HOMEWORK PROBLEMS
Week 4: Due Friday 7 October
1.
Determine the coordinates ¯
x
,
¯
y
of the centroid
C
of the area shaded in Figure 1.
1
1
0
x
y
2
y =
x
y =
x
Figure 1
2.
A distributed load
w
(
x
) =
1
+
3
x

2
x
2
acts on the cantilever beam
AB
, as shown in Figure 2, where
x
is measured in meters and
w
is
in kN/m. Find the reactions (force and moment) at
A
.
2
1 m
(kN/m)
x
w(x) = 1 + 3x  2x
A
B
Figure 2
1
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The Lshaped bar
ACE
in Figure 3 is pinned at
A
and makes contact through a frictionless
roller with the inclined surface at
E
. It is loaded by a vertical force
F
at
D
. Draw a freebody
diagram of the bar, determine the reactions at
A
, and hence find the internal forces (axial force,
shear force and bending moment) at the point
B
.
3
4
F
A
B
C
D
E
a
a
a
a
Figure 3
4.
Figure 4 shows an Lshaped steel pipe
OAB
which is bolted to a vertical wall at
O
and loaded
by two horizontal forces at
B
. Calculate all the reaction forces and moments at the wall
O
and
indicate which moments are bending moments and which are torques.
2 m
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 Fall '07
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 Force, shear force, 2m, 4 foot, 6.5 meters

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