sm10 144

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________________________________________________________________________
PROBLEM (*10.144) For the beam of variable cross section illustrated in Fig. P10.144. Determine
the maximum deflection C
v.
*SOLUTION
Beam is symmetric about C.
33
00
11
,()
12 12 xo
x
IbhIbhII
L
===+, 2
P
M
x=
33
00
13 1
()
12 2 8
C
I
bh bh==
2
2
/0
0
2()
L
AC MPLx
t xdx dx
EI EI L x
== +
∫∫
22
00
33
[ln() ] (0.03)
2282
PL PL
LL
EI EI
⎧⎫
=−=
⎨⎬
⎩⎭
and
33
3
0
0.18 0.0225
CAC C
PL PL
vt Eb h EI == = ↓
x
x
A
tA/C
L/
2
A
B
y
M
L/
2
B
B
A
C
C
v
C
C
P/
2
P/
2
P
L
/
4
P