Mechanics Of Solids (3130608)

Unit-1:  Introduction

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

Flexural stresses

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

Shear stresses

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.

Unit-6:  Torsion

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