   # ,10-6 A prismatic bar with a diameter d 0 = 20 mm is being compared with a stepped bar of the same diameter( d | = 20 mm) that is enlarged in the middle region lo a diameter d 2 = 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm. (a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load for the prismatic bar and the maximum permissible load F, for the enlarged bar, assuming that the allowable stress for the material is 80 MPa. (b) What should be the diameter d 0 of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar? ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 2, Problem 2.10.6P
Textbook Problem
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## ,10-6 A prismatic bar with a diameter d0= 20 mm is being compared with a stepped bar of the same diameter(d| = 20 mm) that is enlarged in the middle region lo a diameter d2= 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm.(a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load for the prismatic bar and the maximum permissible load F, for the enlarged bar, assuming that the allowable stress for the material is 80 MPa.(b) What should be the diameter d0of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar? i.

To determine

We have to determine that does enlarging the bar in the middle region make it stronger

than the prismatic bar.

### Explanation of Solution

Given information:

d1 = 20mm

d1 = 20mm

d2 = 26mm

Allowable stress, st = 80 Mpa

For prismatic bar, P1= σ1A0= σ1(π4)d02

P1= 80(π4)202= 25.1 N

For stepped bar,

R/d1=0.10, d1/d2= 1.25, K1

ii.

To determine

We have to determine that what should be the diameter d0 of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar.

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