Solved GATE Questions on Simple Stress and Strain
Question 1. A 200
100
mm steel block is subjected to a hydrostatic pressure of 15 MPa.The Young’s modulus and ‘Poisson’s ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm3 is
(A) 85
(B) 90
(C) 100
(D) 110
GATE-ME-2007
Hint 1. (Ans. B)
Here,
Now,
Where, 1/m=Poisson’s ratio
Question 2. A steel rod of length D, fixed at both ends, is uniformly heated to a temperature rise of 
. The Young’s modulus is E and the coefficient of linear expansion is 
. The thermal stress in the rod is
(A) 0
(B) 
(C) E
(D) E
GATE-ME-2007
Hint 2. (Ans C)
Since rod is free to expand, therefore 
Since rod is fixed at both ends, so thermal strain will be zero but there will be thermal stresses.
Statement for Linked Answer Question 3 and 4
A cylindrical container of radius R=1m, wall thickness 1 mm is filled with water up to depth of 2m and suspended along its upper rim. The density of water is 1000 kg/m3 and acceleration due to gravity is 10 m/s2. The self-weight of the cylinder is negligible. The formula for hoop stress in a thin-walled cylinder can be used at all points along the height of the cylindrical container.
Question 3. The axial and circumferential stress (
) experienced by the cylinder wall at mid-depth (1 m as shown )are
(A) (10,10)MPa
(B) (5,10) MPa
(C) (10,5) MPa
(D) (5,5) Mpa
GATE-ME-2008
Hint 3. (Ans B)
Pressure at mid depth=
Question 4. If the Young’s modulus and Poisson’s ratio of the container material are 100 GPa and 0.3, respectively, the axial strain in the cylinder wall at mid-depth is
(A) 
(B) 
(C) 
(D) 
GATE-ME-2008
Hint 4. (Ans A)
Axial strain in the cylinder would be produced due to the axial (longitudinal) stress and due to the lateral stress.
i.e., Axial Strain,
Question 5. A rod of length L and diameter D is subjected to a tensile load P. which of the following is sufficient to calculate the resulting change in diameter?
(A) Young’s Modulus
(B) Shear modulus
(C) Poisson’s ratio
(D) Both Young’s modulus and the shear modulus
GATE-ME-2008
Hint 5.(Ans D)
Both Poison’s ratio and Young’s Modulus are required to calculate the lateral strain in rod Now m,E and N are related by
So E and G are required if 
is given
Question 6. A solid steel cube constrained on all six face is heated so that the temperature rises uniformly by 
. If the thermal coefficient of the material is 
, young’s modulus is E and the Poisson’s ratio is v, the thermal stress developed in the cube due to heating is
(A) 
(B) 
(C) 
(D) 
GATE-ME-2012
Hint 6. (Ans B)
Question 7. A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is
(A) 0
(B) 1
(C) 1.08
(D) 2.02
GATE-ME-2012
Hint 7. (Ans D)
% change in hoop stress =2.02%
Question 8. A rod length L having uniform cross-sectional area A is subjected to a tensile strength force P as shown in the figure below. If the Young’s modulus of the material varies linearly from 
along the length of the rod, the normal stress developed at the section SS is
(A) P/A
(B) 
(C) 
(D) 
GATE-ME-2013
Hint 8. (Ans A)
Do the force balance. Force at section P.
Question 9. A long thin walled cylindrical shell, closed at both ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress
(A) 0.5
(B) 1.0
(C) 2.0
(D) 4.0
GATE-ME-2013
Hint 9. (Ans C)
1. (B), 2. (C), 3.(B), 4. (A), 5. (D) 6. (B) 7. (D) 8. (A), 9. (C)