(SEM IV) THEORY EXAMINATION 2024-25 INTRODUCTION TO SOLID MECHANICS

This document contains the complete B.Tech (Semester IV) Theory Examination 2024–25 question paper for Introduction to Solid Mechanics (BCE402). The paper spans four printed pages, carries 70 marks, and evaluates a student's understanding of stress–strain relationships, beam theory, torsion, bending, failure theories, pressure vessels, buckling, and structural analysis.

Section A – Short Conceptual Questions (14 Marks)

Section A includes seven 2-mark questions, covering fundamental definitions and relationships in solid mechanics:

Relationship between Young’s Modulus, Bulk Modulus & Modulus of Rigidity

Significance and occurrence of point of contraflexure in bending moment diagrams

Difference between overhanging beams and propped cantilevers

Procedure to find section modulus for a circular section

Thin vs Thick cylinders based on assumptions & stress variation

Meaning of buckling and importance of slenderness ratio

Definition of torsion with two real-life examples (Page 1)

This section checks foundational clarity on mechanical behavior of materials.
 

Section B – Medium-Level Analytical Questions (21 Marks)

Students must attempt any three of the five questions. Topics include:

Derivation of volumetric strain for an element in uniaxial tension (Page 1, with diagram)

Shear force & bending moment equations for a simply supported beam under UDL and applied couple (diagram on Page 1–2)

Derivation of bending stress equation and assumptions of simple bending, with stress distribution sketch

Failure criteria with mathematical expressions:

Maximum Principal Strain Theory

Maximum Shear Stress Theory

Strain Energy Theory

Distortion Energy Theory

Maximum allowable internal pressure in a cylindrical tank using thin cylinder theory

These questions test derivations, formula application, and ability to interpret mechanical behavior.
 

Section C – Long Numerical & Derivation-Based Questions (35 Marks)

Section C contains five long questions, each requiring students to attempt one part from each.

Q3 – Hydrostatic Stress / Composite Bar (Page 2–3)

Determine Poisson’s ratio and Bulk Modulus of aluminum subjected to hydrostatic pressure

Thermal stress & deformation in a copper–aluminum composite bar, with yielding of support

Q4 – SFD & BMD for Beams (Page 3)

SF & BM diagrams for a beam with linearly varying load

Cantilever with UDL + applied couple at free end → draw SFD & BMD

Q5 – Stress in Beams (Page 4)

Maximum permissible load on simply supported timber beam

Maximum tensile & compressive stresses in a T-section cantilever

Q6 – Compression Members / Stress Transformation (Page 4)

Eccentric loading on rectangular column → compute max compressive & tensile stresses

Using given normal & shear stresses, find principal stresses and maximum shear stress with sketch

Q7 – Pressure Vessels / Torsion (Page 4)

Derive longitudinal strain, hoop strain, and volumetric strain for thin cylindrical shells

Derive the torsion equation with assumptions

This section evaluates deep analytical problem-solving, structural behavior interpretation, and classical mechanics derivations.

Summary

The Introduction to Solid Mechanics (BCE402) exam paper comprehensively covers:

Stress–strain relations & elastic constants

Bending, shear force & moment diagrams

Simple bending theory

Failure theories (Rankine, Guest, Von Mises, etc.)

Pressure vessel stresses

Torsion & shaft design

Buckling & column behavior

Composite bars & thermal stresses

SFD/BMD drawing & interpretation

Principal stresses & Mohr’s circle concepts

This is a complete academic resource for civil/mechanical engineering students learning the fundamentals of solid mechanics and structural analysis.