Civil Engineering Reference
In-Depth Information
Example 4.11
Castigliano's second theorem
Find the reactions for the propped end beam loaded as shown in Figure 4.23.
Since this is a statically indeterminate beam, a redundant force will
be applied at point
A
. The force will be represented as
P
but is actually the
real vertical reaction on the left end
R
A
. The last drawing in Figure 4.23 is
a free-body diagram of a left-hand section of the beam to find the moment
equation by equilibrium.
w
Z
X
A
B
L
w
wL
2
6
-PL
w
2
-P
P
w
L
M
P
x
V
Figure 4.23.
Example 4.11 Castigliano's second theorem.
A free-body diagram for the total beam is drawn in Figure 4.23 with
reactions at the fixed end written in terms of the redundant force
P
. These
reactions are found by equilibrium.
1
23
wL
L
Σ
M
==−−+
0
M PL
B
B
2
wL
M
B
=−
PL
(4.10)
6
1
2
Σ
F
== +−
0
R P L
y
B
wL
Σ
R
B
=−
2
P
(4.11)
