College of Technology, Pantnagar

Mechanics of rigid bodies: various two dimensional system of forces, resultant of forces, equilibrium of forces, free body diagram, parallelogram law, polygon law, moment of a force, couple, resolution of forces into a force and a couple, varignon theorem, various types of supports and corresponding reactions. Concept of centroid: centroid of two dimensional bodies, determination of centroid by integration method, centroid of geometrically composite plane figures. Second moment of area: rectangular second moment of area, polar second moment of area, product second moment of area, radius of gyration, parallel axes theorem, perpendicular axes theorem, second moment of area of geometrically composite sections. Simple stresses and strains: stress, strain, actual stress and strain, nominal stress and strain, stress-strain, curve for ductile and brittle materials, hook’s law, Young’s modulus of elasticity, concept of factor of safety, shear stress, shear strain, modulus of rigidity, complementary shear stress, elongation of various bars under self load and external loads. Temperature stresses due to uniform change in temperature, composite bars subjected to axial forces and temperature change, poison’s ratio, volumetric strain, pressure, bulk modulus, relation between various elastic constants. Complex stresses: stresses on oblique plane induced due to two mutually perpendicular normal stresses and to shear stresses, graphical solution to complex stresses i.e. mohar’s circle method, principal stresses and principal planes. Introduction to bending moment and shear force: concept of bending moment and shear force, calculation of bending moment and shear force at any section, sign convention. B.M.D and S.F.D. for cantilever simply supported and overhanging beams subjected to various types of linearly varying loads. Stresses in beam: simple theory of bending (assumptions and derivation of expression of expression for flexural and shearing resistance. Torsion of circular section: derivation of shear stress produced in a circular shaft subjected to torsion, maximum torque transmitted by solid and hollow circular shaft, power transmitted by shaft, torsional rigidity. Slope and deflection of statically determinate beams: slopes and deflection of cantilever and simply supported beams using Macaulay’s method. Columns and struts: Failure of short column, Euler’s theory for long columns, critical load, effective length of a column, slenderness ratio, limitations of Euler’s theory, critical slenderness ratio, Trusses: introduction to trusses, analysis of planer statically determinate trusses, assumptions in truss analysis, method of joints, method of section.