Civil Engineering Reference
In-Depth Information
If these equations are written using a single term to represent all the
cross-sectional properties, it results in the following:
VQ
It
VAy
It
′
'
V
A
yy
y
y
t
=
=
=
xy
zz
zz
y
′
VQ
It
VAz
It
'
V
A
t
=
=
=
zz
z
z
xz
yy
yy
z
The equations for the shear areas
A
y
and
A
z
can then be found.
It
Ay
A
=
zz
y
′
'
It
Az
yy
A
=
z
′
'
There are three terms in these equations. The first is the centroidal moment
of inertia. The second is the moment of the area,
A
′
y
′ or
A
′
z
′, between the
centroid and the extreme fiber taken about the centroid. The third is the
value
t
, which is the width at the centroid.
Example 5.12
Shear area
Determine the shear areas
A
y
and
A
z
for the a rectangular section.
Figure 5.14 shows the rectangle in the orientation to calculate
A
z
that
corresponds to bending about the Y axis. To find
A
y
the area to the left of
the Z axis will be used.
z
y h
b
Figure 5.14.
Example 5.12 Shear area.
