(SEM-V) THEORY EXAMINATION 2021-22 STRENGTH OF MATERIALS

SECTION A (Any 2 Questions Explained Briefly)
 

Why are stresses called tensor quantities?
Stresses are called tensor quantities because they depend on both magnitude and the direction of the plane on which they act. At a single point inside a material, different normal and shear stresses act on different planes. Since stress cannot be represented completely by a single value or direction, it requires a tensor form to describe all components accurately.
 

Explain section modulus and its significance.
Section modulus is a measure of the bending strength of a beam section. It is defined as the ratio of moment of inertia to the distance of the extreme fiber from the neutral axis. A higher section modulus means the beam can resist higher bending moments without failure, which makes it very important in beam design.
 

SECTION B (Any 2 Questions Explained)
 

Derive the expression for critical buckling load of a column having one end fixed and the other free.
For a column with one end fixed and the other free, buckling occurs at a comparatively low load. According to Euler’s theory, the effective length of such a column is twice its actual length. Substituting this effective length into Euler’s buckling formula gives the critical load expression. This shows that fixed-free columns are weaker against buckling compared to other end conditions.
 

Explain the purpose of compounding thick cylinders.
Compounding of thick cylinders is done to reduce the maximum hoop stress produced by internal pressure. By shrinking one cylinder over another, initial compressive stresses are introduced. When internal pressure is applied, these stresses reduce the net tensile stress, making the stress distribution more uniform and increasing the safety of the cylinder.
 

SECTION C (Any 2 Questions Explained)
 

Explain failure according to Maximum Strain Energy (Haigh) theory.
According to the maximum strain energy theory, yielding begins when the total strain energy per unit volume in a material reaches the strain energy at yield point under simple tension. This theory considers the combined effect of all principal stresses and is mainly applicable to ductile materials.
 

Explain failure according to Maximum Shear Strain Energy (Von Mises) theory.
Von Mises theory states that yielding begins when the distortion or shear strain energy reaches the value at yield point in a tensile test. This theory ignores volumetric strain energy and gives very accurate results for ductile materials, which is why it is widely used in engineering design.
 

Most Questions in This PDF Are Related To
 

Most of the questions in this Strength of Materials (KME-502) paper are mainly related to stress–strain relationships, bending of beams, buckling of columns, thin and thick cylinders, failure theories, and deflection of beams. Numericals are largely based on Euler buckling theory, bending stress equations, Lame’s equations, and strain energy concepts, which are core topics of Strength of Materials.