Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology)
Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology)
6th Edition
ISBN: 9780134441184
Author: Robert L. Mott, Edward M. Vavrek, Jyhwen Wang
Publisher: PEARSON
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Chapter 4, Problem 1P

For the sets of given stresses on an element given in Table4−2, draw a complete Mohr’s circle, find the principal stresses and the maximum shear stress, and draw the principal stress element and the maximum shear stress element. Any stress components not shown are assumed to be zeroChapter 4, Problem 1P, For the sets of given stresses on an element given in Table42, draw a complete Mohr’s circle, find , example  1

Chapter 4, Problem 1P, For the sets of given stresses on an element given in Table42, draw a complete Mohr’s circle, find , example  2

Expert Solution & Answer
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To determine

To draw: Mohr’s circle to determine the principal stresses and maximum shear stress. Also, draw the maximum shear stress element and principal stress element.

Answer to Problem 1P

A complete Mohr’s circle is given as below,

  Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology), Chapter 4, Problem 1P , additional homework tip  1

The maximum principal stress is 24.14 ksi and the minimum principal stress is 4.14 ksi . The maximum shear stress is 14.14 ksi .

The principal stress element is given as,

  Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology), Chapter 4, Problem 1P , additional homework tip  2

The maximum shear stress element is given as,

  Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology), Chapter 4, Problem 1P , additional homework tip  3

Explanation of Solution

Given Information:

Write the stresses in the x-direction, y-direction, and shear stress in the x-y plane.

  σx=20 ksiσy=0 ksiτxy=10 ksi

Calculate the center of Mohr’s circle.

  (a,0)=(σx+σy2,0)=(20 ksi+0 ksi2,0)=(10 ksi,0)

Calculate the radius of Mohr’s circle.

  R=(σxσy2)2+τxy2=(20 ksi0 ksi2)2+(10 ksi)2=14.14 ksi

Draw the complete Mohr’s circle diagram.

  Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology), Chapter 4, Problem 1P , additional homework tip  4

Write the expression of principal stresses.

  σ1,2=σx+σy2±(σxσy2)2+τxy2

Substitute 20 ksi for σx , 0 ksi for σy , and 10 ksi for τxy to calculate the principal stresses.

  σ1,2=σx+σy2±(σxσy2)2+τxy2=20 ksi+0 ksi2±(20 ksi-0 ksi2)2+(10 ksi)2=10±14.14 ksiσ1=24.14 ksiσ2=4.14 ksi

Write the expression of maximum shear stress.

  τmax=|σ1σ22|

Substitute 24.14 ksi for σ1 , and -4.14 ksi for σ2 to calculate the maximum shear stress.

  τmax=|σ1σ22|=|24.14 ksi(4.14 ksi)2|=14.14 ksi

Draw the principal stress elements.

  Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology), Chapter 4, Problem 1P , additional homework tip  5

Draw the maximum shear stress element.

  Machine Elements in Mechanical Design (6th Edition) (What's New in Trades & Technology), Chapter 4, Problem 1P , additional homework tip  6

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