(SEM IV) THEORY EXAMINATION 2023-24 ENGINEERING MECHANICS & STRENGTH MATERIAL

This document is a B.Tech (Semester IV) Theory Examination Question Paper for the subject BME402 – Engineering Mechanics & Strength of Material, conducted in the academic year 2023–2024.
It is a 3-hour, 70-mark examination designed to assess students’ understanding of mechanics, structural analysis, stress–strain concepts, torsion, bending, columns, strain energy, thin cylinders, Mohr’s circle, and beam theory.

The question paper is divided into three sections—A, B, and C—covering conceptual theory, derivations, graphical diagram questions, and numerical problems.

SECTION A – Short Answer Questions (14 Marks)

Seven short 2-mark questions test foundational concepts of mechanics and strength of materials:

Conditions of equilibrium for rigid bodies                 Definition of cantilever truss

Meaning of principal planes & principal stresses      Definition of thermal stress and thermal strain

Meaning of bending stresses in beams                       Definition of slenderness ratio (important for column stability)

Criteria for thin cylindrical shells  

This section checks theoretical basics and terminology.

SECTION B – Derivation-Based & Conceptual Questions (21 Marks)

Students must attempt any three of the following:

a. Parallelogram Law of Forces

State & prove the vector law for force addition.

b. Theorem of Perpendicular Axis

Used for moment of inertia calculation for planar lamina.

c. Torsion of Solid Circular Shaft

Derive the torsion equation:

TJ=τr=GθL\frac{T}{J} = \frac{\tau}{r} = \frac{G\theta}{L}JT​=rτ​=LGθ​

d. Euler’s Crippling Load

Derive load formula for columns with both ends fixed.

e. Thin Cylindrical Shell

Effects of internal fluid pressure & derivation of changes in dimensions (hoop stress, longitudinal stress, radial strain).

This section tests derivations, laws, and structural mechanics concepts.

SECTION C – Long Answer / Numerical / Diagram Problems (35 Marks Total)

Each question contains two options; students must attempt one part from each.

3. Truss Forces / S.F. & B.M. Diagram (7 Marks)

Option 3(a)
Compute forces in truss members from given diagram (Page 1 image).

Option 3(b)
Draw Shear Force Diagram (S.F.D.) and Bending Moment Diagram (B.M.D.) for a 7 m simply supported beam with UDL.

4. Moment of Inertia / Mohr’s Circle Stress Analysis (7 Marks)

Option 4(a)
Moment of inertia of a triangular section with a rectangular hole.

Option 4(b)
A plane element with:

Tensile stresses = 400 MPa & 150 MPa

Shear stress = 100 MPa
Find:

Principal stresses & directions

Maximum shear stress & planes
(Mohr’s Circle application)

5. Beam Deflection / Shaft Design (7 Marks)

Option 5(a)
Slope & deflection of simply supported beam under UDL using Macaulay’s method.

Option 5(b)
Design of solid steel shaft transmitting 100 kW at 160 rpm:

Allowable shear stress = 70 MPa

Max torque = 1.2 × mean torque
Compute diameter.

6. Leaf Spring / Column Buckling (7 Marks)

Option 6(a)
Derive bending stress formula for leaf spring:
Span = l, width = b, thickness = t, plates = n.

Option 6(b)
Euler’s crippling load for hollow steel column:

External diameter = 38 mm

Thickness = 2.5 mm

Length = 2.3 m (hinged at both ends)

E = 205 GPa
Also find load using Rankine’s formula.

7. Thick Cylinder / Thin Cylinder (7 Marks)

Option 7(a)
Cast iron pipe:

Internal diameter = 400 mm                            Thickness = 100 mm

Internal pressure = 8 N/mm²
Find max & min hoop stresses and draw distribution diagram.

Option 7(b)
Thin cylindrical shell:

Diameter = 500 mm                                      Pressure = 4 MPa

Max tensile strength = 400 MPa                   Joint efficiency = 65%

FOS = 5
Find minimum wall thickness.

Overall Purpose of the Document

This exam paper evaluates a student's competency in:

Engineering mechanics fundamentals (forces, equilibrium, trusses)

Strength of materials (stress, strain, bending, torsion, thermal stresses)

Structural analysis (columns, beams, deflection, bending moments)

Material behavior under load (principal stresses, Mohr’s circle)

Pressure vessels (thin & thick cylinders)

Columns & buckling (Euler & Rankine theories)

Section properties (moments of inertia)

It contains theory questions, derivations, calculations, and diagram-based structural problems, ensuring full assessment of the subject.