# Finite Element Method Questions and Answers – Three Dimensional Stress, Solid Mechanics, and Torsion Analysis

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Three Dimensional Stress, Solid Mechanics, and Torsion Analysis”.

1. Traction vector is also referred to as stress vector.
a) True
b) False

Explanation: The given statement is true. Traction vector can be defined as the ratio of force vector on a specified cross sectional area to the same cross sectional area under consideration. As stress is defined as ratio of force to area, both traction and stress vector are considered synonyms of one another.

2. Which of the following defines an isotropic state of stress?
a) No normal stresses
b) No shear stresses
c) No tensile stresses
d) No compressive stresses

Explanation: When a body has no shear stresses acting upon it, regardless of what the orientation of the plane through the point under consideration are considered as states of isotropic stresses. These are also referred to as spherical state of stress.

3. When is an isotropic stress termed as hydrostatic stress?
a) When stress arises in a fluid at rest
b) When stress arises in a fluid at motion
c) When stress arises in a solid at rest
d) When stress arises in a solid at motion

Explanation: The isotropic stress is also termed as hydrostatic state of stress when there are stresses arising in fluids at rest. This obviously cannot support shear stress; leading to –
σ = -pI
where, p corresponds to the scalar hydrostatic pressure

4. Computation of stress and strain components comes under the preprocessing stage of the finite element method.
a) True
b) False

Explanation: The given statement is false. Computation of stress and strain components comes under the post processing stage of the finite element method. Once the displacements are known, the strain components can be found out by making use of the equations responsible for discretization.

5. Which of the following does the maximum shear stress theory correspond to?
a) Failure occurs due to maximum shear stress values
b) Failure occurs due to maximum normal stress values
c) Failure does not occur due to maximum shear stress values
d) Failure does not occur due to maximum normal stress values

Explanation: The maximum shear stress theory states that, in any normal state condition, failure occurs when the maximum shear stress exceeds the maximum shear stress that arises due to an uniaxial tension test at yield point.

6. What does the Distortion energy theory correspond to?
a) Uniform tensile or compressive stress does cause distortion
b) Uniform tensile stress does not cause distortion
c) Uniform tensile or compressive stress does not cause distortion
d) Uniform compressive stress does not cause distortion

Explanation: This theory hails its principle from the strain energy stored in a material under any given state of stress. It states that, for any uniform values of tensile or compressive stress; there is no distortion taking place in the parent material. This in turn implies that, there is no contribution to yielding from the above mentioned stress components.

7. Assumptions are the same for both circular and non circular members undergoing twisting motion.
a) True
b) False

Explanation: The given statement is false. Assumptions in case of circular bodies are different than those of non circular bodies. In case of circular bodies, plane sections remain plane even after twisting. However, this is not the case with non circular bodies, leading to difficulty in computation.

8. Which of the following is an unknown value in finite element formulation of torsional bodies?
a) Angle of twist per unit length
b) Applied torque
c) Geometry cleanup values
d) Material properties

Explanation: In case of finite element formulation of torsional bodies, the angle of twist per unit length is the unknown variable. To compute the same, geometry and material properties, applied torque are specified; in order to arrive at the value of angle of twist per unit length.

Sanfoundry Global Education & Learning Series – Finite Element Method.