Thapar University 2006 M.E Theory of Elasticity & Plasticity - Question Paper
Thapar Institute of Engineering & Technology
M.E. (2nd Year)
Final Term exam
ST003 (Theory of Elasticity & Plasticity )
(3/
END SEMESTER EXAMINATION ST- 003 THEORY OF ELASTICITY AND PLASTICITY THAPAR INSTITUTE OF ENGINEERING AND TECHNOLOGY, PATIALA
Time: 3 HRS.
MM: 100
> Attempt any five questions
> Assuming any missing data suitably
1. (i) Let xj, X2, X3 be rectangular Cartesian co-ordinates and 0i, 02, 03 be spherical polar coordinates having the following relationship:
xi = 0] Sin02 Cos03; X2 = 0i Sin02 Sin03; X3 = 0[ Cos02 Get the components of Euclidian Metric tensor and the length of the line element. (12)
(ii) What do you understand by Cauchys Stress Ellipsoid? Explain. (8)
2. (i) Derive the relation between the Lames Coefficient and the elastic constants. (10)
(ii) State the conditions under which the following is the possible system of strains:
Cxx = a + b (x2+y2) + x1 + y4 Cxx = a + (x2+y2) + x4 + y4 Yxy = A + Bxy (x2+y2 - C2)
(10)
3. As a result of measurements made on the surface of a machine component with strain gages oriented in various ways, it was established that the principal strains on the free surface are Ga = + 400 x 1 O'6; Cb = -50 x 10"6.
(i) Calculate the value of maximum in plane shearing strain.
(ii) Find absolute maximum shearing strain for the system (Given that cc = 0 for the
free surface and Poisson ratio, v = 0.3).
(20)
5. A state of plane stress shown in figure occurs at a critical point of a steel machine component.
|
25MPa | |
 |
80MPa |
(i) Determine whether the machine will fail or not if the tensile yield strength is oy
* 250MPa for the grade of steel used by using maximum shearing stress criteria.
(ii) Determine the factor of safety with respect to yield using both the maximum shearing stress criteria and maximum distortion energy criteria. (20)
6. (i) What is a Viscoelastic material. Explain the different ways to model its behaviour.
(10)
(ii) Explain the true Stress - strain curve for a ductile material. Also, illustrate the influence of Bauschinger Effect, strain rate and temperature on the curve. (10)
(i) Explain the development of Tressca Yield criteria. (10)
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Attachment: |
| Earning: Approval pending. |
