sm10 95

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________________________________________________________________________
PROBLEM (10.95) A nonprismatic cantilever beam propped at end B supports a uniform load of
intensity w, as shown in Fig. P10.95. Determine all of the reactions.
SOLUTION
Use Table B14 (cases 1, 2, and 3):
() () 0
BBwBR
vv v=+= (1)
We have
4
(2)
() () ()() 0
28(2)
Bw Cw CwLwL
vv EI
θ =+ − =
where 33
42
(2) ( 2)(2) ( 8)(2)
83 2
CwL wL L wL L
vEI EI EI =− − −
4
17
384 wL EI
=−
2
32
(2) ( 2)(2) ( 8)(2)
62
CwL wL L wL L
EI EI EI
θ =− − −
3
7
48 wL EI
=−
Thus 444
17 7
() 384 96 256
Bw wL wL wL
vEI EI EI =− − −
4
31
256 wL EI
=− (2)
Continued on next slide
R
B
R
B
R
B
R
A
M
A
2
B
R
L
L/
2
2
wL
w
A
EI
2
8
wL
w
=
+
B
C
C
B
L/
2
2E
I
w
C+
B
2E
I
C+
B
2E
I
C
A

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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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Copyright Act without the permission of the copyright owner is unlawful.
Similarly, 3
23
(2)(2) (2)
5
() 2348
BBB
CR
R
LL RL RL
vEI EI EI =+=
22
(2)(2)(2)
3
() 28
BBB
CR
R
LL RL RL
EI EI EI
θ =+=
Thus, 3
(2)
() () ()()
23(2)
B
BR CR C RL
L
vv EI
θ =+ +
33
53 1 5
()
8648 16
BB
R
LRL
EI EI
=++= (3)
Then, Eq.(1) leads to
31
80
B
R
wL=↑
Statics:
49
0: 80
yA
FRwL==↑
∑
2
9
0: 80
BA
M
MwL==
∑