Propped Cantilever Beam Reaction: Unit-Load Method

_______________________________________________________________________
PROBLEM (12.77) A propped cantilever beam AB is supported at one end by a spring of constant
stiffness k and carries a uniform load of intensity w as shown in Fig. P12.77. Apply the unit-load method
to determine the reaction at A.
1
A
B
x
w
A
R
k
δ
=
A
B
x
Refer to the above figures, we write:
2
11
2
M
Rx wx m x=− =−
Hence, deflection spring at A:
A
M
mR
dx
EI k
δ ==
∫
2
0
11
()()
2
L
R
Rx wx x dx
EI k
=−−
∫=
Solving
3
38
1(3 )
wL
REI kL =+
Reactions at B may then be found from statics.
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