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________________________________________________________________________
PROBLEM (*10.39) A beam AB supported at the ends as shown in Fig. P10.39 carries a
concentrated load P at the mid span C. Determine the vertical deflection of the beam at the end B.
*SOLUTION
For segment AC
1''EIv Px=
2
11
1
'2
EIv Px C=+
3
112
1
6
EIv Px C x C=++
For segment CB
21
'' 2
EIv PL=
13
1
'2
EIv PLx C=+
2
234
1
4
EIv PLx C x C=++
Boundary conditions:
12
(0) 0: 0vC==
23
(0) 0: 0vC==
Then
32
12 1 4
() (): () () ()
2262 244
LLPL LPL
vv C PLC=+=+
2
12 1
'( ) '( ) : ( ) ( )
2222 22
LLPL PL
vv CL=+=−
Solving
23
14
311
848
CPLC PL=− =−
At B(x=0):
33
211 11
(0) 48 48
B
v v PL PL==− = ↓
P
L/2
C
L/
2
Px
x
A
B
R
A=P
P
Px
L/
2
x
1
/
1
100%