sm10 27 28

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________________________________________________________________________
PROBLEMS (10.27 and 10.28) Solve Probs. 10. 25 and 10.26, using the multiple-integration
approach.
SOLUTION (10.27)
001
'''' sin ''' ( )cos
xx
EIv w EIv w C
LLL
π
ππ
=− = +
2
012
'' ( ) sin x EIv w C x C
LL
π
π
=++
32
0123
1
'()cos2
x
EIv w C x C x C
LL
π
π
=− + + + (1)
432
01234
11
()sin 62
x
EIv w C x C x C x C
LL
π
π
=− + + + + (2)
Boundary conditions:
42
(0)0:0''(0)0:0vCv C== ==
13
''( ) 0: 0 ( ) 0: 0vL C vL C== ==
Then, Eqs.(1) and (2) yield the results given in solution of Prob.10.25.
SOLUTION (10.28)
0
0: 4
yAB
FRRwL===
∑
Due to symmetry only segment AC need be considered and
0
2
x
ww
L
=−
Thus,
2
001
2
'''' '''
xx
EIv w EIv w C
LL
=− =− +
3
01 2
'' 3
x
EIv w C x C
L
=− + +
42
01 23
1
'12 2
x
EIv w C x C x C
L
=− + + + (1)
532
01 2 34
11
60 6 2
x
EIv w C x C x C x C
L
=− + + + + (2)
Boundary conditions:
010
11
'''(0) :
44
EIv w L C w L==
24
''(0): 0: 0, (0) 0: 0EIv C v C=== Continued on next slide

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3
30
5
'( ) 0 :
2 192
L
vCwL==−
Then, Eqs.(1) and (2) yield the results given in solution of Prob.10.26.