sm10 55

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PROBLEM (10.55) A cantilever beam carries a concentrated force P and moment M = PL as
shown in Fig. P10.55. Determine the deflection at the free end A.
SOLUTION
For each loading, we determine the deflection at A, using Table B.14:
Loading I:
23
() 22
A
AI ML PL
vEI EI ==
Loading II:
33
(2)
() 324
CII PL PL
vEI EI =− =−
3
10
() () ()()
296
AII CII CII LPL
vv EI
θ =+ =−
32 3
(2) 10
()
24 2 2 96
PL P L L PL
EI EI EI
=− − =−
Deflection at A:
() ()
AAIAII
vv v=+ 3
19
48 PL EI
=
↑
C
L/
2
L/
2
Loading II
A
C
B
P
Loading I
P
L =
L
A
()
CII
θ
B
P
L
A
B
P
+