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This
open resource is a collection of academic course of post graduation program for
M. Tech (Structural Engineering) as per the syllabus of Dr. B.A.T University,
Lonere, Raigad (m.s), India prepared by Dr. Mohd. Zameeruddin, Associate
Professor, of MGM's College of Engineering, Nanded for use in the out-of-class
activity. The content covers both theoretical and analytical studies. There are
six lessons as part of this document, and each deals with an aspect related to
Theory of Elasticity and Plasticity
Module
1: Analysis of Stresses and Strains
Module
2: Stress-Strain Relationship
Module
3: Stress Concentration Problems
Module
4: Torsion
Module
5: Plasticity
Module
6: Yield Criteria & Yield Surface
1. The following diagram shows stress-strain diagram of
any material. Which kind of material is it?
A. Plastic
B. Linear elastic
C. Non-linear elastic
D. Visco-elastic
Answer:
D
2. The following is not the
assumption of classical elasticity
A. The body is continuous
B. The body is elastic
C. Displacements are neglected
D. The body is isotropic
Answer:
C
3. -------------------- is related to change in
length per unit original length of a line segment of infinitesimal length
A. Normal strain
B. Shearing strain
C. None of the above
D. Can’t say
Answer: A
4. Strain has
A. No units but only dimensions
B. Only units but no dimensions
C. No units, no dimension but a constant value
D. No units, no dimensions but a variable value
Answer: B
5. Engineering shear strains are equal to
----------- the tensorial shear strain components
A. Equal
B. Half
C. Twice
D. One-third
Answer: C
6. The displacement field in a solid body is given
by;
U = [(3x2z+60x)I + (5z2
+20xy)j +(6z2+2xyz)k] x 10-3 mm
Evaluate shearing strain components in x-y plane at
a point whose coordinate are (3, 4, 0.5 mm)
A. 8 x 10-2
B. 0.8 x 10-3
C. 3.1 x 10-3
D. 6.9 x 10-3
Answer: A
7. The compatibility conditions in 2-dimensional
elasticity along the x-z plane is given
by
8. What does τxy means?
A. A stress, produced by an internal force in the
direction of Y, acting on a surface, having a normal in the direction of X
B. A stress, produced by an internal force in the
direction of X, acting on a surface, having a normal in the direction of Y
C. A stress, produced by an internal force in the
direction of X, acting on a surface, having a tangent in the direction of Y
D. Can’t say
Answer: A
9. The state of stress at a point is given by
Find the mean stress
A. 4
B. 15
C. 12
D. 20
Answer: A
10. The state of
strain at a point is given by
Find the strain invariant J1,
J2 and J3
A. 0.159, 6.15375 x 10-3
& 6.5641 x 10-5
B. 0.169, 6.17375 x 10-3
& 6.6641 x 10-5
C. 0.179, 6.19375 x 10-3
& 6.7641 x 10-5
D. 0.189, 6.17375 x 10-3
& 6.8641 x 10-5
Answer: A
11. The strains
acting on a
plane which is
equally inclined to
the three co-ordinate
axes are known as -----------
strains.
A. Normal strains
B. Shearing strains
C. Octahedral Strains
D. Hydrostatic
Strains
Answer: C
11. The volumetric
stress component is given by
A. σx
+ σy +σz
B. σx x σy
x σz
C. σx (σy
+σz)
D. σx / (σy
xσz)
Answer: A
12. The stress and strain fields are related to each
other through certain relations known as the ------------
A. Equilibrium
B. Compatibility
C. Constitutive relationships
D. Displacement fields
Answer: C
13. An important relation between the elastic
modulus (E), shear modulus (G) and Poisson’s ratio (µ) is given by
A. G = E/2(1+ µ)
B. G = E/2(1- µ)
C. E = G/2(1+ µ)
D. E = G/2(1- µ)
Answer: C
14. For an isotropic, homogeneous and elastic
material obeying Hooke’s law, the number of independent elastic constants is
A. 2
B. 3
C. 9
D. 81
Answer: D
15. What is the order of the constitutive tensor Cijkl
A. 1st order
B. 2nd order
C. 3rd order
D. 4th order
Answer: D
16. Compute the lame’s constant for mild steel bars
having modulus of elasticity 2 x 105 MPa and Poisson’s ratio 0.20
A. 0.75 x 105 MPa
B. 0.65 x 105 MPa
C. 0.55 x 105 MPa
D. 0.45 x 105 MPa
Answer: C
17. Following is not a two-dimensional idealization
of elasticity
A. Plane stress problem
B. Plane strain problem
C. Axis symmetric problem
D. Stress quadric
Answer: D
18. The state
of stress at
a given point
will only depend
upon the four
stress components such as [σxx
τxy; τyx σyy] in which
the stress components
are functions of
only x and y. This combination of stress components is
called "---------" in the xy plane.
A. Plane stress
B. Plane strain
C. Octahedral
stresses
D. Arbitrator
stresses
Answer: A
19.
Compute the Lame’s constant for a mild steel bar having modulus of elasticity 2
x 105 MPa and Poisson’s ratio 0.20
A.
0.75 x 105 MPa
B.
0.70 x 105 MPa
C.
0.55 x 105 MPa
D.
0.65 x 105 MPa
Answer: C
20.
Time dependent permanent deformation is called ________________
A.
Plastic deformation
B.
Elastic deformation
C.
Creep
D.
Inelastic deformation
Answer: C
21.
According to distortion-energy criterion, yielding occurs when
A.
Distortion energy reaches a critical value
B.
Second invariant of the stress deviator exceeded some critical value
C.
Octahedral shear stress reaches a critical value
D.
All of the above
Answer: D
22.
Von- Mises and Tresca criteria give different yield stress for
A.
Uni-axial stress
B.
Balanced bi-axial stress
C.
Pure shear stress
D.
All of the above
Answer: C
23.
The state of pure shear stress is produced by
A.
Tension in one direction and equal compression in other direction
B.
Equal tension in two directions at right angles
C.
Equal compression in two directions in right angles
D.
None of the above
Answer: A
24. Number
of independent strain compatibility equations for 3D systems?
A.
81
B.
9
C.
6
D.
3
Answer: C
25.
Number of equilibrium equations for 2D systems?
A.
3
B.
6
C.
2
D.
1
Answer: A
26. Beltrami-Michell
compatibility equations are written in terms of
A. Stress
B. Strain
C. Displacement
D. All
of the above
Answer: A
27. What kind of the boundary condition is to be applied at the fixed edge of the beam shown in figure
A. Traction boundary condition
B. Displacement boundary condition
C. Mixed boundary condition
D. Initial conditions
Answer: A
28. What is the number of non-zero strain components for a plane stress problem?
A. 6
B. 4
C. 3
D. 2
Answer: B
29. Choose the correct option regarding a 2D continuum system from the following;
- Airy’s stress function automatically satisfies the equilibrium equations
- In absence of body forces, Airy’s stress function converts Beltrami-Michell equation to a Bi-harmonic equation.
A. Both the statements are true
B. Only the statement 1 is true
C. None of the statements are true
D. Only the statement 2 is true
Answer: A
30. Let us consider a plane stress problem without any body force. The Airy’s stress function (ϕ) is defined as ϕ = 6x2y3. Determine σxx
A. 36x2y2
B. 12y3
C. -36x2y
D. 36xy
Answer: A
31. In a Plane stress problem σxx = 5 MPa, σyy = -10 MPa and τxy = 7.5 MPa. Calculate εxx. Take E = 2 x 105 MPa and µ = 0.15
A. -3.75 x 10-4
B. 0
C. 7.5 x 10-4
D. 1.75 x 10-4
Answer: D
32. Choose the correct statement regarding generalized plane stress problem;
1. The out of plane displacement is zero
2. The average out of plane displacement is zero
A. Only statement 1 is correct
B. Only statement 2 is correct
C. Both of them are correct
D. None of them are correct
Answer: C
33. Let us consider thin cylinder of wall thickness‘t’ and average radius ‘r0’. The cylinder is acted upon by a uniform pressure ‘p’. What is the hoop stressed generated?
A. pr0/t
B. pr0/2t
C. pr0/3t
D. pr0/4t
Answer: A
34. Which one of the following is the compatibility equation for a plane stress problem?
Answer: C
35. In case of a torsional problem the assumption, “Plane sections perpendicular to longitudinal axis before deformation remain plane and perpendicular to the longitudinal axis after deformation” holds true for a shaft having
A. Circular cross section
B. Elliptical cross section
C. Square cross section
D. Triangular cross section
Answer: A
References
https://www.examveda.com/
https://www.sanfoundry.com/
https://www.indiabix.com/
