Civil Engineering Reference
In-Depth Information
∑
∑
(
)
(
)
(
)
EwtH Y
−+ −
E
EAHY
−
ci i
i
s
c
si
si
(7.9 7)
i
i
Y
=
c
EA
∑
∑
EwtB X
(
−+ −
)
(
E
EABX
)
(
−
)
ci i
i
s
c
si
si
(7.98)
X
=
i
i
c
EA
where
Y
i
and
Y
si
are measured from the top extreme fiber, and
X
i
and
X
si
are
measured from the rightmost extreme fiber, as seen in Figure 7.19.
Elastic flexural rigidities about the elastic centroid
EI
X
, EI
y
and
EI
xy
∑
∑
2
2
EI
=
EwtH YY
(
− −+ −
)
(
EEAH YY
)
(
−
−
)
(7.9 9)
x
c
ii
i
c
s
csi
si
c
i
i
∑
∑
2
2
EI
=
EwtB XX
(
− −+ −
)
(
EEAB XX
)
(
−
−
)
(7.10 0)
y
c
ii
i
c
s
csi
si
c
i
i
∑
∑
(
)
EI
=
EwtH YYBX X
(
−
−
)
−
−
xy
c
ii
i
c
i
c
i
(
)
+
(
EEAH YYBX X
−
)
(
−− −−
)
(7.101)
s
csi
si
c
si
c
i
Typically the initial elastic
Y
c
=
H
/2,
X
c
=
B
/2, and
EI
xy
= 0
The depth of the geometric section centroid position from the bottom
and left fibers of the section
Y
G
,
X
G
is
H
(7.10 2)
Y
=
G
2
B
(7.103)
X
=
G
2
2. Defining the eccentricity
e
, which specifies the radial path of loading on the
interaction diagram (Figure 7.20), and also defining the angle α in between
the resultant moment
GM
R
and
GM
X
3. Defining the loading step Δ
GP
as a small portion of the maximum load, and
computing the axial force at the geometric centroid,
(7.10 4)
GP
=
GP
+
GP
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