CIV100
Solutions
Section B/E
Fall 2011
Assignment 6
Due on Monday, October 24
th
2011
Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required.
1 The frame shown is supported by pins at A
and B. Pulley F has a radius of 50mm.
Determine:
(a) the reaction components at A and B,
(b) the force components at C on segment BCF.
Solution
:
(a) Treat the structure as a whole and the FBD is
as follows:
W=(2800kg)(9.81N/kg)=27.468kN
∑
−
=
⇒
=
+
−
−
⇒
=
kN
R
W
R
M
AX
AX
B
4
.
115
0
)
05
.
0
1
(
)
25
.
0
(
0
∑
=
⇒
=
+
−
⇒
=
kN
R
W
R
M
BX
BX
A
4
.
115
0
)
05
.
0
1
(
)
25
.
0
(
0
∑
=
−
+
⇒
=
↑
+
0
0
W
R
R
F
BY
AY
Y
……………….(1)
Separate all segments and analysis them respectively, the FBD is as follows
Analyze the straight bar,
∑
−
=
⇒
=
−
−
⇒
=
kN
R
W
R
M
BY
BY
C
4
.
82
0
)
75
.
0
(
)
25
.
0
(
0
Substitute R
BY
in (1), we have
kN
R
AY
8
.
109
=
(b)
Analyze straight bar again,
kN
R
W
R
R
F
CX
CX
BX
X
9
.
87
0
0
−
=
⇒
=
−
+
⇒
=
→
+
∑
kN
R
W
R
R
F
CY
CY
BY
Y
9
.
109
0
0
=
⇒
=
−
+
⇒
=
↑
+
∑
R
BX
R
BY
R
CX
R
CY
W
W
B
C
W
W
F
F
W
W
R
CX
R
CY
R
AX
R
AY
A
C
W
W
R
AX
R
AY
R
BX
R
BY
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CIV100
Solutions
Section B/E
Fall 2011
Assignment 6
Due on Monday, October 24
th
2011
Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required.
2 The shown frame is supported by pins at A and
C. Point B is an internal pin in the frame. Find:
(a) The reaction components at the supports A and
C.
(b) The magnitude of force acting on the pin at B.
Hint: Split the frame into 2 bodies AB and BC
Solution
:
(a) The FBD for the entire frame has 2
unknown reaction components at A and 2 at
B. But since I have only 3 equilibrium
equations, how can I solve 4 unknowns? The
key lies in the pin at B.
Let’s work with what we have first. Applying the equilibrium equations:
Σ
M
A
= 0
(3)(2) – (2.4)(3) + (3.2)(1.5) + (Cy)(3)=0
Cy = 2.8 kN
Σ
M
C
= 0
(3)(2) + (3.2)(1.5)  (Ay)(3)=0
Ay = 0.4 kN
(Negative value means that it is opposite to the direction shown)
To find Ax and Cx I cannot use
Σ
Fx = 0. Thus I must split the frame at B which will expose 2
internal forces Bx and By.
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 Spring '08
 NAHRVAR
 Force, FBD, kN, Section B/E

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