GATE Past Year Questions: Mohr's Circle

# GATE Past Year Questions: Mohr's Circle | Strength of Materials (SOM) - Mechanical Engineering PDF Download

Q1: Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)    (2023)

(a) M1
(b) M2
(c) M3
(d) M4
Ans: (a,c)
Sol:   Mohr's circle is a graphical representation of plane stress and shear stress.
Mohr's circle is always symmetrical about the x-axis.

Q2: A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress σxx is ________.     (2022 Set - 2)

(a)
(b)
(c)
(d)
Ans: (a)
Sol:

Q3: The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ−τ plane is 1 MPa, the Mohr's circle representation of the state-of-stress is given by    (2020 Set -1)
(a) a circle with a radius equal to principal stress and its center at the origin of the σ−τ plane
(b) a point on the σ axis at a distance of 10 units from the origin
(c) a circle with a radius of 10 units on the σ-τ plane.
(d) a point on the τ axis at a distance of 10 units from the origin

Ans: (b)
Sol:

The given state of stress is represented by a point on  σ−τ graph which is located on σ-axis at a distance of 10 units from origin.

Q4: The state of stress at a point in a component is represented by a Mohr's circle of radius 100MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is ______ MPa.     (2019 Set -2)
(a) 48
(b) 63
(c) 96
(d) 80
Ans: (d)
Sol:

EF→Represents shear stress at the same point =EF=τ=80MPa

Q5: The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress σy  (in kPa) is     (2018 Set - 1)

(a) 9.45
(b) 18.88
(c) 37.78
(d) 75.5
Ans: (c)
Sol:

Q6: If σ1  and σ3 are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is
(a)
(b)
(c)
(d)
Ans: (b)
Sol:
Maximum shear stress is

Q7:  The state of stress at a point is
The maximum normal stress (in MPa) at that point is_____.      (2017 Set -2)
(a) 49
(b) 50
(c) 55
(d) 60
Ans: (b)
Sol: Given state of stress condition indicates pure shear state of stress.
For pure shear state of stress,
Max. tensile stress = Max. comp. stress = Max. Shear stress = τXY =50MPa
Hence, Max. normal stress =50MPa

Q8: In a plane stress condition, the components of stress at a point are σx = 20 M Pa, σy = 80M Pa and τxy=40MPa . The maximum shear stress (in MPa) at the point is     (2015 Set - 2)
(a) 20
(b) 25
(c) 50
(d) 100
Ans:
(c)
Sol:

Question for GATE Past Year Questions: Mohr's Circle
Try yourself:The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis.
The maximum and minimum principal stresses respectively from the Mohr's circle are

[2003]

Question for GATE Past Year Questions: Mohr's Circle
Try yourself:The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis.
The directions of maximum and minimum principal stresses at the point P from the Mohr's circle are

[2003]

Question for GATE Past Year Questions: Mohr's Circle
Try yourself:The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the x and y directions are 100 MPa and 20 MPa respectively. The radius of Mohr's stress circle representing this state of stress is

[2004]

Question for GATE Past Year Questions: Mohr's Circle
Try yourself:The Mohr's circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer chooses a ductile material whose yield strength is

[2005]

Question for GATE Past Year Questions: Mohr's Circle
Try yourself:A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is 1 unit. Radius of the Mohr's circle, characterizing the state at that point, is

[2008]

Question for GATE Past Year Questions: Mohr's Circle
Try yourself:The state of stress at a point under plane stress condition is
σxx = 40 MPa, σyy = 100 MPa and σxy  =40 MPa
The radius of Mohr's circle representing the given state of stress in MPa is

[2012]

The document GATE Past Year Questions: Mohr's Circle | Strength of Materials (SOM) - Mechanical Engineering is a part of the Mechanical Engineering Course Strength of Materials (SOM).
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## FAQs on GATE Past Year Questions: Mohr's Circle - Strength of Materials (SOM) - Mechanical Engineering

 1. What is Mohr's Circle used for in mechanical engineering?
Ans. Mohr's Circle is a graphical method used to determine principal stresses, maximum shear stress, and stress transformation in materials under different loading conditions in mechanical engineering.
 2. How is Mohr's Circle constructed for a given stress state?
Ans. Mohr's Circle is constructed by plotting normal and shear stresses on the x-y plane and then drawing a circle with the center at the average normal stress and radius equal to the maximum shear stress.
 3. What is the significance of Mohr's Circle in material analysis?
Ans. Mohr's Circle helps engineers analyze and visualize stress states in materials, determine the critical stress conditions, and make informed design decisions for structures and components.
 4. How can Mohr's Circle be used to determine the principal stresses of a material?
Ans. By finding the intersection points of the Mohr's Circle with the normal stress axis, engineers can determine the principal stresses of a material under different loading conditions.
 5. Can Mohr's Circle be used for strain analysis in addition to stress analysis?
Ans. Yes, Mohr's Circle can also be used for strain analysis in materials to determine principal strains, maximum shear strain, and strain transformation under various loading scenarios in mechanical engineering.

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