sm10 104

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PROBLEM (10.104) A cantilever beam AB and a simple beam CD are supported and loaded as
shown in Fig. P10.104. A roller fits snugly between the two beam at point B. Determine:
(a) The force F transmitted between the beams at B.
(b) The reactions RC and RD for the lower beam.
Assumption: The flexural rigidity EI is constant for both beams.
SOLUTION
(a) Refer to Table B.14.
0: 2
CD
F
MR
=
=
∑ (1)
3
48
BPL
vEI
=
↓
33
(2)
'324
BPL PL
vEI EI
=
=↓
33
(2)
'' 324
BFL FL
vEI EI
=
=↑
Condition of compatibility at B:
''
BBB
vvv
=
+↓
333
48 24 24
FL PL FL
EI EI EI
=−
or 2
3
FP=
(b) Substitute 23FP= into Eq. (1): 1
3
D
C
R
PR
=
=
P
D
B
v
B
A
C
B
v
R
C
RD
F
=
L/
2
L/
2
B
F
P
''
B
v
'
B
v
+