(SEM IV) THEORY EXAMINATION 2022-23 INTRODUCTION TO SOLID MECHANICS

This question paper of Introduction to Solid Mechanics (KCE402) for B.Tech 4th semester is designed to test a student’s understanding of the fundamentals of strength of materials, beam theory, columns, springs, and stress analysis. The paper is of 100 marks and is divided into three sections – A, B and C, combining theory, numerical problems, and derivations. It checks both basic conceptual clarity and ability to solve practical engineering problems related to solids under different types of loads.

SECTION A – Short Conceptual Questions (2 × 10 = 20)

This section contains 10 brief questions, each of 2 marks.

It covers the basic definitions and core ideas of solid mechanics.

Main topics covered:

Difference between stress and pressure → fundamental mechanical quantities.

Elongation of a bar → axial deformation due to tensile or compressive load.

Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) → graphical representation of internal forces in beams.

Point of inflexion → location on a beam where bending moment changes sign and curvature reverses.

Neutral axis → line in the beam cross-section where bending stress is zero.

Simple numerical on a solid shaft (screwdriver) → maximum torque using torsion theory.

Methods for slope and deflection → such as double integration, Macaulay’s method, moment area method, conjugate beam, etc.

Limitations of Euler’s formula → when it is not valid for column buckling.

Functions of springs → energy absorption, shock resistance, maintaining force, etc.

Thin-walled spheres → shells with small wall thickness compared to diameter used for internal pressure analysis.

This section checks if the student is comfortable with basic terms, ideas and simple applications.

SECTION B – Descriptive / Numerical Questions (10 × 3 = 30)

In this section, the student has to attempt any three questions, each of 10 marks.

It focuses on numerical problems and short theoretical notes.

Main areas covered:

Axial deformation of bar with varying cross-section → calculation of decrease in length using ΔL=PLAE\Delta L = \frac{PL}{AE}ΔL=AEPL​ for each segment.

Important points for drawing SFD and BMD → sign conventions, steps, positions of maximum moment, relation between load, shear and moment.

Shear stress distribution in a rectangular beam → calculation of shear stress at different distances from neutral axis and sketch of variation (parabolic nature).

Euler’s crippling load for a column with one end fixed and other pinned → use of Euler’s buckling formula with appropriate effective length.

Short notes on compound cylinders → concepts of shrinking stress and compounding for high internal pressure applications.

This section tests problem-solving ability, use of standard formulas, plotting of stress distributions and understanding of column stability.

SECTION C – Long Answer / Derivation / Advanced Numerical (10 × 4 = 40)

In Section C, the student must attempt one part from each question (3 to 7).
These questions involve Mohr’s circle, beams, shear distribution, slope & deflection, columns, springs, and thick cylinders.

Q3 – Mohr’s Circle & Strain Energy Comparison

(a) Construction of Mohr’s circle for a rectangular element under normal stresses σx,σy\sigma_x, \sigma_yσx​,σy​ and shear stress → used to find principal stresses and maximum shear stress graphically.

(b) Strain energy comparison of three bars with area ratio 1:2:3 under equal loads and equal stresses → energy stored in elastic members.

Q4 – Cantilever Beam / Load–Shear–Moment Relation

(a) Cantilever with UDL + point load → drawing complete SFD and BMD over the length.

(b) Derivation of relation between load, shear force and bending moment for a simply supported beam with UDL → fundamental beam theory.

Q5 – Shear Distribution & Section Modulus / Strongest Beam

(a) Shear distribution for rectangular section → deriving expression and understanding parabolic shear stress variation.

(b) Section modulus and strongest beam from a circular log → choosing the best rectangular section that can be cut out.

Q6 – Deflection of Beams and Buckling of Columns

(a) Simply supported beam with two equal point loads using Macaulay’s method → finding maximum slope, maximum deflection and deflection under loads.

(b) Euler’s crippling load for a hinged–hinged column and maximum lateral deflection at buckling condition.

Q7 – Springs and Thick Cylinders

(a) Derivation for closed-coiled helical spring → expressions for maximum shear stress and axial deflection in terms of load, mean coil radius, wire diameter, number of turns and modulus of rigidity.

(b) Thick cylinder with internal pressure + axial load → using Lame’s theory to find safe internal pressure based on allowable stress of material.

This section checks deep understanding, derivation skills, complex numerical handling, and ability to connect theory with design-type problems in solid mechanics.