Civil Engineering Reference
In-Depth Information
For the beam element loaded as shown in Figure P4.2, construct the shear force
and bending moment diagrams. What is the significance of these diagrams with
4.2
d
M
d
x
respect to Equations 4.10, 4.17, and the relation
V
=
from strength of
materials theory?
F
F
L
M
1
M
2
Figure P4.2
4.3
For a uniformly loaded beam as shown in Figure P4.3, the strength of materials
theory gives the maximum deflection as
5
qL
4
384
EI
z
at
x
=
L
/
2
.
Treat this beam as a single finite element and compute the maximum
deflection. How do the values compare?
v
max
=−
y
q
x
L
Figure P4.3
The beam element shown in Figure P4.4 is subjected to a linearly varying load
of maximum intensity
q
o
. Using the work-equivalence approach, determine the
nodal forces and moments.
4.4
y
q
o
x
L
Figure P4.4
4.5
Use the results of Problem 4.4 to calculate the deflection at node 2 of the beam
shown in Figure P4.5 if the beam is treated as a single finite element.
y
q
o
x
1
2
E
,
I
z
,
L
Figure P4.5
