How to Draw Mohr'south Circle with Previous Yr Questions & Study Notes for GATE & SSC JE

Testbook | Updated: Jul 7, 2018 nineteen:22 IST

Mohr's circumvolve was named after a German Ceremonious Engineer, Christian Otto Mohr, is a two-dimensional graphical representation of the transformation police for the Cauchy stress tensor. If you are preparing for Engineering exams like GATE or SSC JE, yous might find questions from Mohr'due south Circumvolve frequently. In this article, you lot will larn almost the Mohr's Circle, how to draw information technology along with Previous Year Questions & quick quiz to test your cognition. Aspirants of GATE ME & GATE CE , besides as SSC JE ME & SSC JE CE, will do good from this article.

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Also check Part II & Function Iii of Mohr Circle by clicking the links beneath;

Mohr's Circle Quiz & Study Notes on Biaxial Stresses for SSC JE & GATE (Part-II)

Solve Combined Stresses in Mohr'due south Circle (Part III)

Mohr's Circle – An Introduction

Mohr circle is a graphical representation of plane stress which helps in determining the relationships between normal and shear stresses acting on whatever inclined airplane at a point in a stressed torso.

A fellow member subjected to direct stress in one direction only –

1

Stress on X-face up, A(σ, 0)

Stress on Y-face, B(0,0)

Mohr Circle –

x-coordinate on Mohr' circumvolve – Normal stress

y-coordinate on Mohr' circle – Shear stress

2

3

  • Every plane is represented in Mohr's circle past doubles it bodily angle
  • Every aeroplane is represented by a radial line in Mohr's cirle:
  • Centre of the Mohr circle always prevarication on X axis:
    Coordinates are2

Stress on an inclined plane AM, inclined at an angle θ with normal face up:

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Normal Stress (σnorthward) and Shear Stress (τsouthward) on an oblique plane:

σn = O'M' = O'O + OM cos 2θ = R + R cos 2θ = R (1 + cos 2θ)

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τs=  OM sin 2θ = R sin 2θ

Normal Stress volition be maximum when:

2θ = 0°, 180° ⇒ θ = 0° or 90°

Shear stress will be maximum when:

2θ = 90°, 270° ⇒ θ = 45°, 135°

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10

  • Plane on which normal stress attains its maximum and minimum values are called primary planes.
  • The shear stress on principal airplane is zero.
  • The planes of maximum and minimum normal stresses are at angle of ninety° to each other.
  • Planes of maximum shear stress occur at 45° to the principal planes.
  • Plane normal to the axis of loading volition comport the maximum normal stress.
  • Shear stress will be max on two planes inclined at 45° & 135°.

1. Primary planes are the planes on which the shear components are zero.

i.e. it is represented on the Mohr's circle by the radial lines lying on 10-axis.

Its magnitude is equal to the 10-coordinate of the signal of intersection where circle intersect 10-axis.

The sum of the complementary normal and shear stress at a point is always remains abiding and their sum is equal to (σ10 + σy)

σn + σ'n = σmax + σmin = const.

2. Maximum shear planes are planes on which normal stress may or may not be zero.

τmax planes are represented on the Mohr'due south circle by the radial lines parallel to y axis.

Normal stress on τmax airplane (σnorth*) is equal to x-coordinate of centre of Mohr's circle.

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Previous Year Questions on Mohr'south Circumvolve asked in SSC JE ME

Q1. At the primary planes _______________.
  1. The normal stress is maximum or minimum and the shear stress is zero.
  2. The tensile and compressive stresses are zero.
  3. The tensile stress is aught and the shear stress is maximum.
  4. No stress acts.

Ans: 1

Solution:

Chief planes are the planes on which the shear components are zero. Aeroplane on which normal stress attains its maximum and minimum values are called chief planes.

Q2. Main plane is one which carries _________.
  1. No shear stress
  2. Maximum shear stress
  3. No normal stress
  4. Maximum resultant of stresses

Ans: 1

Solution:

Principal planes are the planes on which the shear components are zero. Plane on which normal stress attains its maximum and minimum values are called chief planes.

Q3. The shear stress along the principal airplane subjected to maximum principal stress is ________.
  1. Minimum
  2. Maximum
  3. Nil
  4. Any value depending on loading weather

Ans: three

Solution:

Primary planes are the planes on which the shear components are zero. Plane on which normal stress attains its maximum and minimum values are called principal planes.

Q4. Mohr'southward circle can exist used to determine the following stress on an inclined surface:

A. Chief stress
B. Normal stress
C. Tangential stress
D. Maximum shear stress

  1. Only A
  2. But B
  3. Just C
  4. A, B, C and D

Ans: 4

Solution:

Mohr circle is a graphical representation of plane stress which helps in determining the relationships between normal and shear stresses acting on whatsoever inclined plane at a point in a stressed body.

Mohr's circle of stresses is a graphical method of finding normal, tangential and resultant stresses on an oblique plane.

Solve Mohr's Circumvolve Questions for GATE

Mohr's Circle for Principal Stress and Maximum Shear Stress_Uniaxial Case

Que. one

A rectangular bar of cross sectional area 10000 mmii is subjected to an axial load of twoscore kN. Determine the normal stress on the section which is inclined at an bending of xxx° with normal cross-section of the bar.

Solution

Answer:

\(\sigma = \frac{P}{A} = \frac{{xl \times 1000}}{{1000}} = 4\;MPa\)

Normal stress on inclined plane:

σn = BM' = R + R cos lx° = R(1 + cos lx)

σn = two(1 + 0.5) = 3 MPa

Some more important calculations which may be asked in exams:

Shear stress on inclined plane:

\({\tau _s} = R\sin 60^\circ = \frac{{2 \times \sqrt 3 }}{two} = ane.732\;MPa\)

Maximum principal stress, σone = 4 MPa (θ = 0°)

Minimum principal stress, σ2 = 0 MPa (θ = xc°)

Radius of the Mohr circle R = σ1/2 = two MPa

Maximum shear stress, τmax = R = 2 MPa (θ = 45°)

To sympathize this concept in more detail and uncomplicated way, Click Here

Que. two

Mohr circle for given stress condition will be

Solution

Answer:

Concept:

Stress of x confront, A(σ1, 0), Stress of y face up, B(0, 0)

And so Mohr's circumvolve volition be

Que. three

Angle between the planes of maximum normal stress and minimum normal stress is ________ and bending between planes of maximum shear stress and principal planes is ________ respectively.

Solution

Answer:

The plane on which normal stress attains its maximum and minimum values are called principal planes. The shear stress on the principal airplane is zip.

The planes of maximum and minimum normal stresses are at an bending of 90° to each other.

Planes of maximum stress occur at 45° to the principal planes.

To empathise this concept in more detail and elementary way, Click Here

Que. four

Mohr circumvolve for the given stress condition will be

Solution

Reply:

Stress on 10 confront, A(-σ, 0) and Stress on y face, B(0, 0)

And so Mohr's Circle will be:

To empathize this concept in more particular and unproblematic style, Click Here

Que. five

The stress at a point in a bar is 200 MPa tensile. Determine the intensity of maximum shear stress in the fabric.

Solution

Answer:

Stress on x face, A(200, 0) and Stress on y face, B(0, 0)

Maximum shear stress = Radius of Mohr circle

τmax= σ/2 = 100 MPa

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