j . 21 + 3 − 2 × 10 > 0 4 > 0 Hence, the given truss is statically indeterminate of 4 degree. The following figure shows the free body diagram of the truss. Figure-(1) Write the equation for moment about D. Σ M B = 0 ( B y × 6 m ) − ( 5 kN × 9 m ) − ( 10 kN × 3 m ) + ( 5 kN × 3 m ) = 0 B y × 6 m = 60 kN ⋅ m B y = 10 kN Here, vertical reaction at B is B y . Write the Equation for sum of vertical forces. Σ F y = 0 B y + D y − 5 kN − 10 kN − 5 kN = 0 B y + D y = 20 kN .....(I) Here, vertical reaction at D is D y . Substitute 10 kN for B y in Equation (I). 10 kN + D y = 20 kN D y = 20 kN − 10 kN D y = 10 kN Consider the forces in the member JB and AI as F. F J B = F F A I = F Use the method of section and cut the section as shown in the following figure and calculate the forces in the members. Figure-(2) Calculate the angles as shown below. cos θ = 3 5 sin θ = 4 5 Consider the joint J. Write the Equation for sum of vertical forces. Σ F y = 0 5 kN − F sin θ − F sin θ = 0 Substitute 4 5 for sin θ . 5 kN − F × 4 5 − F × 4 5 = 0 5 kN − 2 F × 4 5 = 0 F = 3.125 kN ( Compression ) Hence, the forces in the member JB and AI is shown below. F J B = 3.125 kN ( Compression ) F A I = 3.125 kN ( Tension ) Write the Equation for moment about J. ( F J I × 4 + F cos θ × 4 ) kN ⋅ m = 0 Substitute 3 5 for cos θ and 3.125 kN for F ( F J I × 4 + 3.125 kN × 3 5 × 4 ) kN ⋅ m = 0 F J I = 1.875 k ( Tension ) Write the Equation for sum of horizontal forces. Σ F x = 0 F J I − F − F + F A B = 0 F J I + F A B = 0 Substitute 1.875 k for F J I . 1.875 k + F A B = 0 F A B = 1.875 k ( Compression ) Here, force in the member AB is F A B . Consider the joint A. Figure-(3) Write the equation for sum of vertical forces. Σ F y = 0 F J A = 3.125 sin θ Substitute 4 5 for sin θ . F J A = 3.125 × 4 5 = 2.5 kN ( Compression ) Here, force in the member JA is F J A . Consider the forces in the member IC and BH as F. F I C = F F B H = F Use the method of section and cut the section as shown in figure below and calculate the forces in the members. Figure-(4) Write the equation for sum of vertical forces. Σ F y = 0 10 kN − 5 kN − F sin θ − F sin θ = 0 2 F sin θ = 5 kN Substitute 4 5 for sin θ . 2 × 4 5 F = 5 kN F = 3

Structural Analysis, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (10th Edition)

10th Edition

ISBN: 9780134702216

Author: Russell C. Hibbeler

Publisher: PEARSON

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Plane and Space Trusses

In civil engineering, a truss is the most important structure that forms the most fundamental member of any building structure and commercial complexes. Trusses are composed of individual members or links that are interconnected by suitable joints, such …

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Chapter 12, Problem 12.3P

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The forces in each member of the truss.

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Structural Analysis, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (10th 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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