Civil Engineering Reference
In-Depth Information
F
A
,
w
A
A
B
F
B
,
w
B
F
,
w
F
F, w
w
x
x
x
L
F
IGURE
17.1
Axially loaded
member
(a)
(b)
so that
F
AE
d
x
Therefore the axial displacement at the section a distance
x
from A is given by
d
w
=
x
F
AE
d
x
w
=
0
which gives
F
AE
x
w
=
+
C
1
in which
C
1
is a constant of integration. When
x
=
0,
w
=
w
A
so that
C
1
=
w
A
and the
expression for
w
may be written as
F
AE
x
w
B
=
+
w
A
(17.1)
In the absence of any loads applied between A and B,
F
=
F
B
=−
F
A
and Eq. (17.1)
may be written as
F
B
AE
x
w
=
+
w
A
(17.2)
Thus, when
x
=
L
,
w
=
w
B
so that from Eq. (17.2)
F
B
AE
L
w
B
=
+
w
A
or
AE
L
(
w
B
−
F
B
=
w
A
)
(17.3)
Furthermore, since
F
B
=−
F
A
we have, from Eq. (17.3)
AE
L
(
w
B
−
−
F
A
=
w
A
)
or
AE
L
(
w
B
−
F
A
=−
w
A
)
(17.4)
