**CAMA Lab Viva Questions :-**

**1. Theories of failure.**

**a. Maximum Principal Stress Theory-** A material in complex state of stress fails, when the maximum principal stress in it reaches the value of stress at elastic limit in simple tension.

**b. Maximum Shear Stress Theory-** A material in complex state of stress fails when the maximum shearing stress in it reaches the value of shearing stress at elastic limit in uniaxial tension test.

**c. Maximum Principal Strain Theory-** Failure in a complex system occurs when the maximum strain in it reaches the value of the strain in uniaxial stress at elastic limit.

**d. Maximum Strain Energy Theory-** A material in complex state of stress fails when the maximum strain energy per unit volume at a point reaches the value of strain energy per unit volume at elastic limit in simple tension test.

**e. Maximum Distortion Energy Theory-** This theory is also known as Von-Mises criteria for failure of elastic bodies. According to this theory part of strain energy causes only changes in volume of the material and rest of it causes distortion. At failure the energy causing distortion per unit volume is equal to the distortion energy per unit volume in uniaxial state of stress at elastic limit.

**2. What is factor of safety?**

The maximum stress to which any member is designed is much less than the ultimate stress and this stress is called working stress. The ratio of ultimate stress to working stress is called factor of safety.

**3. What is Endurance limit?**

The max stress at which even a billion reversal of stress cannot cause failure of the material is called endurance limit.

**4. Define: Modulus of rigidity, Bulk modulus**

**Modulus of rigidity:**It is defined as the ratio of shearing stress to shearing strain within elastic limit.**Bulk modulus:**It is defined as the ratio of identical pressure ‘p’ acting in three mutually perpendicular directions to corresponding volumetric strain.

**5. What is proof resilience?**

The maximum strain energy which can be stored by a body without undergoing permanent deformation is called proof resilience.

**6. What is shear force diagram?**

A diagram in which ordinate represent shear force and abscissa represents the position of the section is called SFD.

**7. What is bending moment diagram?**

A diagram in which ordinate represents bending moment and abscissa represents the position of the section is called BMD.

**8. Assumptions in simple theory of bending.**

a. The beam is initially straight and every layer of it is free to expand or contract.

b. The material is homogeneous and isotropic.

c. Young’s modulus is same in tension and compression.

d. Stresses are within elastic limit.

e. Plane section remains plane even after bending.

f. The radius of curvature is large compared to depth of beam.

**9. State the three phases of finite element method.**

Preprocessing, Analysis & Post processing

**10. What are the h and p versions of finite element method?**

Both are used to improve the accuracy of the finite element method. In h version, the order of polynomial approximation for all elements is kept constant and the numbers of elements are increased. In p version, the numbers of elements are maintained constant and the order of polynomial approximation of element is increased.

**11. What is the difference between static analysis and dynamic analysis?**

**Static analysis:** The solution of the problem does not vary with time is known as static analysis.

**E.g.:** stress analysis on a beam.

**Dynamic analysis:** The solution of the problem varies with time is known as dynamic analysis.

**E.g.:** vibration analysis problem.

**12. What are Global coordinates?**

The points in the entire structure are defined using coordinates system is known as global coordinate system.

**13. What are natural coordinates?A natural coordinate system is used to define any point**

inside the element by a set of dimensionless number whose magnitude never exceeds unity. This system is very useful in assembling of stiffness matrices.

**14. What is a CST element?**

Three node triangular elements are known as constant strain triangular element. It has 6 unknown degrees of freedom called u1, v1, u2, v2, u3, v3. The element is called CST because it has constant strain throughout it.

**15. Define shape function.**

In finite element method, field variables within an element are generally expressed by the following approximate relation:

- Φ (x,y) = N1(x,y) Φ1+ N2(x,y) Φ2+N3(x,y) Φ3+N4(x,y) Φ4 where Φ1, Φ2, Φ3 and Φ4 are the values of the field variables at the nodes and N1, N2, N3 and N4 are interpolation function.
- N1, N2, N3, N4 are called shape functions because they are used to express the geometry or shape of the element.

**16. What are the characteristics of shape function?**

The characteristics of the shape functions are as follows:

- The shape function has unit value at one nodal point and zero value at the other nodes.
- The sum of shape functions is equal to one.

**17. Why polynomials are generally used as shape function?**

- Differentiation and integration of polynomials are quite easy.
- The accuracy of the results can be improved by increasing the order of the polynomial.
- It is easy to formulate and computerize the finite element equations.

**18. State the properties of a stiffness matrix.**

The properties of the stiffness matrix [K] are:

- It is a symmetric matrix.
- The sum of the elements in any column must be equal to zero.
- It is an unstable element, so the determinant is equal to zero.

**19. What are the difference between boundary value problem and initial value problem?**

The solution of differential equation obtained for physical problems which satisfies some specified conditions known as boundary conditions. If the solution of differential equation is obtained together with initial conditions then it is known as initial value problem. If the solution of differential equation is obtained together with boundary conditions then it is known as boundary value problem.

**20. What is meant by plane stress?**

Plane stress is defined as a state of stress in which the normal stress (α) and the shear stress directed perpendicular to plane are zero.

**21. Define plane strain.**

Plane strain is defined to be a state of strain in which the strain normal to the xy plane and the shear strains are assumed to be zero.

**22. Define Quasi-static response.**

When the excitations are varying slowly with time then it is called quasi-static response.

**23. What is a sub parametric element?**

If the number of nodes used for defining the geometry is less than the number of nodes used for defining the displacements is known as sub parametric element.

**24. What is a super parametric element?**

If the number of nodes used for defining the geometry is more than the number of nodes used for defining the displacements is known as sub parametric element.

**25. What is meant by isoparametric element?**

If the number of nodes used for defining the geometry is same as number of nodes used for defining the displacements then it is called parametric element.

**26. What is the purpose of isoparametric element?**

It is difficult to represent the curved boundaries by straight edges finite elements. A large number of finite elements may be used to obtain reasonable resemblance between original body and assemblage. In order to overcome this drawback, iso parametric elements are used i.e for problems involving curved boundaries, a family of elements ‘isoparametric elements’ are used.

**27. What are isotropic and orthotropic materials?**

A material is isotropic if its mechanical and thermal properties are the same in all directions. Isotropic materials can have homogeneous or non-homogeneous microscopic structures.

Orthotropic materials:A material is orthotropic if its mechanical or thermal properties are unique and independent in three mutually perpendicular directions.

**28. What is discretization?**

Discretization is the process of dividing given problem into several small elements, connected with nodes.

**29. Steps in FEM**

- Discretization
- Selection of the displacement models
- Deriving element stiffness matrices
- Assembly of overall equations/ matrices
- Solution for unknown displacements
- Computations for the strains/stresses