Explanation Calculation: The following figure shows the free body diagram of space truss. Figure (I) Here, the vertical reaction at A is V A , the vertical reaction at B is V B and the horizontal and vertical reaction at C are H C and V C respectively. Write the expression to calculate the forces along x-axis. ∑ F x = 0 Here, the forces in x direction are F x . H C = 0 k Write the expression to calculate the forces along y-axis. ∑ F y = 0 Here, the forces along y-axis are F y . V A + V B + V C = 8 k ...... (I) Write the expression to calculate the moments about x-axis at point C. ∑ M x = 0 Here, the moment about C is M x . V A × 3 ft + V B × 3 ft − 8 k × ( 3 + 4 ) ft = 0 3 V A + 3 V B = 56 k-ft V A + V B = ( 56 3 ) k ...... (II) Substitute ( 56 3 ) k for ( V A + V B ) in Equation (I). ( 56 3 ) k + V C = 8 k V C = 8 k − ( 56 3 ) k V C = − ( 32 3 ) k Write the expression to calculate the moments about y-axis at point C. ∑ M y = 0 Here, the moment about C is M y . ( − V A × 3 ft ) + ( V B × 3 ft ) = 0 3 V A = 3 V B V A = V B ...... (III) Substitute V B for V A in Equation (II). 2 V B = ( 56 3 ) k V B = ( 28 3 ) k Substitute ( 28 3 ) k for V B in Equation (III). V A = ( 28 3 ) k Calculate the coordinates and projection of the members. Coordinates of point A ( x 1 , y 1 , z 1 ) = ( 3 , 3 , 0 ) . Coordinates of point B ( x 2 , y 2 , z 2 ) = ( − 3 , 2 , 0 ) . Length of member AB. l A B = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 + ( z 1 − z 2 ) 2 = ( 3 − ( − 3 ) ) 2 + ( 3 − 3 ) 2 + ( 0 − 0 ) 2 = 36 ft 2 + 0 ft 2 + 0 ft 2 = 6 ft Here, the length of member AB is l A B . Calculate the projection of member AB along the x-axis. x A B = | x 1 − x 2 | = | 3 − ( − 3 ) | = 6 ft Here, the projection of member AB along the x-axis is x A B . Calculate the projection of member AB along y-axis. y A B = | y 1 − y 2 | = | 3 − 3 | = 0 ft Here, the projection of member AB along y-axis is y A B . Calculate the projection of member AB along z-axis. z A B = | z 1 − z 2 | = | 0 − 0 | = 0 ft Here, the projection of member AB along z-axis is z A B . Calculate the length and projection of all the members. S.No. Point Member Length(l)(ft) Projection along x-axis ( ft . ) y-axis ( ft . ) z-axis ( ft . ) 1 A AB 6 6 0 0 2 B BC 3 2 3 3 0 3 C CD 73 0 3 8 4 D DE 4 0 4 0 5 E EA 89 3 4 8 6 BD 73 3 0 8 7 AD 73 3 0 8 8 AC 3 2 3 3 0 9 BE 89 3 4 8 The following figure shows the free body diagram of joint C. Figure (2) Write the expression to calculate the forces along x-axis. ∑ F x = 0 F C A ( x C A l C A ) − F C B ( x C B l C B ) = 0 ...... (IV) Substitute 3 ft for x C A , 3 ft for x C B , 3 2 ft for l C A and 3 2 ft for l C B in Equation (IV). F C A ( 3 ft 3 2 ft ) − F C B ( 3 ft 3 2 ft ) = 0 F C A = F C B ...... (V) Write the expression to calculate the forces along y-axis. ∑ F y = 0 F C A ( y C A l C A ) + F C B ( y C B l C B ) + F C D ( y C D l C D ) = 0 ...... (VI) Substitute 3 ft for y C A , 3 ft for y C B , 3 2 ft for l C A and 3 2 ft for l C B and 73 ft for l C D in Equation (VI). F C A ( 3 ft 3 2 ft ) + F C B ( 3 ft 3 2 ft ) + F C D ( 3 ft 73 ft ) = 0 F C A ( 1 2 ) + F C B ( 1 2 ) + F C D ( 3 73 ) = 0 ...... (VII) Write the expression to calculate the forces along z-axis. ∑ F z = 0 F C D ( z C D l C D ) + ( 32 3 k ) = 0 ...... (VIII) Substitute 8 ft for z C D and 73 ft for l C D in Equation (VIII). F C D ( 8 ft 73 ft ) − ( 32 3 ) k = 0 F C D ( 8 ft 73 ft ) = ( 32 3 ) k F C D = ( 4 73 3 ) k F C D = 11.392 k Substitute ( 4 73 3 ) k for F C D and F C B for F C A in Equation (VII). F C B ( 1 2 ) + F C B ( 1 2 ) + ( 4 73 3 ) k × ( 3 73 ) = 0 2 F C B = − ( 4 2 ) F C B = − 2

10th Edition

ISBN: 9780134610672

Author: Russell C. Hibbeler

Publisher: PEARSON

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Question

Chapter 3, Problem 3.38P

To determine

The force in each member of the space truss, to state if the members are in tension or compression and to check if the truss is stable.

Expert Solution & Answer

Chapter 3 Solutions

Structural Analysis (10th Edition)

Ch. 3 - Classify each of the following trusses as...Ch. 3 - Prob. 3.2P Ch. 3 - Prob. 3.3P Ch. 3 - Prob. 3.4P Ch. 3 - Prob. 3.5P Ch. 3 - Prob. 3.6P Ch. 3 - Prob. 3.7P Ch. 3 - Prob. 3.8P Ch. 3 - Prob. 3.9P Ch. 3 - Prob. 3.10P

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