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109
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
R. J. ELLWANGER
are impeded to develop their natural deflected shapes, as shown
in figure 3-d. The frame will be subject to a global shear forces
distribution given by:
(19)
ò
+ + - =
l
l
x
T
d u
Q x w xQ
x x
)(
)
(
)(
1
As was seen in section 2.1, the frame behavior is described by
equation (16). Writing this equation, introducing (18) and (19) and
isolating the terms regarding to the internal forces, gives:
(20)
)
(
)(
4
)(
1
2
1
x w x EJ
d u
Q
x
T
- -
=
+
ò
l
l
l
f
x x
In its turn, the wall will be subject to a bending moments distribu-
tion given by:
(21)
ò
-
- - -
- =
l
l
l
x
T
dx
u x
Q x w xM
x xx
)
()(
)
(
2/ )
(
)(
2
2
As was also seen in section 2.1, the wall behavior is described by
equation (13). Writing this equation, introducing
M(x)
given by (21)
and deriving both members, gives successively:
(22)
ò
-
- - -
- =
l
l
l
x
T
dx
u x
Q x w
dx
d EJ
x xx
f
)
()(
)
(
2/ )
(
2
2
2
(23)
ò
+ + - -=
l
l
x
T
d u
Q x w
dx
d EJ
x x
f
)(
)
(
2
2
2
2
Substituting (20) into (23) and re-arranging:
(24)
0 )
(
)
(
)(
4
2
1
2
1
2
2
2
= - + - +
-
x w x w x EJ
dx
d EJ
l
l
l
f
f
Considering that
w
1
+
w
2
=
w
(total wind load acting on the system)
and defining a new variable
K
=
2 1
/
JJ
, the solution for equa-
tion (24) may be expressed as follows:
(25)
)
(
4
)(
1
2
/ 2
2
/ 2
1
x
EJ
w
eC eC x
Kx
Kx
-
+
+
=
-
l
l
l
l
f
where
(26)
1 e
2 e
8
4
2
1
3
1
+
-
=
K
K
K
KEJ
w C
l
(27)
1 e
e e2
8
4
2
4
1
3
2
+
+
-
=
K
K K
K
KEJ
w C
l
Figure 3 – Association of rigid frames with walls or cores