Matematica
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:
ΣM B = 0: ( 6.25 m ) C y − ( 4 m )( 315 N ) = 0
ΣFy = 0: By − 315 N + C y = 0
C y = 240 N
B y = 75 N
ΣFx = 0:
Bx = 0
Joint FBDs: Joint B:
N
FAB F 75 N = BC = 5 4 3
FAB = 125.0 N C FBC = 100.0 N TJoint C:
N
By inspection:
FAC = 260 N C
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:
ΣM A = 0: (14 ft ) Cx − ( 7.5 ft )( 5.6 kips ) = 0 ΣFx = 0: − Ax + Cx = 0 ΣFy = 0: Ay − 5.6 kips = 0
C x = 3 kips
A x = 3 kips A y = 5.6 kips
Joint FBDs:Joint C: FBC F 3 kips = AC = 5 4 3 FBC = 5.00 kips C FAC = 4.00 kips T Joint A: FAB 1.6 kips = 8.5 4 FAB = 3.40 kips T
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:
ΣM B = 0: ( 6 ft )( 6 kips ) − ( 9 ft ) C y = 0 ΣFy = 0: By − 6 kips − C y = 0 ΣFx = 0: C x = 0
C y =4 kips
B y = 10 kips
Joint FBDs:
Joint C: FAC F 4 kips = BC = 17 15 8 FAC = 8.50 kips T FBC = 7.50 kips C
Joint B:
By inspection:
FAB = 12.50 kips C
FAB 10 kips = 5 4
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:
ΣM B = 0: (1.5 m ) C y + ( 2 m)(1.8 kN ) − 3.6 m ( 2.4 kN ) = 0
C y = 3.36 kN
ΣFy = 0: By + 3.36 kN − 2.4 kN = 0
B y = 0.96 kN
Joint FBDs:
Joint D: ΣFy = 0:
2 FAD − 2.4 kN = 0 2.9 ΣFx = 0: FCD − 2.1 FAD = 0 2.9
FAD = 3.48 kN T
FCD = Joint C:
2.1 (3.48 kN) 2.9
FCD = 2.52 kN C
By inspection:
FAC = 3.36 kN C FBC = 2.52 kN C
Joint B:
ΣFy = 0:
4 FAB − 0.9 kN = 0 5
FAB = 1.200 kN TPROBLEM 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:
ΣFx = 0 : C x = 0
By symmetry: C y = D y = 6 kN
Joint FBDs:
Joint B:
ΣFy = 0: − 3 kN +
1 FAB = 0 5
FAB = 3 5 = 6.71 kN T
ΣFx = 0: 2 FAB − FBC = 0 5
FBC = 6.00 kN C
Joint C:
ΣFy = 0: 6 kN − ΣFx = 0: 6 kN− Joint A:
3 FAC = 0 5
FAC = 10.00 kN C FCD = 2.00 kN T
4 FAC + FCD = 0 5
1 3 ΣFy = 0: − 2 3 5 kN + 2 10 kN − 6 kN = 0 check 5 5
By symmetry:
FAE = FAB = 6.71 kN T FAD = FAC = 10.00 kN C FDE = FBC = 6.00 kN C
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 orcompression.
SOLUTION
FBD Truss:
ΣM A = 0: ( 25.5 ft ) C y + ( 6 ft )( 3 kips ) − ( 8 ft )( 9.9 kips ) = 0
C y = 2.4 kips
ΣFy = 0: Ay + 2.4 kips − 9.9 kips = 0
A y = 7.4 kips
ΣFx = 0: − Ax + 3 kips = 0
A x = 3 kips Joint FBDs:
Joint C: 2.4 kips F F = CD = BC 12 18.5 18.5 FCD = 3.70 kips T FBC = 3.70 kips C or: ΣFx = 0: FBC = FCD ΣFy = 0: 2.4 kips − 2 6 FBC = 0 18.5
same answers
JointD: ΣFx = 0: 3 kips +
17.5 4 ( 3.70 kips ) − FAD = 0 18.5 5
FAD = 8.13 kips T
FAD = 8.125 kips ΣFy = 0:
6 3 ( 3.7 kips ) + (8.125 kips ) − FBD = 0 18.5 5
FBD = 6.075 kips FBD = 6.08 kips C
PROBLEM 6.6 CONTINUED
Joint A:
ΣFx = 0: −3 kips + FAB = 4.375 kips
4 4 (8.125 kips ) − FAB = 0 5 5
FAB = 4.38 kips C
PROBLEM 6.7
Using the method of joints, determine the force in eachmember of the truss shown. State whether each member is in tension or compression.
SOLUTION
FBD Truss:
ΣFy = 0: Ay − 480 N = 0
A y = 480 N Dx = 0 Ax = 0
ΣM A = 0: ( 6 m ) Dx = 0 ΣFx = 0: − Ax = 0
Joint FBDs:
Joint A: 480 N F F = AB = AC 6 2.5 6.5
FAB = 200 N C FAC = 520 N T
Joint B:
200 N F F = BE = BC 2.5 6 6.5
FBE = 480 N C FBC = 520 N T
PROBLEM 6.7 CONTINUED...
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