Teaching Scheme (in Hours)
Subject Credit : 5
Examination Scheme (in marks)
ESE Viva (V)
Syllabus Content Download
Definition of space, time, particle, rigid body, deformable body. Force, types of forces, Characteristics of a force, System of forces, Composition and resolution of forces. Fundamental Principles of mechanics: Principle of transmissibility, Principle of superposition, Law of gravitation, Law of parallelogram of forces, Newton’s Laws of Motion
Unit-2: Fundamentals of Statics
Coplanar concurrent and non-concurrent force system:
Resultant, Equilibrant, Free body diagrams.Coplanar concurrent forces:
Resultant of coplanar concurrent force system by analytical and graphical method, Law of triangle of forces, Law of polygon of forces, Equilibrium conditions for coplanarconcurrent forces, Lami’s theorem. Application of these principles.Coplanar non-concurrent forces:
Moments & couples, Characteristics of moment and couple, Equivalent couples, Force couple system, Varignon’s theorem, Resultant of non-concurrent forces by analytical method and graphical method, Equilibrium conditions of coplanar non-concurrent force system, Application of these principles.
Concept of statically determinate and indeterminate problems.Plane Truss
assumptions used in the analysis of Truss. Perfect, imperfect and redundant truss, analysis of Truss by method of joints and method of sections.
Unit-3: Applications of fundamentals of statics
Statically determinate beams:
Types of loads, Types of supports, Types of beams; Determination of support reactions, Relationship between loading, shear force & bending moment, Bending moment and shear force diagrams for beams subjected to only three types of loads :i) concentrated loads ii) uniformly distributed loads iii) couples and their combinations; Point of contraflexure, point & magnitude of maximum bending moment, maximum shear force
Unit-4: Stresses in Beams
Theory of simple bending, Assumptions, derivation of equation of bending, neutral axis, determination of bending stresses, section modulus of rectangular & circular (solid & hollow), I,T,Angle, channel sections
Derivation of formula, shear stress distribution across various beam sections like rectangular, circular, triangular, I, T, angle sections.
Unit-5: Centroid and moment of inertia and mass moment of inertia
Centroid: Centroid of lines, plane areas and volumes, Examples related to centroid of composite geometry, Pappus – Guldinus first and second theorems.
Moment of inertia of planar cross-sections: Derivation of equation of moment of inertia of standard lamina using first principle, Parallel & perpendicular axes theorems, polar moment of inertia, radius of gyration of areas, section modulus. Examples related to moment of inertia of composite geometry.
Derivation of equation of torsion, Assumptions, application of theory of torsion equation to solid & hollow circular shaft, torsional rigidity
Unit-7: Simple stresses & strains
Basics of stress and strain: 3-D state of stress (Concept only)
Normal/axial stresses: Tensile & compressive
Tangential Stresses :Shear and complementary shear
Strains: Linear, shear, lateral, thermal and volumetric
Hooke’s law, Elastic Constants: Modulus of elasticity, Poisson’s ratio, Modulus of rigidity and bulk modulus and relations between them with derivation
Application of normal stress & strains: Homogeneous and composite bars having uniform & stepped sections subjected to axial loads and thermal loads, analysis of homogeneous prismatic bars under multidirectional stresses
Unit-8: Principle stresses
Two dimensional system, stress at a point on a plane, principal stresses and principal planes, Mohr’s circle of stress, ellipse of stress and their applications.
Unit-9: Physical & Mechanical properties of materials: (laboratory hours)
Elastic, homogeneous, isotropic materials; Stress –Strain relationships for ductile and brittle materials, limits of elasticity and proportionality, yield limit, ultimate strength, strain hardening, proof stress, factor of safety, working stress, load factor, Properties related to axial, bending, and torsional & shear loading, Toughness, hardness, Ductility ,Brittleness
Unit-10: Simple Machines: (laboratory hours)
Basics of Machines, Definitions: Velocity ratio, mechanical advantage, efficiency, reversibility of machines.
Law of Machines, Application of law of machine to simple machines such as levers, pulley and pulley blocks, wheel and differential axle, Single purchase, double purchase crab, screw jacks. Relevant problems
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