(SEM III) THEORY EXAMINATION 2017-18 MECHANICS OF SOLIDS

This document contains the complete B.Tech (Semester III) Theory Examination 2017–18 question paper for Mechanics of Solids (RME-303). The paper spans two printed pages, carries 70 marks, and evaluates core engineering concepts including stresses, strains, torsion, bending, columns, deflection, thick/thin cylinders, shear center, and failure theories.
 

Section A – Short Conceptual Questions (14 Marks)

Section A includes seven brief questions, each testing a fundamental principle of solid mechanics:

Principal planes & principal stresses

Definitions of resilience, proof resilience, and modulus of resilience

Methods to determine slope & deflection in a cantilever

Meaning of torsional rigidity

Concept of shear center

Understanding of buckling in columns

Difference between thin and thick cylinders

This section checks conceptual clarity and core definitions essential for structural analysis.
 

Section B – Numerical & Analytical Problems (21 Marks)

Students must attempt any three questions involving formulas, calculations, and analytical reasoning:

Maximum deflection of a simply supported beam under two point loads

Diameter design of a hollow shaft transmitting power with torsion and bending

Crippling load of a hollow column using Rankine’s formula

Derivation of maximum principal stress for a thick cylinder under internal pressure

Determining wall thickness for a tube based on hoop stress and internal pressure

These questions test ability to apply solid mechanics equations to engineering problems.
 

Section C – Advanced Derivations & Design-Based Problems (35 Marks)

1. Columns & Springs

Derivation of Euler’s equation for long columns with both ends built-in

Deflection, rotation & stresses in open-coil helical springs, plus effect of coil angle

2. Shear Centre & Bending

Determining the shear center for a channel section

Maximum bending stress in an unequal angle section subjected to bending moment

3. Principal Stresses & Failure

Resultant stress, principal planes, principal stresses & maximum shear stress

Explanation of theories of failure with graphical representation

4. Curved Beams & Shafts

Maximum tensile & compressive stresses in a crane hook of trapezoidal section

Design of a hollow shaft with torque, shear stress & twist angle constraints

5. Thick Cylinders & Buckling

Assumptions in Lame’s theory and derivation for thick-shell stress distribution

Euler’s buckling load for a column with one end fixed and the other hinged

These problems assess deep understanding of material behavior under complex loading, advanced derivations, and engineering design skills.
 

Summary

The Mechanics of Solids (RME-303) exam paper thoroughly evaluates:

Stress, strain & resilience

Bending, shear, and torsional behavior

Deflection of beams

Column buckling (Euler & Rankine)

Thick & thin cylinder stresses

Shear center & curved beam theory

Failure theories

Shaft design & spring mechanics

It is a complete academic resource for students of mechanical and civil engineering studying the fundamentals of strength of materials.