Civil Engineering Reference
In-Depth Information
A
w
B
M
A
M
B
EI
R
A
R
B
L
(a)
F
IGURE
13.29
Fixed beam carrying
a uniformly
distributed load
(Ex. 13.21)
M
A
M
B
ve
ve
wL
2
8
ve
(b)
so that
wL
2
12
M
A
=
M
B
=
From statics
wL
2
R
A
=
R
B
=
E
XAMPLE
13.22
The fixed beam of Fig. 13.30 carries a uniformly distributed load
over part of its span. Determine the values of the fixed-end moments.
w
A
B
M
A
M
B
EI
x
x
F
IGURE
13.30
Fixed beam with
part span uniformly
distributed load
(Ex. 13.22)
a
R
A
R
B
b
L
Consider a small element
x
of the distributed load. We can use the results of Ex. 13.20
to write down the fixed-end moments produced by this elemental load since it may be
regarded, in the limit as
δ
δ
x
→
0, as a concentrated load. Therefore from Eq. (v) of
Ex. 13.20 we have
x
)
2
x
x
(
L
−
δ
M
A
=
w
δ
L
2
The total moment at A,
M
A
, due to all such elemental loads is then
b
w
L
2
x
(
L
x
)
2
d
x
M
A
=
−
a
