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 By y MC Σ= = = C 0: 315 N 0 75 N yy y y FB C + = = B 0: 0 xx F = B 75 N 54 3 AB BC FF == 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 Ax x MC Σ= = = C 0: 0 3 kips xx x x FA C Σ= − + = = A 0: 5.6 kips 0 5.6 kips yy y = = A 3 kips 54 3 BC AC FF == 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
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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 By y MC Σ= = = C 0: 6 kips 0 10 kips yy y y FB C − = = B 0: 0 xx F = C 4 kips 17 15 8 AC BC FF == 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 54 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 By MC Σ= + = 3.36 kN y = C 0: 3.36 kN 2.4 kN 0 yy FB + = 0.96 kN y = B 2 0: 2.4 kN 0 2.9 yA D FF = 3.48 kN T AD F = W 2.1 0 2.9 xC D A D F = 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 B = 1.200 kN T AB F = W
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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 yy == CD 1 3 kN 0 5 yA B FF Σ= − + = 3 5 6.71 kN T AB F W 2 0 5 xA B B C F = 6.00 kN C BC F = W 3 0: 6 kN 0 5 C = 10.00 kN C AC F = W 4 0: 6 kN 0 5 C C D F + = 2.00 kN T CD F = W 13 2 3 5 kN 2 10 kN 6 kN 0 check 5 5 y F  + =   By symmetry: 6.71 kN T AE AB W 10.00 kN C AD AC W 6.00 kN C DE BC 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 Ay MC Σ= + = 2.4 kips y = C 0: 2.4 kips 9.9 kips 0 yy FA + = 7.4 kips y = A 0: 3 kips 0 xx Σ= − + = 3 kips x = A 2.4 kips 12 18.5 18.5 CD BC FF == 3.70 kips T CD F = W 3.70 kips C BC F = W or: 0: x BC CD F = 6 0: 2.4 kips 2 0 18.5 yB C = same answers 17.5 4 0: 3 kips 3.70 kips 0 18.5 5 xA D + = 8.125 kips AD F = 8.13 kips T AD F = W 63 0: 3.7 kips 8.125 kips 0 18.5 5 D + = 6.075 kips BD F = 6.08 kips C BD F = W
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Joint A : PROBLEM 6.6 CONTINUED () 44 0: 3 kips 8.125 kips 0 55 xA B FF 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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CHAPTER 6 - PROBLEM 6.1 Using the method of joints,...

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