ME 360 – Fall 2014 – H03
Name _________________________
1) Norton text problem 4-75a. Use D = 40 mm, d = 20 mm, r = 4 mm, h = 10 mm and P = 8kN.
The value M is not needed for problem 4-75a. See Section 4.15 in Norton for help with stress
concentration.
ME 360 – Fall 2014 – H03
Name _________________________
2) Norton text problem 5-70. See Section 4.9 in Norton for help with curved beams.
MACHINE DESIGN - An Integrated Approach, 4th Ed.
4-75a-1
PROBLEM 4-75a
Statement:
For a filleted flat bar in tension similar to that shown in Appendix Figure C-9 and the data from
row a from Table P4-4, determine the nominal stress, the geometric stress concentration factor,
and the maximum axial stress in the bar.
Given:
Widths
Thickness
Force
Solution:
See Appendix Figure C-9 and Mathcad file P0475a.
1.
P
σnom  40.0 MPa
h d
Determine the geometric stress concentration factor using Appendix Figure C-9.
Width ratio
D
d
3.
d  20 mm
Radius r  4  mm
Determine the nominal stress in the bar using equation 4.7.
σnom 
2.
D  40 mm
h  10 mm
P  8000 N
 2.00
From Figure E-9
A  1.0966
SCF
Kt  A  
r
b  0.32077
b

d
Kt  1.838
Determine the maximum stress in the bar using equation 4.31.
σmax  Kt σnom
σmax  73.5 MPa
© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be
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P0475a.xmcd
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MACHINE DESIGN - An Integrated Approach, 4th Ed.
5-70-1
PROBLEM 5-70
Statement:
A C-clamp as shown in Figure P5-24a has a rectangular cross section as in Figure P5-24c. Find the
static factor of safety if the clamping force is 1.6 kN and the material is class 50 gray cast iron.
Given:
Clamping force F  1.6 kN
Distance from center of screw to throat
Section dimensions:
Material properties
Solution:
1.
Width b  6.4 mm
S ut  359  MPa
Depth h  31.8 mm
S uc  1131 MPa
See Figure P5-24 and Mathcad file P0570.
Determine the distance from the centerline of the screw to the centroid of the section at the throat.
rc  ri 
2.
ri  63.5 mm
h
rc  79.4 mm
2
Using equation 4.12a and Figure 4-16, calculate the distance to the neutral axis, rn, and the distance from the
centroidal axis to the neutral axis, e.
Distance from the screw centerline to the outside fiber
Cross section area
Distance to neutral axis
A  b  h
rn 
A
ro
rn  78.327 mm
dr
i
e  rc  rn
e  1.073 mm
M  rc F
M  127 N  m
Calculate the distances from the neutral axis to the inner and outer fibers.
ci  rn  ri
ci  14.827 mm
co  ro  rn
co  16.973 mm
Using equations 4.12d and 4.12e, calculate the stresses at the inner and outer fibers of the throat section.
σi 
 ci  F

e A  ri  A
M
σo  
6.
2
Take a section through the throat area and draw a FBD. There will be a vertical axial force through the section
CG (at a distance rc from the screw centerline) which will form a couple of magnitude rc x F. This couple will be
balanced by an internal moment of equal magnitude.
Internal moment
5.
b
r
Distance from centroidal to neutral axis
4.
ro  95.300 mm
A  203.520 mm



r
3.
ro  ri  h

σi  143.7 MPa
 co  F

e A  ro  A
M

σo  95.8 MPa
These are the principal stresses so,
Inner radius
σ1i  σi
σ2i  0  MPa
σ3i  0  MPa
Outer radius
σ1o  0  MPa
σ2o  0  MPa
σ3o  σo
© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be
obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic,
P0570.xmcd
mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department,
Pearson Education, Inc., Upper Saddle River, NJ 07458.
MACHINE DESIGN - An Integrated Approach, 4th Ed.
7.
5-70-2
Calculate the factor of safety using equations 5.12c, 5.12d, and 5.12e.
Inner radius
C1i 
1
C2i 
1
C3i 
1
2
2
2

S uc  2  S ut

S uc

S uc  2  S ut

S uc

S uc  2  S ut

S uc
  σ1i  σ2i 
  σ2i  σ3i 
  σ3i  σ1i 

  σ1i  σ2i
C1i  98.09 MPa


  σ2i  σ3i
C2i  0.00 MPa


  σ3i  σ1i
C3i  98.09 MPa

σeff  max C1i C2i C3i σ1i σ2i σ3i
Ni 
S ut
σeff  143.707 MPa
Ni  2.5
σeff
Outer radius
C1o 
1
C2o 
1
C3o 
1
2
2
2

S uc  2  S ut

S uc

S uc  2  S ut

S uc

S uc  2  S ut

S uc
  σ1o  σ2o 
  σ2o  σ3o 
  σ3o  σ1o 

  σ1o  σ2o


  σ2o  σ3o


  σ3o  σ1o

σeff  max C1o C2o C3o σ1o σ2o σ3o
No 
S ut
σeff
C1o  0.00 MPa
C2o  30.39 MPa
C3o  30.39 MPa
σeff  30.394 MPa
No  11.8
© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be
obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic,
P0570.xmcd
mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department,
Pearson Education, Inc., Upper Saddle River, NJ 07458.