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Descripción: OPOSICIONES INFANTIL
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: Σ M
= B0 :
( 6.25 m ) C
− y4
0: B
315 N
ΣF y=
y−
(
ΣF x =
m ) (315 N ) +
C
y=
=
C
0
0
B
y=
= y240
N
75 N
Bx = 0
0:
Joint FBDs:
Joint B:
F
5
AB
=
F
4
BC
=
75 N 3
N
Joint C :
By inspection: N
F AB
=
125.0 N C
F BC
=
100.0 N T
F AC
=
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:
Σ M
= A0:
(14 ft ) C ΣF x =
ΣF
= y
(
− x 7.5
0:
−
0: A
A
−y
x+
ft ) (5.6 kips ) C
x=
5.6 kips
A
0
=
=
A
0
C = x3 kips
0 x=
3 kips
= y
5.6 kips
Joint FBDs:
Joint C : F
5
BC
=
F
4
AC
=
3 kips 3 F BC
=
5.00 kips C
F AC
=
4.00 kips T
F AB
=
3.40 kips T
Joint A: F AB
8.5
=
1.6 kips 4
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: Σ M
=B0:
ΣF y=
( 6 ft )( 6 kips ) − (9 ft )C 0: B
y−
6 kips
−
C
y=
B
0
0: C x
ΣF x =
C = y 4 kips
= y0
=
y=
10 kips
0
Joint FBDs:
Joint C :
F
17
AC
=
F
BC
15
=
4 kips 8 F AC
=
8.50 kips T
F BC
=
7.50 kips C
Joint B:
By inspection:
F AB
5
=
10 kips 4
F AB
=
12.50 kips C
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:
Σ M B =
0: (1.5 m ) C y
+
(2 m )(1.8 kN ) − 3.6 m (2.4 kN ) = 0
C y = 3.36 kN ΣF y =
0: B y
+
3.36 kN
−
2.4 kN
=
0
B y = 0.96 kN
Joint FBDs:
Joint D:
ΣF
2
= y0:
2.9 ΣF
F CD
=
− AD2.4
F
= x
0: F
2.1 2.9
kN
− CD
=
2.1 2.9
(3.48 kN)
0
F
= AD
F AD
=
3.48 kN T
F CD
=
2.52 kN C
F AC
=
3.36 kN C
F BC
=
2.52 kN C
0
Joint C :
By inspection:
Joint B:
ΣF
=y 0:
4 5
F
− AB0.9
kN
=
0
F AB
=
1.200 kN T
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:
ΣF x =
By symmetry: C y
= Dy =
Joint FBDs:
ΣF
0 : C x
=
0
6 kN
0: y− 3 kN
=
Joint B:
1
+
F
5
0 AB
=
F AB
2
ΣF
= x
0:
ΣF
=
0:y 6 kN
Joint C :
ΣF
=x 0:
5
6 kN
− AB
F
−
−
4 5
3 5
F
F
= 0 BC
= 0 AC
+ ACF
F
3 5
=
6.71 kN T
F BC
=
6.00 kN C
=
F AC
= 0 CD
=
10.00 kN C
=
F CD
2.00 kN T
Joint A:
ΣF y =
0:
1
− 2
5
3 5 kN
By symmetry:
+
3 2 10 kN 5
6 kN
−
F
AE=
F
F
AD=
F
F
DE=
=
6.71 kN T
AB = AC =
F
0 check
10.00 kN C
BC =
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 or compression.
SOLUTION FBD Truss:
Σ M A =
0: ( 25.5 ft ) C y
+
( 6 ft )(3 kips ) − (8 ft )(9.9 kips ) =
0
C y = 2.4 kips ΣF y =
0: Ay
+
2.4 kips
−
9.9 kips
=
0
A y = 7.4 kips ΣF x =
0:
−
Ax
+
3 kips
=
0
A x = 3 kips
2.4 kips
Joint FBDs:
12
=
FCD
18.5
=
F BC
18.5
Joint C :
or:
ΣF x=
0: F
F
BC=
ΣF
CD
=
0: 2.4 y kips
−
F CD
=
3.70 kips T
F BC
=
3.70 kips C
2
6 18.5
F
=
0
BC
same answers
Joint D: ΣF
=
0: 3 kipsx + F AD
ΣF
=
0:
6 18.5 F BD
=
17.5 18.5
( 3.70 kips ) −
8.125 kips
4 5
F
F AD
=
=
3
( 3.7 (8.125 kips ) − F y kips ) + 6.075 kips
F BD
=
AD
8.13 kips T =
5
=
0
0
BD
6.08 kips C
PROBLEM 6.6 CONTINUED
Joint A:
ΣF
F AB
=
4.375 kips
=
0: −3 kips x
+
4 5
( 8.125 kips ) −
4 5
F AB
F =
=
0
AB
4.38 kips C
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.
SOLUTION FBD Truss:
ΣF
= y
0: A Σ M
−y
480 N
0: ( 6 m ) D
= A
0:
ΣF x=
−
A
A
0
=
x=
0
= x
= y
480 N
D = x 0
0 A
x=
0
Joint FBDs:
Joint A: 480 N 6
Joint B:
200 N 2.5
=
=
F
AB
2.5
F
6
=
BE
=
F
AC
6.5
F
BC
6.5
F AB
=
200 N C
F AC
=
520 N T
F BE
=
480 N C
F BC
=
520 N T
PROBLEM 6.7 CONTINUED
Joint C : FCD
By inspection:
ΣF
Joint D:
=
0:
2.5 x
6.5
( 520 N ) − F
=
0 DE
=
F CE
=
F DE
520 N T
=
200 N C
PROBLEM 6.8
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:
0: ( 9 ft ) F y
Σ M E =
−
( 6.75 ft )( 4 kips ) − (13.5 ft )(4 kips ) = 0 F y = 9 kips
