Hindustan Institute of Technology and Science (HITE) 2010-1st Sem M.E Aeronautical Engineering M.EAeronautical engineeringtheory of elasticity - Question Paper
M.E DEGREE exam , NOVEMBER 2010
(AERONAUTICAL ENGINEERING)
FIRST SEMESTER
THEORY OF ELATICITY
AE 1613
PART - A
1. Explain the difference ranging from the strength of material approach and elasticity approach.
2. How many material constants are needed to describe stress -strain relation for a isotropic material?
3. Write down the expression for the strain components for the 3D Cartesian coordinate system.
4. Write down the relationship ranging from modulus of elasticity and modulus of rigidity.
5. Explain the significance of compatibility condition.
6. Define the principle plane and principle stress.
7. Write down the expression for 2D stress components in Cartesian coordinate system in terms of stress function.
8. Define plane stress issue with suitable example.
9. Define axisymmetric issue with suitable example.
10. Explain the semi – inverse method.
PART - B
11. a) (i) Derive the equilibrium formula in 3D Cartesian coordinate system.
(ii) provided the subsequent stress components determine the body forces needed for equilibrium and the magnitude of its resulting at x = -10mm, y = 30mm and z = 60mm. ?xx = x2 + 2y, ?yy = xy-y2z, ?xx= x2 -y2 , t xy = -xy2+1 t yz = 0 t xz= xz-2x2 y.
or
b) (i) Derive strain compatibility equations in 3D Cartesian coordinate system.
(ii) A displacement field in the body is provided by u = c (x2 +10), v = 2c yz and w = c (-xy+ z2) where c = 10-4. Determine the state of strain at (0,2,1).
12. a) Derive the expression for a principle stresses of a general biaxial stress field in 2D Cartesian coordinate system. Also find the expression for maximum shear stress and its plane.
or
b) compute the magnitude and direction of principle stresses for the subsequent stress field described as follows.
12 six 9
six 10 three Mpa
nine three 14
13. a) Derive the governing formula for a plane stress issue in terms of Airy's stress function and body force components.
or
b) Derive the equilibrium formula in polar coordinates for a 2D issue.
14. a) find the general solution for biharmonic formula of a axisymmetric issue.
or
b) A force P is appilied vertically at the vertex of semi infinite wedge of included angle 2a where a is the angle ranging from slant edge of the wedge and vertical through the vertex of the wedge. find the expression for the distribution. Also find the stress distribution expression when the load is applied in a direction perpendicular to the vertical through the vertex of the wedge.
15. a) Derive the expression for stress distribution in a solid circular rotating disc.
or
b) (i). Derive the governing formula and the boundary condition for non circular part subjected to torque load. Use Prandtl stress function approach.
(ii). find the stress distribution and the expression for the warping of an elliptical part using stress function approach.
M.E DEGREE EXAMINATION , NOVEMBER 2010
(AERONAUTICAL ENGINEERING)
FIRST SEMESTER
THEORY OF ELATICITY
AE 1613
PART - A
- Explain the difference between the strength of material approach and elasticity approach.
- How many material constants are required to define stress -strain relation for a isotropic material?
- Write down the expression for the strain components for the 3D Cartesian coordinate system.
- Write down the relationship between modulus of elasticity and modulus of rigidity.
- Explain the significance of compatibility condition.
- Define the principle plane and principle stress.
- Write down the expression for 2D stress components in Cartesian coordinate system in terms of stress function.
- Define plane stress problem with suitable example.
- Define axisymmetric problem with suitable example.
- Explain the semi inverse method.
PART - B
- a) (i) Derive the equilibrium equation in 3D Cartesian coordinate system.
(ii) Given the following stress components determine the body forces required for equilibrium and the magnitude of its resultant at x = -10mm, y = 30mm and z = 60mm. бxx = x2 + 2y, бyy = xy-y2z, бxx= x2 -y2 , τ xy = -xy2+1 τ yz = 0 τ xz= xz-2x2 y.
or
b) (i) Derive strain compatibility equations in 3D Cartesian coordinate system.
(ii) A displacement field in the body is given by u = c (x2 +10), v = 2c yz and w = c (-xy+ z2) where c = 10-4. Determine the state of strain at (0,2,1).
12. a) Derive the expression for a principle stresses of a general biaxial stress field in 2D Cartesian coordinate system. Also obtain the expression for maximum shear stress and its plane.
or
b) Calculate the magnitude and direction of principle stresses for the following stress field defined as follows.
 |
|
12 6 9
6 10 3 Mpa
9 3 14
13. a) Derive the governing equation for a plane stress problem in terms of Airys stress function and body force components.
or
b) Derive the equilibrium equation in polar coordinates for a 2D problem.
14. a) Obtain the general solution for biharmonic equation of a axisymmetric problem.
or
b) A force P is appilied vertically at the vertex of semi infinite wedge of included angle 2α where α is the angle between slant edge of the wedge and vertical through the vertex of the wedge. Obtain the expression for the distribution. Also obtain the stress distribution expression when the load is applied in a direction perpendicular to the vertical through the vertex of the wedge.
15. a) Derive the expression for stress distribution in a solid circular rotating disc.
or
b) (i). Derive the governing equation and the boundary condition for non circular section subjected to torque load. Use Prandtl stress function approach.
(ii). Obtain the stress distribution and the expression for the warping of an elliptical section using stress function approach.
| Earning: Approval pending. |
