(SEM IV) THEORY EXAMINATION 2024-25 ENGINEERING MECHANICS & STRENGTH MATERIAL

This document contains the complete B.Tech (Semester IV) Theory Examination 2024–25 question paper for Engineering Mechanics & Strength of Materials (BME402). The paper spans two printed pages, carries 70 marks, and evaluates the student’s understanding of mechanics, structural analysis, stress–strain behaviour, beam theory, columns, cylinders, springs, trusses, and torsion.
 

Section A – Short Conceptual Questions (14 Marks)

Section A includes seven 2-mark fundamental questions, as seen on Page 1. These assess clarity of basic engineering principles:

Definition and importance of Free Body Diagram (FBD)

Significance of Centroid in structural analysis

Difference between Normal Stress and Shear Stress

Meaning of Principal Stresses

Definition of Macaulay’s Method for beam deflection

Euler’s Formula for column buckling

Difference between Thin and Thick Cylinders

These questions test foundational knowledge in statics, strength of materials, and deformation behavior.
 

Section B – Analytical & Numerical Questions (21 Marks)

Students attempt any three of the five 7-mark questions shown on Page 1. These cover problem-solving ability and theoretical understanding:

Ladder Equilibrium Problem

A 5 m ladder leaning at 60° with friction at wall & floor must support 900 N — find the horizontal force P needed to prevent slipping.

Lami’s Theorem

State and prove the theorem used for solving three-force equilibrium systems.

Bending Equation Derivation

Derive the flexural/bending equation, including assumptions and stress distribution.

Combined Bending & Torsion

A solid circular shaft subjected to 3000 N-m bending and 10000 N-m torque, with given steel properties, requires diameter calculation using Factor of Safety.

Crippling Load

Find the critical load for a long column with one end fixed and the other hinged.

These questions test application of mechanics in real structures and machine components.
 

Section C – Long, Advanced Questions (35 Marks)

Each question has two alternatives, and students must attempt one part from each (Pages 1–2).

Q3 – Truss Analysis / SFD–BMD

Find magnitude and nature of forces in members of the truss shown in the diagram (Page 1)

OR

Draw Shear Force (S.F.) and Bending Moment (B.M.) diagrams of the simply supported beam shown (Page 2 diagram with UDL & triangular loading)

Q4 – Thick Cylinder / Helical Spring

Derive Lame’s Equation for thick cylinders with assumptions

OR

For a helical spring (12 coils, wire dia 16 mm, coil dia 250 mm, load 300 N), find:

Axial deflection

Strain energy

Max torsional shear stress

Max shear stress
using Wahl’s correction factor

Q5 – Beam Deflection / Shaft Design

Using Macaulay’s Method, find slope & deflection of a simply supported beam under UDL

OR

For a shaft transmitting 100 kW at 160 RPM, with allowable shear stress of 70 MPa and 20% torque fluctuation, compute suitable shaft diameter

Q6 – Rankine’s Formula / Leaf Spring

A hollow CI column (D=200 mm, t=20 mm, L=4.5 m), fixed at both ends — find safe load using Rankine’s formula

OR

Derive bending stress expression for a leaf spring (span L, width b, thickness t, n plates)

Q7 – Thick Cylinder Stress / Cylindrical Shell Stress

For a cast iron pipe (ID 400 mm, thickness 100 mm, pressure 8 N/mm²), find maximum & minimum hoop stress, with radial pressure diagram

OR

For a cylindrical shell (D=0.6 m, t=15 mm, P=1.2 N/mm²), find:

Longitudinal stress

Circumferential (hoop) stress

Max shear stress

Change in diameter, length & volume
using E = 200 GPa and 1/m = 0.3

These questions assess mastery of advanced topics in mechanics, stress analysis, pressure vessels, and deflection theory.

Summary

The Engineering Mechanics & Strength of Materials (BME402) exam paper comprehensively covers:

Free body diagrams, centroids, basic stresses

Principal stresses, columns, Euler buckling

Beam theory, bending equation & deflection

Shafts under combined loading

Columns: Euler & Rankine’s formula

Thick & thin cylinder stresses

Helical and leaf springs

Truss forces & equilibrium

SFD–BMD analysis

Pressure vessel stresses

Structural mechanics & machine component behavior

This paper is an essential resource for mechanical/civil engineering students learning the fundamentals of structural analysis and strength of materials.