Explanation Calculation: The following diagram shows the free body diagram of the truss: Figure-(1) Calculate the angles as shown below. cos θ = 1.5 2.5 sin θ = 2 2.5 Write the Equation for moment about A. Σ M A = 0 B y × 1.5 m − ( 10 × 2 + 8 × 4 ) kN ⋅ m = 0 B y × 1.5 m = 52 kN ⋅ m B y = 34.67 kN Here, vertical reaction at B is B y . Write the Equation for sum of vertical forces. Σ F y = 0 A y + B y = 0 .....(I) Here, vertical reaction at A is A y . Substitute 34.67 kN for B y in Equation (I). 34.67 kN + A y = 0 A y = − 34.67 kN Write the Equation for sum of horizontal forces. Σ F x = 0 A x − 10 kN − 8 kN = 0 A x = 18 kN Here, horizontal reaction at A is A x . Consider vertical section of the top panel as shown below: Figure-(2) Consider diagonal force F C E and F D F as compressive and tensile and consider it equal to F . F C E = F F D F = F Write the Equation for sum of horizontal forces. Σ F x = 0 F C E cos θ + F D F cos θ − 8 kN = 0 Here, force in member CE and DF are F C E and F D F . Substitute 1.5 2.5 for cos θ , F for F C E and F D F . F ( 1.5 2.5 ) + F ( 1.5 2.5 ) − 8 kN = 0 0.6 F + 0.6 F − 8 kN = 0 F = 6.67 kN Calculate the F C E and F D F as shown below. F C E = 6.67 kN ( C ) F D F = 6.67 kN ( T ) Write the Equation for moment about E. Σ M E = 0 ( F C D × 1.5 ) + ( ( F D F sin θ ) × 1.5 ) = 0 Here, force in member CD is F C D . Substitute 2 2.5 for sin θ and 6.67 kN for F D F . F C D × 1.5 m + ( 2 2.5 × 6.67 kN ) × 1.5 m = 0 F C D × 1.5 m = − 8 kN ⋅ m F C D = 5.33 kN ( C ) Write the Equation for moment about D. Σ M D = 0 F E F × 1.5 − ( F C E sin θ ) × 1.5 = 0 Here, force in member EF is F E F . Substitute 2 2.5 for sin θ and 6.67 kN for F C E . F E F × 1.5 − ( 6.67 kN × 2 2.5 ) × 1.5 = 0 F E F × 1.5 − 6.67 × 1.2 = 0 F E F = 5.33 kN ( T ) Consider joint D. Figure-(3) Write the Equation for sum of horizontal forces. Σ F x = 0 F D E + F D F cos θ = 0 Substitute 1.5 2.5 for cos θ and 6.67 kN for F D F . F D E + 6.67 kN ( 1.5 2.5 ) = 0 F D E = 4 kN ( C ) Here, force in member DE is F D E . Consider vertical section of the bottom panel as shown below:d Figure-(4) Consider diagonal force F A C and F B F as tensile and compressive and consider as F . F A C = F F B F = F Write the Equation for sum of horizontal forces. Σ F x = 0 F A C cos θ + F B F cos θ − A x = 0 Here, force in member AC and BF are F A C and F B F

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ISBN: 9780134610672

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 12.11P

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The force in each member of the truss.

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Chapter 12 Solutions

Structural Analysis (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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