sm9 78

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PROBLEM (9.78) Redo Prob. 9.77 for P = 40R and Q = 0.
SOLUTION
At the fixed end:
1.5 2
z
TRMR
=
=
40
xy
PRVR
=
=−
The effect of y
V may be neglected. Therefore, at point A:
4
2
40
' 2.037 10
(0.05)
4
x
xPR
R
A
σπ == = ×
4
33
32 32(2 )
' 16.298 10
(0.05)
xR
R
d
σππ == = ×
4
33
16 16(1.5 ) 6.116 10
(0.05)
TR
R
d
τππ =− =− =− ×
422
1,2 18.34 18.34
10 [ ( ) ( 6.116) ]
22
R σ =±+−
44 4
12max
20.196 10 1.852 10 11.024 10
R
RR σσ τ =× =−× =×
(a) 64
130 10 11.024 10 , 590
2
R
RN
×=× =
(b) 1
22
2
1122
[]
2y
σ
σσσσ −+ =
1
42 2 6
2
10 [(20.196) (20.196)( 1.852) ( 1.852) ] 130 10R−−+− =×
Solving,
614
R
N=
A
x
σ
τ
z
2
m
x
A
y
40 R
50 mm
R
C
B