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________________________________________________________________________
PROBLEM (10.107) A cantilever beam AB supports a couple moment M0 at the free end A as
shown in Fig. 10.107. Determine the vertical displacements of points A and C for this beam.
SOLUTION
The
M
EI diagram and elastic curve of the beam is as shown below.
We have
21
2AA
=
. Thus
AAB
vt
=
2()
2
L
A=
0
()()()
2
ML
L
EI
=−
22
00
22
M
LML
EI EI
=
−= ↓
1()
4
CCB L
vt A== 0
( )()()
24
MLL
EI
=−
22
00
88
M
LML
EI EI
=− = ↓
B
A
C
L/
2
B
-M0
L/
2
t
A
/B
x
Tangent at A
tC/B
A
M/EI
A
1
A
1
L/
4
1
/
1
100%