Civil Engineering Reference
In-Depth Information
Simplifying Eq. (i) we have
L
/
2
x
)
2
d
x
L
W
2
EIL
x
2
)d
x
θ
A
=
(
Lx
−
+
(
L
−
(ii)
0
L
/
2
Hence
.
/
!
L
x
2
2
L
/
2
3
(
L
x
)
3
L
L
/
2
x
3
3
W
2
EIL
1
θ
A
=
−
−
−
0
"
0
from which
WL
2
16
EI
which is the result that may be obtained from Eq. (iii) of Ex. 13.5.
θ
A
=
E
XAMPLE
15.6
Calculate the vertical deflection of the joint B and the horizontal
movement of the support D in the truss shown in Fig. 15.12(a). The cross-sectional
area of each member is 1800mm
2
and Young's modulus,
E
, for the material of the
members is 200 000N/mm
2
.
40 kN
E
F
4 m
A
D
B
C
100 kN
4 m
4 m
4 m
(a)
E
F
E
F
D
A
D
A
1
F
IGURE
15.12
Deflection of a truss
using the unit load
method
B
C
B
C
1
(b)
(c)
The virtual force systems, i.e. unit loads, required to determine the vertical deflection
of B and the horizontal deflection of D are shown in Fig. 15.12(b) and (c), respectively.
Therefore, if the actual vertical deflection at B is
δ
B,v
and the horizontal deflection at D
is
δ
D,h
, respectively.
The internal actual and virtual force systems comprise axial forces in all the members.
δ
D,h
the external virtual work done by the unit loads is 1
δ
B,v
and 1
