Explanation Given information: Area of all bars = 2 in . 2 . The value of E is 29 , 000 kips/in . 2 . The support at E displaces vertically downward by 0.6 in . and the support at A moves to the right by 0.4 in . . Procedure to find the deflection of truss by virtual work method is shown below. For Real system: If the deflection of truss is determined by the external loads, then apply method of joints or method of sections to find the real axial forces in all the members of the truss. For virtual system: Remove all given real loads, apply a unit load at the joint where is deflection is required and also in the direction of desired deflection. Use method of joints or method of sections to find the virtual axial forces in all the member of the truss. Finally use the desired deflection equation. 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 joints: The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates tension (T). Condition for zero force members: 1. If only two non-collinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both the members is zero. 2. If three members, two of which are collinear are connected to a joint that has no external loads or reactions applied to it, then the force in non-collinear member is zero. Calculation: Find the bar forces F P produced by the P -system as follows: Let A x and A y be the horizontal and vertical reactions at the hinged support A . Let E y be the vertical reaction at the roller support E . Find the reactions at the supports using equilibrium equations: Summation of moments about A is equal to 0. ∑ M A = 0 E y ( 16 ) − 24 ( 6 ) − 48 ( 12 ) = 0 E y = 45 kips ↑ Summation of forces along y -direction is equal to 0. + ↑ ∑ F y = 0 − A y + E y = 0 A y = 45 kips ↓ Summation of forces along x -direction is equal to 0. + → ∑ F x = 0 − A x + 24 + 48 = 0 A x = 72 kips ← Find the member forces using method of joints: The force in the member DF is zero as it satisfies zero force member condition. Apply equilibrium equation to the joint E : + ↑ ∑ F y = 0 45 + F D E sin 36.87 ° = 0 F D E = − 75 kips + → ∑ F x = 0 − F E F − F D E cos 36.87 ° = 0 − F E F − ( − 75 ) cos 36.87 ° = 0 F E F = 60 kips Apply equilibrium equation to the joint F : + ↑ ∑ F y = 0 − F A F + F E F = 0 F A F = 60 kips Apply equilibrium equation to the joint A : + → ∑ F x = 0 − 72 + F A F − F A D cos 36.87 ° = 0 − 72 + 60 − F A D cos 36.87 ° = 0 F A D = 15 kips + ↑ ∑ F y = 0 − 45 + F A B + F A D sin 36.87 ° = 0 − 45 + F A B + ( 15 ) sin 36.87 ° = 0 F A B = 36 kips Apply equilibrium equation to the joint B : + → ∑ F x = 0 24 + F B D = 0 F B D = − 24 kips + ↑ ∑ F y = 0 − F A B + F B C = 0 F B C = 36 kips Apply equilibrium equation to the joint C : + → ∑ F x = 0 48 + F C D cos 36.87 ° = 0 F C D = − 60 kips Sketch the bar forces produced by the P -system as shown in Figure 1. Consider a dummy load of 1 kips directed horizontally at joint C with the bar forces F Q . Find the reactions at the supports using equilibrium equations: Summation of moments about A is equal to 0. ∑ M A = 0 E y ( 16 ) − 1 ( 12 ) = 0 E y = 0

5th Edition

ISBN: 9781260083330

Author: Leet, Kenneth

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 8, Problem 8P

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Chapter 8 Solutions

Fundamentals Of Structural Analysis:

Ch. 8 - Prob. 1P Ch. 8 - For the truss in Figure P8.1, compute the vertical...Ch. 8 - Prob. 3P Ch. 8 - Prob. 4P Ch. 8 - The pin-connected frame in Figure P8.3 is...Ch. 8 - For the pin-connected frame in Figure P8.5, in...Ch. 8 - Prob. 7P Ch. 8 - Prob. 8P Ch. 8 - Prob. 9P Ch. 8 - (a) Compute the horizontal displacement of joint B...

Ch. 8 - Prob. 11P Ch. 8 - Prob. 12P Ch. 8 - (a) Compute the vertical deflection of joint D...Ch. 8 - Prob. 14P Ch. 8 - (a) In Figure P8.15 compute the vertical and...Ch. 8 - Prob. 16P Ch. 8 - Prob. 17P Ch. 8 - Prob. 18P Ch. 8 - Prob. 19P Ch. 8 - Prob. 20P Ch. 8 - Prob. 21P Ch. 8 - Prob. 22P Ch. 8 - Prob. 23P Ch. 8 - Prob. 24P Ch. 8 - Prob. 25P Ch. 8 - If supports A and E in Figure P8.26 are...Ch. 8 - In Figure P8.27 support D is constructed 1.5 in....Ch. 8 - Prob. 28P Ch. 8 - Prob. 29P Ch. 8 - Compute the vertical displacement of joints B and...Ch. 8 - Prob. 31P Ch. 8 - (a) Compute the slope at A and the horizontal...Ch. 8 - Prob. 33P Ch. 8 - Prob. 34P Ch. 8 - Prob. 35P Ch. 8 - Compute the vertical deflection of joint C in...Ch. 8 - Compute the vertical deflection at B and the...Ch. 8 - Prob. 38P Ch. 8 - Prob. 39P Ch. 8 - Prob. 40P Ch. 8 - Prob. 41P Ch. 8 - Prob. 43P

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Find the horizontal and vertical deflection at joint C .

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Find the horizontal and vertical deflection at joint C.

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