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PROBLEM (10.87) A propped cantilever beam with an overhang is loaded as shown in Fig. P10.87.
Determine:
(a) The reaction at support A.
(b) The deflection at the midspan.
SOLUTION
(a)
2
0
'' 22 2
ALw L
EIv M R x x=− + <−>−<−>
23
01
'2262
A
RLw L
EIv M x x x C=− + <−>−<−>+
234
012
1
262242
A
RLw L
EIv M x x x C x C=− + <−>− <−>+ + (1)
Boundary condition:
23
10
3311
'( ) 0 :
2226
A
vL C ML RL wL==−+
234
20
511
() 0:
28412
A
L
vCMLRLwL==−+−
0
333
()0:
228
AM
vL R wL
L
==+↑
(b) Make x=L in Eq.(1) and simplify:
24
0
535
16 384
M
EIv M L wL=− −
or
22
0
5(24 7 )
384
ML
vMwL
EI
=+↓
L
L/
2
R
A
A
C
B
y
RB
M0
w
x
MB
1
/
1
100%