# Mech.of Solids (110010)

Syllabus

Sr. Topics Teaching Hours Module Weightage
1
Introduction
Scalar and Vector Quantities, composition and resolution of vectors, system of units, definition of space, time, particle, rigid body, force.
2
Fundamentals of Statics:
Force:
Types of Forces, Characteristics of a force, System of forces.
Coplanar concurrent forces:

Resultant of coplanar concurrent force system by analytical method only- Law of parallelogram of forces, Law of triangle of forces, Law of polygon of forces, Composition and resolution of forces, Equilibrium conditions for coplanar concurrent forces, Equilibrant, Free body diagrams, Lami’s theorem.
Coplanar non-concurrent forces:

Moments & couples, Characteristics of moment and couple, Equivalent couples, Force couple system, Varignon’s theorem, Parallel forces, Resultant of non-concurrent forces by analytical method only, Equilibrium conditions of coplanar non-concurrent force system, Equilibrant, Free body diagrams.
3
Truss
Analysis of plane truss, Static determinacy of plane truss, Methods of analysis of truss, Zero force members, Analysis of simple determinate plane trusses using method of joints and method of sections.
4
Center of gravity and moment of inertia
Center of gravity and centroid:
Centroid of lines, plane areas and volumes, Pappus – Guldinus first and second theorems.
Moment of inertia of planar cross-sections:

Parallel & perpendicular axes theorems, polar moment of inertia, radius of gyration of areas.
5
Friction
Theory of friction, Types of friction, Static and kinetic friction, Cone of friction, Angle of repose, Coefficient of friction, Laws of friction, Friction on inclined plane, ladder friction, wedge friction, belt and rope friction.
6
Simple stresses & strains
Normal/axial stresses:
Tensile & compressive, Shear and complementary shear.
Strains:

Linear, shear, lateral, thermal and volumetric. Elastic Constants: Modulus of elasticity, Poisson’s ratio, Modulus of rigidity and bulk modulus (Definitions only)
Analysis of normal stress & strains:

Homogeneous and composite bars having uniform & stepped sections axial loads and thermal loads, hoop stresses, analysis of homogeneous prismatic bars under multidirectional stresses.
7
Statically determinate beams
Beams:
Types of loads, Types of supports, Types of beams; Determination of support reactions.
Bending moment and shear force:

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.
8
Stresses in homogeneous beams
Bending stress in beams:
Pure bending, Theory of pure bending, Neutral axis, Moment of resistance, Relationship between moment of resistance, Bending stress, moment of inertia, Radius of curvature and modulus of elasticity; Section modulus.
Shear stress in beams:

Horizontal shear stress, Relationship between shear force, shear stress and moment of inertia; Horizontal shear stress distribution diagrams across beam section; average shear stress
9
Principal stresses
Analytical solution for elements under axial and shear stress: Normal, tangential and resultant stress on inclined plane, angle of obliquity of resultant stress, maximum shear stress, principal planes and principal stresses, principal stresses in beams under bending and shear.