Faculty of Engineering & Technology (Co-Ed)
M.TECH - MDE
QUESTION BANK
Academic Year: 2024-25 Sem: 2
Course Title: Theory of Elasticity Course Code:23MDE12
Course Teacher: Dr. Sharan kumar Course Type: Theory
Contact No: 8277144619 Email ID: sharanhene@gmail.com
MODULE - 1
Q.No. QUESTIONS Marks CO RBT
1. Define stress and strain at a point. 05
CO1 L1
2. Explain with equations the stress and strain components in Cartesian
10 CO1 L2
coordinates.
3. Define stress and strain at a point. 05 CO1 L1
4. Derive the equations for stress and strain components in Cartesian 10 CO1 L3
coordinates for a three-dimensional state of stress.
5. Define stress tensor. Explain the concept of a stress tensor with application. 10 CO1 L2
6. Derive the compatibility equations for a two-dimensional strain field. 10 CO1 L3
7. Discuss a real-world engineering application where elasticity theory is used to L4
10 CO1
analyze stress and strain. Solve a sample problem to illustrate the application of
principal stress and strain analysis.
8.
10 CO1 L3
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MODULE - 2
Q.No. QUESTIONS Marks CO RBT
1. Derive the expressions for the stress components (σx,σy and τxy) in terms 10 CO2 L2
of the Airy’s stress function ϕ(x,y) in Cartesian coordinates.
2. Explain the significance of compatibility conditions.
10 CO2 L2
3. Solve a two-dimensional plane stress problem of a rectangular plate under 10 CO2 L3
uniform uniaxial tensile stress using Airy’s stress function.
4. Derive the stress components and verify equilibrium conditions. 10 CO2 L2
5. A rectangular plate is subjected to pure shear stress. Propose a suitable 10
Airy’s stress function and determine the stress components. Prove that the
CO2 L3
chosen stress function satisfies the biharmonic equation.
6. 10 CO2 L3
7. Derive the biharmonic equation for Airy’s stress function in polar
10 CO2 L2
coordinates. Explain the boundary conditions required to solve problems
in polar coordinates.
MODULE - 3
Q.No. QUESTIONS Marks CO RBT
1. Derive the generalized Hooke’s law for a three-dimensional isotropic 10 CO3 L2
linearly elastic material.
2. Explain the physical significance of the elastic constants (Young’s
10 CO3 L2
modulus, Poisson's ratio, shear modulus, and bulk modulus).
3. 10 CO3 L2
4. Discuss the solution methodology for axi-symmetric problems in 05 CO3 L2
elasticity.
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5. Derive the governing equations for stress and displacement in a thick- 10 CO3 L3
walled cylinder subjected to internal and external pressures.
7. Derive the stress distribution around a circular hole in an infinite plate L3
10 CO3
subjected to uniform tension at infinity.
8. Explain the concept of stress concentration factor (SCF) and its L3
10 CO3
importance in design.
MODULE - 4
Q.No. QUESTIONS Marks CO RBT
1. Explain St. Venant’s approach to torsion. 05 CO4 L1
2. Explain Prandtl’s membrane analogy
05 CO4 L2
3. Discuss the assumptions made and derive the governing differential equation for 10 CO4 L3
the torsion of prismatic bars.
4. Explain the significance of the membrane analogy in solving torsion 10 CO4 L3
problems and how it helps in understanding stress distribution.
5. A solid circular shaft of 100 mm diameter is subjected to a torque of 5 10 CO4 L2
kNm. Determine the shear stress developed and the angle of twist per
meter length if the modulus of rigidity G=80 GPa.
6. A thin walled box section having dimensions 2𝑎 × 𝑎 × 𝑡 is to be
10 CO4 L3
compared with a solid circular section of diameter as shown in the
fig.8.a. Determine the thickness ‘t’ so that the two sections have:
a) Same maximum shear stress for the same torque.
b) The same stiffness.
7. Explain the torsion of an Elliptical cross – section. Take 𝜑 = L2
10 CO4
𝐴𝑥𝑦 as working function.
MODULE - 5
Q.No. QUESTIONS Marks CO RBT
1. Explain the physical assumptions in plasticity theory 05 CO5 L1
Page 3 of 4
2. Compare Tresca and Von Mises yield criteria.
05 CO5 L1
3. Discuss the difference between elastic and plastic deformation and the 10 CO5 L2
significance of the yield criterion.
4. Derive the mathematical expressions for both criteria and discuss their 10 CO5 L3
practical applications in engineering.
5. Write not on 10 CO5 L2
i) Plastic potential
ii) Strain hardening hypothesis.
6. A cylindrical metal specimen is subjected to a uniaxial tensile stress of 300 10 CO5 L3
MPa. If the material follows Von Mises yield criterion and has a yield strength
of 250 MPa, determine whether the material will yield. Also, calculate the
equivalent stress using Von Mises theory.
7. A rectangular beam of width 50 mm and height 100 mm is subjected to 10 CO5 L3
a bending moment of 5 kNm. If the yield stress of the material is 250
MPa, determine the elastic and plastic moments using the concept of
elastic-plastic bending.
Page 4 of 4
