(SEM IV) THEORY EXAMINATION 2023-24 INTRODUCTION TO SOLID MECHANICS

The uploaded document is the B.Tech Semester IV Theory Examination Paper (2023–24) for the subject BCE402 – Introduction to Solid Mechanics. It is an official university-level exam paper designed to assess a student’s understanding of the core principles of mechanics of solids, including stress–strain relationships, internal forces in beams, deformation of structural members, torsion, bending, buckling, and various failure theories. The examination carries a total of 70 marks, must be attempted within 3 hours, and is organized into Section A, Section B, and Section C, as clearly shown on Page 1 and Page 2 of the uploaded file.

 

The paper begins with Section A, which contains seven compulsory short-answer questions, each worth 2 marks. These questions are crafted to test fundamental conceptual clarity. Students must define allowable stress, explain the meaning of resilience, and state the basic relationship between shear force and bending moment in beams. The section also examines the student’s understanding of the assumptions involved in pure bending, which form the basis of bending theory. A question on von Mises stress theory requires explaining its importance as an energy-based failure criterion for ductile materials. The section further asks for the torsion equation, emphasizing the role of shear stress in circular shafts, and concludes with a question on elastic constants, reflecting the interrelation among Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio. Section A ensures that students possess foundational knowledge before moving into the more detailed parts of the exam.
 

Section B contains five descriptive questions, out of which students must attempt any three, each worth 7 marks. This section requires detailed explanation, sketches, derivations, and sometimes numerical calculations. One question instructs students to draw the Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) for a simply supported beam subjected to a uniformly distributed load, testing their ability to compute reactions, locate maximum bending moment, and present the diagrams clearly. Another question deals with biaxial stress systems and requires students to determine stresses on an oblique plane, testing their understanding of stress transformation. There is also a question on the principal strain theory, requiring explanation of strain transformation and the conditions under which failure occurs according to this theory. Another question asks students to compute the maximum torque and maximum shear stress in a hollow shaft subjected to torsion, requiring knowledge of torsion mechanics and polar moment of inertia. The section concludes with a question on strain energy due to gradually applied loads, testing the ability to relate load application to stored elastic energy. Section B assesses the student's ability to apply theoretical principles to practical structural scenarios.
 

Section C, the analytical and long-answer section, is divided into multiple subsections (Q3 to Q7). Students must attempt one question from each subsection, with each question carrying 7 marks. The questions in this section require deeper mathematical derivations and engineering reasoning. The first subsection includes a question on thermal stresses, asking students to calculate internal forces developed in composite bars or constrained members under temperature change. The alternate question requires solving a beam deflection problem using Macaulay’s method, which demands stepwise application of the deflection formula with piecewise load functions.

The next subsection contains a question asking to compare the section modulus of a hollow circular shaft and a solid circular shaft, requiring an understanding of bending strength and material economy. The alternative question asks students to determine the shear stress distribution in a T-section, requiring detailed knowledge of shear flow, centroid location, and moment of inertia.

Another subsection contains a question requiring students to draw Mohr’s circle and determine principal stresses and maximum shear stresses for a given stress system. This tests a student's understanding of graphical stress transformation and failure prediction. The alternative option asks them to explain Euler’s buckling theory, including the critical load formula for long columns under different end conditions.

The final subsection covers thin shell theory. One question asks students to calculate the hoop stress and longitudinal stress developed in a thin cylindrical shell subjected to internal pressure. The alternative question examines the change in volume or change in diameter of pressure vessels, requiring use of compatibility equations and material elastic constants.

Overall, this exam paper offers a complete and rigorous evaluation of solid mechanics principles. It tests a student’s ability to analyze internal stresses, compute deflections, understand the behavior of structural members under torsion and bending, evaluate failure theories, and apply advanced analytical methods such as Mohr’s circle, Euler’s buckling theory, torsion equations, and strain-energy concepts. The combination of theoretical questions, numerical problems, and diagram-based analysis ensures a comprehensive assessment of both conceptual understanding and practical engineering ability. With its structured format and wide coverage of essential topics, the question paper fully reflects the core curriculum of Introduction to Solid Mechanics for engineering students.