Cylinder Stress Analysis: Axial Load & Torsion Problem Solution

PROBLEM (9.1) A cylinder with external diameter D and internal diameter d is subjected to an
axial compressive load P and a torque T (Fig. P9.1). Calculate the maximum principal stress and the
maximum shearing stress. Show the results on a properly oriented element.
Given: D = 6 in., d = 4 in., P = 20
π
kips, T = 15
π
kip
⋅
in.
SOLUTION
State of stress on an element at the cylinder’s surface is
3
22
20 10 4
(3 2 )
xksi
π
σπ
−×
==−
−
3
44
15 10 (3) 1.385
(3 2 )
2
ksi
π
τπ
×
=− =−
−
xP
σ =A
xy J
τ =Tc
Equation (9.1):
22
1,2 44
( ) ( 1.385) 2.433
22
σ =− ± − + − =−
ksiksiksi 433.2433.4433.0 max21
=
−
=
=
τ
σ
σ
Equation (9.3):
2( 1.385)
tan2 , 2 34.7
4o
pp
θθ
−
==
−
Equation (4.4a) gives
'11
( 4) ( 4)cos34.7 1.385sin34.7
22 oo
x
σ =−+− −
ksi433.4−=
Thus
" 17.35o
p
θ =
ksi433.2 ksi433.4
17.35o
ksi433.0
x
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