Civil Engineering Reference
In-Depth Information
23. The propped cantilever shown in Figure 4.58 has a constant
E
and a linearly varying
I
. Use two beam elements to estimate the reaction force at B.
Ans:
R
B
=
177
.
1 (analytical 168.75)
q=50
E= 100
I(0) = 100
I(10)= 20
B
x
10
Figure 4.58
24. The column shown in Figure 4.59 has been subjected to a gradually increasing axial
load
P
. The onset of instability was observed when
P
=
102
.
7. Estimate the stiffness
EI
of the lower half of the column.
Ans:
EI
=
100
P= 102.7
5
EI= 200
5
EI= ?
Figure 4.59
25. A single railway track resting on a ballast sub-grade can be approximated as a beam
of length
L
of stiffness
EI
resting on an elastic foundation of stiffness
k
. If a single
concentrated load
acts on a rail between the ties which can be assumed to be
rigid supports, use a single finite element to estimate the relationship between
EI
,
k
P
so that the rail deflection can be limited to 5 units. (Hint: Consider the
cases of both simply supported and fully clamped end conditions since reality will
lie somewhere in between. In the fully clamped case you will need to consider just
half the problem and account for symmetry.)
Ans:
,
P
,and
L
320
EI
L
8
k
3
960
EI
L
13
kL
7
P<
+
simply supported;
P<
+
clamped
3
3
26. A laterally loaded pile is to be modelled as a beam on an elastic foundation system as
shown in Figure 4.60. Use a single beam element to estimate the lateral deflection of
the pile cap under a unit load. (Hint: You may assume the base of the pile is clamped.)
Ans: 0.489
