sm9 26

_______________________________________________________________________
PROBLEM (9.26) A hollow shaft with outer diameter D and inner diameter d is acted upon by an
axial tensile load P, a torque T, and a bending moment M, as portrayed in Fig. P9.26. Use Mohr’s
circle to determine the principal stresses and the plane on which they act.
Given: D = 50 mm, d = 30 mm, P = 40 kN, T = 500 N
⋅
m, M = 200 N⋅m
SOLUTION
M
M
P
P
T T
A
222 6.1256)1525( mmA =−=
π
44 3
(25 15 ) 534 10
2
Jm
4
m
π
=−=×
43
102672 mmJI ×==
3
9
500(25 10 ) 23.4
534 10
M
Pa τ
−
−
×
=− =−
×
33
69
40 10 200(25 10 ) 31.83 18.73 50.56
1256.6 10 267 10
x
M
Pa σ
−
−−
××
=+ =+=
××
22
(25.28) (23.4)
34.45
R
MPa
=+
=
MPa28.25'
=
σ
23.4
tan2 ' , ' 21.4
25.28 o
pp
θθ ==
MPa73.5945.3428.25
1=+=
σ
225.28 34.45 9.17
M
Pa
σ
=−=−
A
2
1.4
ο
59.73 MPa
9.17 MPa
Tc
τ =J
x
σ =+
PMc
AI
A
'
σ
τ
(
MPa
)
2
σ
(
50.56, 23.4
)
2θp’
C
R
σ
(MPa)
1
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.