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.
