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MAE 101. Statics and Strength of Materials
© G. E. Orient 2006
1
Midterm  Solution
MAE 101. Statics and Strength of Materials
© G. E. Orient 2006
2
Problem 1
•
The horizontal bar of weight
W
is supported by a roller support at
A
and the cable
BC
. Apply
rigorous analysis of equilibrium to determine the angle
α
, the tension in the cable, and the
magnitude of the reaction at
A
. (The answer may be intuitively obvious, but prove it using
basic principles)
–
Free body diagram and equations of equilibrium
–
From
(*)
either
T=0
or
cos α=0
•
If
T=0
then
(**)
cannot be satisfied
•
If
cos α=0
then
α=π/2
and
T=W/2
A
y
W
T
2
sin
0
sin
2
sin
0
cos
2
0
2
)
(
W
T
T
W
T
W
A
F
T
F
W
A
W
L
LA
M
y
y
x
y
y
B
=
→
=
+

=
+

=
=
=
=
→
=
+

=
∑
∑
∑
α
(*)
(**)
MAE 101. Statics and Strength of Materials
© G. E. Orient 2006
3
Problem 2
•
The Pratt bridge truss supports loads at
F
,
G
, and
H
. Determine the axial forces in members
BC
,
BG
, and
FG
.
l=4m, F
1
=60 kN, F
2
=80 kN, F
3
=20 kN
–
Global FBD,
Equilibrium
–
Method of joints
•
Joint A
A
x
A
y
E
y
F
2
F
1
F
3
∑
∑
∑
=
→
=
=
=

+
+
=
→
=
+



=
=
+
+
=
→
=
+



=
0
0
90
0
70
4
3
2
0
4
3
2
3
2
1
3
2
1
3
2
1
3
2
1
)
(
x
x
x
y
y
y
y
y
y
y
A
A
A
F
kN
E
F
F
F
A
E
F
F
F
A
F
kN
F
F
F
E
l
E
l
F
l
F
l
F
M
P
AF
A
y
P
AB
kN
A
P
P
P
P
F
kN
A
A
P
P
A
F
y
AB
AF
AF
AB
x
y
y
AB
AB
y
y
90
tan
cos
0
cos
3
.
127
2
sin
0
sin
=

=

=
→
=
+
=

=

=

=
→
=
+
=
∑
∑
α
F
2
F
1
F
3
l
l
l
l
l
α=45
o
MAE 101. Statics and Strength of Materials
© G. E. Orient 2006
4
Problem 2 – cont’d
–
Method of joints
•
Joint
F
•
Joint
B
F
1
P
AF
P
FG
P
FB
kN
F
P
F
P
F
T
kN
P
P
P
P
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