Civil Engineering Reference
In-Depth Information
E
XAMPLE
9.8
A beam having the cross section shown in Fig. 9.25 is subjected to
a hogging bending moment of 1500Nm in a vertical plane. Calculate the maximum
direct stress due to bending stating the point at which it acts.
40 mm
80 mm
y
A
B
8 mm
D
y
C
z
G
z
80 mm
EF
8 mm
F
IGURE
9.25
Beam section of Ex. 9.8
The position of the centroid, G, of the section may be found by taking moments of
areas about some convenient point. Thus
×
+
×
¯
y
=
×
×
+
×
×
(120
8
80
8)
120
8
4
80
8
48
which gives
y
¯
=
21
.
6mm
and
×
+
×
¯
z
=
×
×
+
×
×
(120
8
80
8)
80
8
4
120
8
24
giving
¯
z
=
16mm
The second moments of area referred to axes G
zy
are now calculated.
(8)
3
(80)
3
12
120
×
8
×
(17
.
6)
2
(26
.
4)
2
I
z
=
+
120
×
8
×
+
+
80
×
8
×
12
10
6
mm
4
=
1
.
09
×
(120)
3
12
(8)
3
12
8
×
80
×
(8)
2
(12)
2
I
y
=
+
120
×
8
×
+
+
80
×
8
×
10
6
mm
4
=
1
.
31
×
I
zy
=
120
×
8
×
(
−
8)
×
(
+
17
.
6)
+
80
×
8
×
(
+
12)
×
(
−
26
.
4)
10
6
mm
4
=−
0
.
34
×
Since
M
z
=−
1500Nm and
M
y
=
0 we have from Eq. (9.31)
10
3
10
6
)
z
10
3
10
6
)
y
×
×
−
×
+
×
×
×
1500
(
0
.
34
1500
(1
.
31
σ
x
=−
10
6
10
6
10
6
)
2
1
.
09
×
×
1
.
31
×
−
(
−
0
.
34
×
