In a general two dimensional stress system, the planes on which shear stress is zero

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‘p1’ and ‘p2’ are two equal tensile principal stresses. On the plane AB inclined at 45° to the plane of ‘p1’ as shown in the figure below,
In a Mohr’s circle, the radius of the circle is taken as (adsbygoogle = window.adsbygoogle || []).push({});
For a general two dimensional stress system, what are the coordinates of the centre of Mohr’s circle?

Test: Analysis of Stress & Strain - 2 for Mechanical Engineering 2022 is part of Topicwise Question Bank for Mechanical Engineering preparation. The Test: Analysis of Stress & Strain - 2 questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Analysis of Stress & Strain - 2 MCQs are made for Mechanical Engineering 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Analysis of Stress & Strain - 2 below.

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Test: Analysis of Stress & Strain - 2 - Question 1

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‘p1’ and ‘p2’ are two equal tensile principal stresses. On the plane AB inclined at 45° to the plane of ‘p1’ as shown in the figure below,

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 1

The plane AB is principal plane, and at the principal plane shear stress is zero.

Test: Analysis of Stress & Strain - 2 - Question 2

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In a Mohr’s circle, the radius of the circle is taken as (adsbygoogle = window.adsbygoogle || []).push({});

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Test: Analysis of Stress & Strain - 2 - Question 3

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For a general two dimensional stress system, what are the coordinates of the centre of Mohr’s circle?

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 3

From the above figure coordinates of the centre are

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 4

When the normal stresses on the two mutually perpendicular planes are equal and alike then radius of Mohr’s circle will be zero.
i.e.

Hence Mohr’s circle reduces to a point.

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 5

The principal stress given are unlike i.e if one is tensile and other is compressive. Let σ1 be tensile and σ2 be compressive, then

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 6

Radius of the Mohr’s Circle

Maximum shear stress,

∴ Radius of Mohr’s circle is equal to maximum shear stress

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 8

Principal stresses,

Since minimum principal stress is zero, so

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 9

Mohr’s circle for pure shear stress

Since neither tensile nor compressive stress exists, the Mohr’s diagram is simply a circle of radius τxy and centre at the intersection of the two axes. It can also be verified by transformation of plane formula.

Detailed Solution for Test: Analysis of Stress & Strain - 2 - Question 10

Maximum principal stress,

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System stresses are distributed within the pipework and are maximised at terminal weldments to heaters, reactors and heat exchangers where the dead weight imbalance loadings are reacted.

From: Corrosion in Refineries, 2007

This set of Materials Science Multiple Choice Questions & Answers (MCQs) focuses on “Stress Transformation”.

1. How many shear stress components can act on a 3-D object? a) 2 b) 4 c) 5 d) 6

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Answer: d
Explanation: On a 3-dimensional body, total 9 stress components can act, out of which 3 are normal stress components while 6 of the other are tangential or shear stress component.

2. Which type of stress is plane stress? a) One dimensional b) Two dimensional c) Zero dimensional d) Three dimensional

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Answer: b
Explanation: Plane stress is a two-dimensional stress in which stress components on any one direction is zero. For eg. All the stress components pertaining to z component is zero.

3. Principal plane is the plane in which ___________ a) Shear stress is maximum b) Normal stress is zero c) Shear stress is zero d) It doesn’t depend upon stresses

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Answer: c
Explanation: Principle planes are those planes where the value of shear stress is equal to zero and maximum or minimum value of normal stress is present at these points.

4. In a Mohr’s circle drawn on the x-y plane, which axis is the axis where normal stress is plotted? a) X-axis b) Y- axis c) Z-axis d) Normal stress isn’t related to Mohr’s circle

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Answer: a
Explanation: In a Mohr’s circle, the x-axis or the horizontal axis in the x-y plane is the axis on which normal stress is plotted on. This axis is also called the abscissa.

5. In a Mohr’s circle drawn on the x-y plane, which axis is the axis where shear stress is plotted? a) X-axis b) Y- axis c) Z-axis d) Shear stress isn’t related to Mohr’s circle

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Answer: b
Explanation: In a Mohr’s circle, the y-axis or the vertical axis in the x-y plane is the axis on which normal stress is plotted on. This axis is called the ordinate.

Check this: Chemical Engineering Books | Mechanical Engineering MCQs

6. Which of following is not a graphical method for representing stress? a) Lame’s stress ellipsoid b) Cauchy’s stress quadric c) Lame’s stress circle d) Mohr’s circle

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Answer: c
Explanation: Lame’s stress circle cannot be used for graphical representation of stresses while Lame’s stress ellipsoid, Mohr’s circle and Cauchy’s stress quadric are used for graphically representing stress.

7. Double angle method is a method to solve the problem in Lame’s stress ellipsoid. a) True b) False

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Answer: b
Explanation: Double angle method cannot be used to solve Lame’s stress ellipsoid problems, it is used in case of Mohr’s circle. This method mainly has two rule you need to follow.

8. Principal stress is only the minimum stress. a) True b) False

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Answer: b
Explanation: Principal stresses are maximum and minimum stresses which act on the body and planes on which they act are called the principal plane.

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