Civil Engineering Reference
In-Depth Information
Moment divided by
EI
,
M
/
EI
, diagrams are drawn by parts. Moment
diagrams by parts assume each force is acting about point B as if it was the
only force. The vertical reaction on the left,
R
A
, is used as the redundant
force. The method of superposition will be used to solve for the assumed
redundant,
R
A
. The reactions at the fixed-end on the right can be written in
terms of the load,
w
, as follows from equilibrium on Figure 4.9 (ignoring
R
A
):
L
MM
wL
2
−∴=
==−+∴=
==
Σ
MwL
0
B
B
B
2
2
Σ
F
0
wLR R L
y
B
B
The
M
/
EI
diagram and the deflected shape for the uniformly distributed
load,
w
, is shown in Figure 4.10.
w
wL
2
2
t
AB
wL
wL
2
2EI
3L/4
Figure 4.10.
Example 4.5 Area moment.
The reactions at the fixed-end on the right can be written in terms of the
vertical reaction,
R
A
, as follows from equilibrium on Figure 4.9 (ignoring
the distributed load):
Σ
Σ
M
==−−∴=−
== +∴=−
0
R LM MRL
B
A
B
B
A
F
0
R RR R
y
A
B
B
A
The
M
/
EI
diagram and the deflected shape for the vertical reaction,
R
A
, is
shown in Figure 4.11.
t
AB
R
A
L
R
A
R
A
2L/3
R
A
L
EI
Figure 4.11.
Example 4.5 Area moment.
