sm10 143

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PROBLEM (10.143) Redo Prob. 10.142 for a beam of solid circular cross section and diameters h0
and 2h0 at the ends A and B, respectively.
SOLUTION
4
0()
64 A
h
x
IIII
L
π
==+
Referring to solution of Prob.10.38, we now write.
4
(1 )
A
MPx
x
EI EI L
−
=
+
and 2
03
(1 )
L
AAB A
Mx P x dx
v t Ax dx dx
x
EI EI L
=== =−
+
∫∫
32
0
122( )
12( )
L
A
PL L L
xx
EI L x
wx
LL
−
=− + − +
++
33
11 1 1
[11]
2424 3 24
A
PL PL
EI EI
=− − + − + − + = 3
24 A
PL
EI
=
↓
h0
L
h
y
2h0
P
A
x
B