Theory Of Elasticity & Plasticity M.Tech Question Paper : vardhaman.org
College : Vardhaman College Of Engineering
Degree : M.Tech
Semester : I
Department : Structural Engineering
Subject :Theory Of Elasticity & Plasticity
Document type : Question Paper
Website : vardhaman.org
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Vardhaman Theory Of Elasticity Question Paper
M. Tech I Semester Supplementary Examinations July – 2014
(Regulations: VCE-R11)
(Structural Engineering)
Date: 22 July, 2014
Time: 3 hours
Max Marks: 60
Answer any Five Questions.
All Questions carries equal marks.
Related / Similar Question Paper :
Vardhaman College M.Tech Detection & Estimation Theory Question Paper
All parts of the question must be answered in one place only.
1. a) The state of stress in MPa at a point is given by 120, x ? ? ? 140, y ? ? 66, z ? ? 65 yz ? ? ? , 25 zx ? ? . Determine three principle stresses and direction associated with the three principle stresses. 6M
b) Find the components of linear strain and component of rotation for the given displacement components : Ux = Cx( y + z)2 , Uy = Cy( z + x)2 , Uz = Cz( x + y)2 where C is a constant. 6M
2. a) Prove that the following are Airy’s stress function and examine the stress distribution represented by them.
F = Ax2 + By2
F = A(x4 – 3x2y2)
F = Ax3
6M
b) The state of stress at a particular point relative to the xyz coordinates system is given by the stress matrix given below. Determine the normal stress, magnitude and direction of shear stress on a surface intersecting a point and parallel to the plane given by the equation 2x – y + 3x = 9
15 10 10
19 10 10
10 0 40
3. a) Determine the stress components from the following stress functions and calculate their values when a = 200 and a = 300. F = Cr2(a – ?) + r2sin? cos? – r2 cos2?tan?. 6M
b) Write basic equation of equilibrium of plane stress and plane strain in polar coordinates. 6M
4. Determine the normal stress, circumferential stress and shear stress for a stress function F = A log r + Br2log r + Cr2 + D. 12M
5. a) Explain and illustrate the principle of superposition and uniqueness theorem. 6M
b) Write and explain equations of equilibrium in terms of displacements. 6M
6. Prove that 2 = -2G? , Poisson’s equation for torsion of prismatic bar of non circular cross section. 12M
7. a) Derive the equation of shear stress txy =4/3(P/A) along with the horizontal dia. of the cross section of the bar subjected to bending using elementary beam theory. 6M
b) Determine the max. stress in the cantilever beam of 5 m span subjected to a load of 1 kN at the free end of a cross section of (80 x 100) mm at an angle of 300 to the vertical. 6M
8. a) Explain Elastic- Perfectly plastic material 6M
b) Explain Elastic linear strain hardening material with the stress – strain diagram for the material. 6M
February – 2014
Two Year M. Tech I Semester Regular Examinations,
THEORY OF ELASTICITY AND PLASTICITY
(Structural Engineering)
Date : 05 February, 2014
Time : 3 Hours
Max. Marks : 60
Answer any FIVE Questions.
All Questions carry equal marks
All parts of the question must be answered in one place only
1. a) Derive an expression for stress components on an arbitrary plane in three dimensions. Also obtain the resultant stress and normal stress. 6M
b) A rope of length ‘L’ is hung from the ceiling. The density of the material of the rope is ?. Find the stress in the rope in its free end, as well as value of maximum tension. 6M
2. a) Prove that the following are Airy’s stress function and examine the stress distribution represented by them.
F = Ax2 + By2
F = A(x4 – 3x2y2)
F = Ax3 6M
b) The state of stress at a particular point relative to the xyz coordinates system is given by the stress matrix given below. Determine the normal stress, magnitude and direction of shear stress on a surface intersecting a point and parallel to the plane given by the equation 2x – y + 3x = 9 6M
15 10 10
19 10 10
10 0 40
Sample Questions
3. If the state of stress at a point is given by ? x = y2 + µ(x2 + y2), ? y = x2 + µ(y2 – z2) and ? z = (x2 + y2), txy = f(x, y), tyz = tzx = 0. Determine the values of txy in order that the stress distribution is in equilibrium if µ is Poisson’s ratio.12M
4. a) Write a note on practical significance of compatibility equations, if C and C1 are some constants. Under what circumstances the following strain system is compatible. ex = C(x2 – y2), ey = Axy, and exy = C1xy. 6M
b) A rectangular stress rosette gives e0 = 670, e45 = 330 µm/m. , e90 = 150 µm/m. Find the principal stresses ?1 and ?2 if E = (2 x 10 5) MPa, µ = 0.3 6M
5. a) Derive compatibility equation in terms of stresses for plane stress problems including body forces. 6M
b) Distinguish between plane stress and plane strain problems.6M
6. a) Using stress function method, obtain the solution for a cantilever beam subjected to pure bending. 6M
b) A steel tube has an outer diameter of 100mm and inner diameter of 50mm. It is subjected to an internal pressure of 14 MPa and external pressure of 5.5 MPa. Calculate maximum hoop stress in the tube. 6M
7. a) Determine the maximum stress in a cantilever beam of 4.0m span subjected to a load of 1 kN at free end of the cross section (60 x 90) mm at an angle of 400 to vertical. 6M
b) Also find the effect of size of the beam on maximum stress if the cross section of the beam is changed to (70 x 95)mm. 6M
8. a) Explain Elastic- Perfectly plastic material. 6M
b) Explain Elastic linear strain hardening material with the stress – strain diagram for the material. 6M