Chapter 4 (Solution) - ENGINEERING WORKSHOP 2025

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Chapter 4 (Solution) -

ENGINEERING WORKSHOP 2025




CHAPTER 4

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PROBLEM 4.1

Knowing that the couple shown acts in a vertical plane, determine the
stress at (a) point A, (b) point B.




SOLUTION




1
For rectangle: I bh3
12
For cross sectional area:
1 1 1
I  I1  I 2  I 3  (2)(1.5)3  (2)(5.5)3  (2)(1.5)3  28.854 in4
12 12 12
MyA (25)(2.75)
(a) y A  2.75 in. A      A  2.38 ksi ◀
I 28.854
MyB (25)(0.75)
(b) yB  0.75 in. B      B  0.650 ksi ◀
I 28.854




PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
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PROBLEM 4.2
Knowing that the couple shown acts in a vertical plane, determine
the stress at (a) point A, (b) point B.




SOLUTION
1
For rectangle: I  bh3
12
1
Outside rectangle: I1  (80)(120)3
12

I1  11.52  106 mm4  11.52  106 m4
1
Cutout: I2  (40)(80)3
12

I2  1.70667  106 mm4  1.70667  106 m4

Section: I  I1  I2  9.81333  106 m4

MyA  (15  103)(0.040)
(a) yA  40 mm  0.040 m  A    61.6  10 6 Pa
I 9.81333  106
 A  61.6 MPa ◀

MyB (15  103)(0.060)  91.7  10 6 Pa
(b) yB  60 mm  0.060 m  B    
I 9.81333  106
 B  91.7 MPa ◀




PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A student using this manual is using it
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PROBLEM 4.3

Using an allowable stress of 16 ksi, determine the largest couple that can be
applied to each pipe.




SOLUTION

 4 
(a) I 
4
 4

ro  ri4  (0.64  0.54 )  52.7  10 3 in 4

c  0.6 in.
Mc I (16)(52.7  103)
  : M  
I c 0.6
M  1.405 kip  in ◀

(b) I  (0.74  0.54)  139.49  103 in4
4
c  0.7 in.
Mc I (16)(139.49  103)
  : M  
I c 0.7
M  3.19 kip  in ◀




PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A student using this manual is using it
without permission.



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