sm12 69

________________________________________________________________________
PROBLEM (12.69) For the beam loaded as shown in Fig. P12.69, applying the unit-load method,
determine:
(a) The vertical deflection of the free end.
B
v
(b) The slope A
θ
of the free end.
SOLUTION
(a) 00
1()()
LL
BMm
vdxPx
EI EI
==−−
∫∫
xdx
33
0
33
L
Px PL
EI EI
== ↓
(b) 00
'1
()(1)
LL
BMm dx Px dx
EI EI
θ ==−−
∫∫
2
2
PL
EI
=
1 lb⋅in.
A
P
x
M
Px=−
B
A
1 lb
x
mx
=
−
B
A
x
'1m
=
−
B
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