This course enable the learners to understand about Deflection and torsion produced in beams, stresses in springs, design of thin and thick shells and corresponding their failures.
Deflection of Beam - Beam deflection, Elastic curve of neutral axis of the beam under normal load, Relationship between loading S.F, B.M, slope and deflection, Finding slope and deflection. Double Integration method - Cantilever with concentrated load at the end, Cantilever with uniformly distributed load at the end, Simply supported beam with uniformly distributed load at the end, Simply supported beam with concentrated load at mid – span. Macaulay's method - Macaulay's method for UDL, Macaulay's method for beam with UDL applied over part of the beam. Mohr Moment-Area method - Cantilever with concentrated load at the tip, Cantilever with UDL, Simply supported beam with UDL, Simply supported beam with central concentrated load. Conjugate Beam method - Conjugate beam theorem I, Conjugate theorem II, Maxwell's reciprocal theorem.
Torsion of Shafts - Introduction, Definition of shaft, Torsion in shafts, Assumptions for torsion equation. Stresses in shafts - Angle of twist, Stresses in shafts, Torsion equation for solid shafts, Torsion equation for hollow circular shaft, Torsion rigidity, Modulus of rupture, Composite shafts - serial connection, Composite shafts - parallel connection, Comparison of solid and hollow shafts. Combined bending and torsion.
Springs – Introduction, Types of springs, Material characteristics of springs. Helical Springs - Classification, Advantages, Application. The Close-coiled Helical Springs - Terms used in close-coiled helical springs, Close-coiled helical springs with axial load, Rectangular and square section wire springs, Close-coiled helical springs with axial twist. Springs in Series and Parallel - Springs in series, Springs in parallel. Leaf Springs - Types of leaf spring, Stresses and deflection of leaf springs.
Thin cylindrical Shells – Introduction, Circumferential or hoop stresses, Longitudinal stresses, Maximum shear stress, Design of thin cylindrical shells, Cylindrical shell with hemispherical ends, Built-up cylindrical shells, Change in dimensions of a thin cylindrical shell due to an internal pressure, Spherical shells, Spherical shells-change in dimension. Thick Cylinders – Introduction, Lame's theory, Thick cylinders subjected to inside and outside pressures, Shear stress, Introduction to compound cylinders.
Definitions of column and strut – Introduction to column, Slenderness ratio, Classification of columns, Failure of columns, Slenderness ratio, End conditions, Equivalent length of column. Euler's Theory - Assumptions in Euler theory, Euler theory for column with both ends hinged, Euler formula for column with one end fixed and other end free, Euler theory for column with one end fixed and other end hinged, Euler theory for column with both end fixed. Euler's Formula - Limitations for uses of Euler formula. Problems - Column with both ends hinged, Column with both ends fixed, Column with one end fixed and other end free, Column with one end fixed and other end hinged, Design of columns.
Theories of Failure – Theory of Strength, Principal Stresses at a Point, Principal Stress-Strain Relation, Biaxial Stress State, Theories of Strength / Failure, Normal Stress Theory (Rankine), Normal Strain Theory (St Venant's), Shear Stress Theory (Coulomb, Guest, Tresca), Strain Energy Theory (Beltrami), Von Mises Theory.
