Civil Engineering Reference
In-Depth Information
B
A
D
F
IGURE
9.28
Distribution of direct stress
in beam section of Ex. 9.10
C
SECOND MOMENTS OF AREA OF INCLINED AND
CURVED THIN-WALLED SECTIONS
Thin-walled sections frequently have inclined or curved walls which complicate the
calculation of section properties. Consider the inclined thin section of Fig. 9.29. The
second moment of area of an element
δ
s about a horizontal axis through its centroid
sy
2
. Therefore the total second moment of area of the section about
G
z
,
I
z
, is given by
G is equal to
t
δ
y
a
/2
s
s
a
/2
b
G
z
F
IGURE
9.29
Second moments of area of an
inclined thin-walled section
t
a
/
2
a
/
2
ty
2
d
s
t
(
s
sin
β
)
2
d
s
I
z
=
=
−
a
/
2
−
a
/
2
i.e.
a
3
t
sin
2
β
12
I
z
=
Similarly
a
3
t
cos
2
β
12
The product second moment of area of the section about G
zy
is
I
y
=
a
/
2
a
/
2
I
zy
=
tzy
d
s
=
t
(
s
cos
β
)(
s
sin
β
)d
s
−
a
/
2
−
a
/
2
i.e.
a
3
t
sin 2
β
24
I
zy
=
