sm10 142

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________________________________________________________________________
PROBLEM (*10.142) Determine the free-end deflection A v of the cantilever beam loaded as
shown in Fig. P10.142.
Assumption: The beam has a rectangular cross section of constant width b.
*SOLUTION
0
0(1 ) ( )
h
x
hh Lx
LL
=+= +
33
03
1()
12 A
AI
I
bh I L x
L
==+ 3
3
(1 )
A
MPxL
EI EI x
−
=+
23
/3
(1 )
AAB A
Px L dx
vt Ax EI x === +
∫
32
3
()
A
PL x dx
EI L x
=− +
∫
32
0
2
ln( ) 2( )
L
A
PL L L
Lx
EI Lx Lx
=− + + −
++
33
5
(ln2 ) 0.06815
8
AA
PL PL
EI EI
=− − =− 3
0.06815
A
PL
EI
=
↓
A
dx
M/EI
h0
L
h
x
y
2h0
b
P
A
x
-PL/EIB
B
x
x