sm9 13

_______________________________________________________________________
PROBLEM (9.13) A thin-walled cylinder of radius r and wall thickness t is acted upon by an internal
pressure p and a torque T. Calculate the largest shearing stress and its orientation in the wall of this
closed-ended vessel.
Given: r = 250 mm, t = 10 mm, p = 3 MPa, T = 40 kN
⋅
m
SOLUTION
33 6
2 2 (250) (10) 981.7 10Jrt m ππ == =× 4 m
6
3 10 (250)
2(10)
x
σ
×
=MPa5.37
=
275
tx
M
Pa
σ
σ
=
=
33
6
40 10 (250 10 ) 10.19
981.7 10
M
Pa τ
−
−
−× ×
==−
×
MPa25.56'
=
σ
22
(18.75) (10.19)R=+
21.34
=
18.75
t an2 " , " 30.7
10.19 o
ss
θθ ==
max 21.34
M
Pa
τ
=
2
x
p
r
t
σ =
xy J
τ =Tc
p
tr
σ =t
3
0.7o
21.34 MPa
5
6.25 ΜPa
(
37.5, 10.19
)
τ
Pa)
(M
σ
(MPa)
s"
2θ
C
O
R
(75, -10.19)
'
σ
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.