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 σ_xx 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 σ_y  (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 = τ_XY =50MPa
Hence, Max. normal stress =50MPa

Q8: In a plane stress condition, the components of stress at a point are σ_x = 20 M Pa, σ_y = 80M Pa and τ_xy=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 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]

• A.

  120 MPa
• B.

  80 MPa
• C.

  60 MPa
• D.

  40MPa

Explanation

∴ Radius of Mohr’s circle = 60 MPa

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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]

• A.

  45 MPa
• B.

  50 MPa
• C.

  90 MPa
• D.

  100 MPa

Explanation

Applying maximum shear stress theory

∴ 

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