Civil Engineering Reference
In-Depth Information
200 mm
y
150 N/mm
2
P
20 mm
y
z
G
85.3 N/mm
2
200 mm
20 mm
F
IGURE
9.10
Direct stress
distribution in
beam section of
Ex. 9.5
79.1 N/mm
2
(a)
(b)
The second moment of area of the section about the
z
axis is then obtained using the
methods of Section 9.6 and is
65
3
45
3
155
3
3
×
×
×
200
180
20
10
6
mm
4
I
z
=
−
+
=
×
37
.
7
3
3
Since the line of action of the load intersects the
y
axis,
e
z
in Eq. (9.15) is zero so that
P
A
+
Pe
y
I
z
σ
x
=
y
(i)
Also
e
y
=+
55mm so that
Pe
y
=+
55
P
and Eq. (i) becomes
P
1
10
6
y
55
σ
x
=
8000
+
37
.
7
×
or
10
−
4
10
−
6
y
)
σ
x
=
P
(1
.
25
×
+
1
.
46
×
(ii)
It can be seen from Eq. (ii) that
σ
z
varies linearly through the depth of the beam
from a tensile value at the top of the flange where
y
is positive to either a tensile or
compressive value at the bottom of the leg depending on whether the bracketed term
is positive or negative. Therefore at the top of the flange
10
−
4
10
−
6
+
150
=
P
[1
.
25
×
+
1
.
46
×
×
(
+
65)]
which gives the limiting value of
P
as 682 kN.
At the bottom of the leg of the section
y
=−
155mm so that the right-hand side of
Eq. (ii) becomes
10
−
4
10
−
6
10
−
4
P
P
[1
.
25
×
+
×
×
−
≡−
×
1
.
46
(
155)]
1
.
01
