Civil Engineering Reference
In-Depth Information
occurs in the web, the top lamination of the top chord, and the bottom lamination of the
top chord. All these net moments of inertia must be calculated if joints occur at those
locations.
Moment of inertia of the individual section members (two 2× flat, three 2× on edge
and plywood web) about their own neutral axis, where
t
�
= total thickness of continu-
ous parallel plies of the plywood:
td
()
3
bt
()
2
12
3
3
12
td
3
�
3
I
o
=
+
+
12
∑
I
t
=+
I
Ax
2
=+
I
() () (
2
tbx
2
+
3
td xt dx
2
+
)
2
o
o
3
4
�
3
pw
eb only
I
n
=+
I
() ()
2
tb x
2
+
3
tdx
2
if jointoccurs in w
o
3
4
Determine Shear Properties
Q
t
and
Q
f
The section property
Q
t
is equal to the first statical moment (in
3
) lying above or below
the neutral axis of all parallel-grain material, regardless of any butt joints, and is used
to calculate the horizontal shear stresses in the section.
2
C
C
2
Qtbx
=
()
2
+
t
3
or
Qtdx
=
()
3
+
t
4
�
�
t
3
2
t
4
2
The section property
Q
f
is equal to the first statical moment (in
3
)
about the neutral axis
of all parallel-grain material in the upper or lower flanges, regardless of any butt joints,
and is used to calculate the shear flow from the web to the flanges, rolling shear stresses.
Qtbx
=
()
2
or
Qtdx
=
()
3
f
3
f
4
Transformed Sections
If the modulus of elasticity of the members varies, then a transformed section must be
used. Sections should be transformed to the material of the most highly stressed portion
of the section. For bending, the section is normalized to the flange. For rolling shear and
horizontal shear, the section is normalized to the web. The location of the neutral axis
for a transformed section is as follows:
=
∑
∑
AyE
AE
y
E
= modulus of elasticity of individual material being calculated.
E
top pl
= modulus of elasticity of top plate, psi
E
bot hdr
= modulus of elasticity of bottom header built up 2×, psi
E
pw
= modulus of elasticity of plywood, psi
td
(
)
3
3
3
bt
()
2
12
2
12
td
�
3
EI
=
E
+
E
+
E
o
top pl
bothdr
pw
12
2
2
2
EI
=+
EI
E
()
2
tbx
+
E
()
3
tdx
+
E
(
td x
�
3
)
t
o
toppl
3
bot hdr
4
p
w
pw
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