Civil Engineering Reference
In-Depth Information
P
1,0
EI
L
0,0
Figure 4.45
7. A cantilever of unit length and stiffness supports a unit load at its tip. The governing
equation for the transverse deflection
y
as a function of
x
is given by
d
2
y
=
1
−
x
2
d
x
Estimate the tip deflection using the trial solution,
2
3
y
=
C(
3
x
−
x
)
and Galerkin's weighted residual method.
Ans: 1
/
3
8. A beam (
1), fully clamped at one end and simply supported at the
other, supports a unit point transverse load (
L
=
1,
EI
=
Q
=
1) at its mid-span. The beam is
also subjected to a compressive axial force
which will reduce the bending stiff-
ness of the beam. Using two ordinary beam elements of equal length, assemble the
global stiffness equations for this system in matrix form, but do not attempt to solve
them.
P
=
(
192
−
24
P/
5
)
0
(
24
−
P/
10
)
U
1
U
2
U
3
−
1
0
0
Ans:
0
(
16
−
2
P/
15
)(
4
+
P/
60
)
(
24
−
P/
10
)
(
4
+
P/
60
)(
8
−
P/
15
)
9. A simply supported beam of stiffness
EI
andlength2
L
rests on an elastic foundation
at its mid-span. By discretising half the
beam, estimate the value of P that would result in a mid-span transverse deflection
of 1 unit.
Ans:
of stiffness
k
and supports a point load
P
3
2
2
2
3
P
=
24
EI
/L
+
26
kL/
35
−
(
13
kL
/
210
−
12
EI
/L
)
/(kL
/
105
+
4
EI
/L)
