sm9 91

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PROBLEM (9.91) A cast iron ASTM grade A-48 shaft of circular cross section is subjected
simultaneously to a torque T and a vertical load P (Fig. P9.91). Calculate the diameter d of the shaft
based on the of a safety factor of ns, employing:
(a) The maximum normal stress theory of failure.
(b) The Coulomb-Mohr theory of failure.
Given: u
σ
=25 ksi, '
u
σ
= 95 ksi (from Table B.4), L = 10 in., T = 5 kip
⋅
in.,
s
n= 2
Assumption: The effect of transverse shear may be disregarded.
SOLUTION
33
32 16
xxy
M
T
dd
στ
π
π
==
200(10) 2 .
M
kip in==⋅
25
( ) 12.5
2
uall ksi
σ ==
95
(') 42.5
2
uall ksi
σ ==
Also
22
1,2 ()
22
xx
x
y
σσ
σ
τ =± + 22
3
16 ()
M
MT
d
π
=±+
Substituting the given data
22
1,2 3
16 (2 2 5 )
d
σπ =±+
or
12
33
37.61 17.24
dd
σσ ==−
(a) Maximum Principal Stress Theory
3
37.61 12.5
d= or 1.44 .din
=
(b) Coulomb-Mohr Theory:
12 33
37.61 17.24
1; 1
( ) ( ') 12.5 42.5
u all u all dd
σ
σ
σσ
−
−= −=
or
1.5 .din=