Civil Engineering Reference
In-Depth Information
4. The governing equation for the axial displacement
of a 1D rod embedded in an
elastic medium and subjected to a distributed axial load
u
F
is:
d
2
u
EA
2
−
ku
+
F
=
0
d
x
where
EA
is the axial stiffness of the rod and
k
is the stiffness of the surrounding
elastic material.
Use a 2-element discretization to estimate the axial displacement at the mid point
and tip of the rod shown in Figure 4.43 which is subjected to a
point
load of 5 at its
tip.
Ans: 0.0098, 0.0588
EA = 100
k = 60
Elastic medium
5
4
Figure 4.43
5. A propped cantilever is subjected to the loads and displacements indicated in Fig-
ure 4.44. Using two finite elements estimate the internal moment at the center of the
beam.
Ans:
M
=
1975
EI= 4000
Uniform load
q= -600
Fixed translation
=0.1
Fixed nodal
rotation =0.1
1
1
Figure 4.44
6. Use a single finite element to estimate the lowest buckling load of a column fully
fixed at one end and restrained at the other in such a way that it can translate but
not rotate as shown in Figure 4.45. Express your solution in terms of
EI
and
L
.
2
Ans:
P
crit
=
10
EI
/L
