CHAPTER 6

# CHAPTER 6 - PROBLEM 6.1 Using the method of joints...

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PROBLEM 6.1 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION FBD Truss: Joint FBDs: Joint B : N Joint C : N ( ) ( )( ) 0: 6.25 m 4 m 315 N 0 240 N B y y M C Σ = = = C 0: 315 N 0 75 N y y y y F B C Σ = + = = B 0: 0 x x F Σ = = B 75 N 5 4 3 AB BC F F = = 125.0 N C AB F = W 100.0 N T BC F = W By inspection: 260 N C AC F = W

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PROBLEM 6.2 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION FBD Truss: Joint FBDs: Joint C : Joint A : ( ) ( )( ) 0: 14 ft 7.5 ft 5.6 kips 0 3 kips A x x M C Σ = = = C 0: 0 3 kips x x x x F A C Σ = + = = A 0: 5.6 kips 0 5.6 kips y y y F A Σ = = = A 3 kips 5 4 3 BC AC F F = = 5.00 kips C BC F = W 4.00 kips T AC F = W 1.6 kips 8.5 4 AB F = 3.40 kips T AB F = W
PROBLEM 6.3 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION FBD Truss: Joint FBDs: Joint C : Joint B : ( )( ) ( ) 0: 6 ft 6 kips 9 ft 0 4 kips B y y M C Σ = = = C 0: 6 kips 0 10 kips y y y y F B C Σ = = = B 0: 0 x x F Σ = = C 4 kips 17 15 8 AC BC F F = = 8.50 kips T AC F = W 7.50 kips C BC F = W By inspection: 12.50 kips C AB F = W 10 kips 5 4 AB F =

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PROBLEM 6.4 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION FBD Truss: Joint FBDs: Joint D : Joint C : Joint B : ( ) ( )( ) ( ) 0: 1.5 m 2 m 1.8 kN 3.6 m 2.4 kN 0 B y M C Σ = + = 3.36 kN y = C 0: 3.36 kN 2.4 kN 0 y y F B Σ = + = 0.96 kN y = B 2 0: 2.4 kN 0 2.9 y AD F F Σ = = 3.48 kN T AD F = W 2.1 0: 0 2.9 x CD AD F F F Σ = = 2.1 (3.48 kN) 2.9 CD F = 2.52 kN C CD F = W By inspection: 3.36 kN C AC F = W 2.52 kN C BC F = W 4 0: 0.9 kN 0 5 y AB F F Σ = = 1.200 kN T AB F = W
PROBLEM 6.5 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION FBD Truss: Joint FBDs: Joint B : Joint C : Joint A : 0 : x F Σ = 0 x = C By symmetry: 6 kN y y = = C D 1 0: 3 kN 0 5 y AB F F Σ = + = 3 5 6.71 kN T AB F = = W 2 0: 0 5 x AB BC F F F Σ = = 6.00 kN C BC F = W 3 0: 6 kN 0 5 y AC F F Σ = = 10.00 kN C AC F = W 4 0: 6 kN 0 5 x AC CD F F F Σ = + = 2.00 kN T CD F = W 1 3 0: 2 3 5 kN 2 10 kN 6 kN 0 check 5 5 y F Σ = + = By symmetry: 6.71 kN T AE AB F F = = W 10.00 kN C AD AC F F = = W 6.00 kN C DE BC F F = = W

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PROBLEM 6.6 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION FBD Truss: Joint FBDs: Joint C : Joint D : ( ) ( )( ) ( )( ) 0: 25.5 ft 6 ft 3 kips 8 ft 9.9 kips 0 A y M C Σ = + = 2.4 kips y = C 0: 2.4 kips 9.9 kips 0 y y F A Σ = + = 7.4 kips y = A 0: 3 kips 0 x x F A Σ = + = 3 kips x = A 2.4 kips 12 18.5 18.5 CD BC F F = = 3.70 kips T CD F = W 3.70 kips C BC F = W or: 0: x BC CD F F F Σ = = 6 0: 2.4 kips 2 0 18.5 y BC F F Σ = = same answers ( ) 17.5 4 0: 3 kips 3.70 kips 0 18.5 5 x AD F F Σ = + = 8.125 kips AD F = 8.13 kips T AD F = W ( ) ( ) 6 3 0: 3.7 kips 8.125 kips 0 18.5 5 y BD F F Σ = + = 6.075 kips BD F = 6.08 kips C BD F = W
Joint A : PROBLEM 6.6 CONTINUED ( ) 4 4 0: 3 kips 8.125 kips 0 5 5 x AB F F Σ = + = 4.375 kips AB F = 4.38 kips C AB F = W

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PROBLEM 6.7 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.
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• Spring '08
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