sm10 52

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PROBLEM (10.52 ) A simple beam AB is subjected to couple M0 at midspan acting as shown in
Fig.P10.52.Determine:
(a) The equation of the deflection curve.
(b) The deflection at midspan.
(c) The magnitude and location of the maximum deflection.
(d) The slope at the free end.
SOLUTION
0
00
'' 2
ML
EIv x M x
L
=−<−>
2
001
'22
ML
EIv x M x C
L
=−<−>+ (a)
32
00 12
622
MM L
EIv x x C x C
L
=−<−>++ (b)
Boundary conditions:
2
(0) 0: 0vC==
0
1
() 0: 24
M
L
vL C==−
Equations (a) and (b) become
22
0
' [12 24 ]
24 2
ML
EIv x L x L
EIL
=−<−>− (1)
322
0[4 12 ]
24 2
ML
EIv x L x L x
EIL
=−<−>−
(2)
These lead to the results given in solution of Prob. 10.31.
L
M0
L/
2
L/
2
M0/L
A
C
B
M0/L
y
x