This is the first course where deformation of solid bodies and the underlying concepts are introduced to undergraduate students. The course begins by building foundation of the concepts of stress and strain in three-dimensional deformable bodies. It further uses these concepts to study extension, torsion and bending of beams. The one-dimensional theory of beams are also introduced. We also discuss various theories of failure which are critical for design of machine elements in industry.INTENDED AUDIENCE: Any Interested LearnersPREREQUISITES:1st year Engineering Mechanics
Overview
Syllabus
Week 1: Mathematical preliminaries and notation; Concept of Traction vector; Concept of Stress tensorWeek 2: Stress tensor and its representation in Cartesian coordinate system; Transformation of stress matrix; Equations of equilibrium; Symmetry of stress tensor
Week 3: State of stress in simple cases; Principal stress components and principal planes; Maximizing shear component of traction; Mohr’s circle
Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor
Week 5: Longitudinal, shear and volumetric strains; Local infinitesimal rotation; Strain compatibility condition
Week 6: Linear stress-strain relation for isotropic bodies; Relation between material constants
Week 7: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system
Week 8: Axisymmetric deformations: combined extension-torsion-inflation of a cylinder
Week 9: Bending of beams having symmetrical and non-symmetrical cross-section
Week 10: Shear center, Shear flow in thin and open cross-section beams; Euler Bernouli and Timoshenko beam theories; beam buckling
Week 11: Energy methods, Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
Week 12: Various theories of failure and their application
Week 3: State of stress in simple cases; Principal stress components and principal planes; Maximizing shear component of traction; Mohr’s circle
Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor
Week 5: Longitudinal, shear and volumetric strains; Local infinitesimal rotation; Strain compatibility condition
Week 6: Linear stress-strain relation for isotropic bodies; Relation between material constants
Week 7: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system
Week 8: Axisymmetric deformations: combined extension-torsion-inflation of a cylinder
Week 9: Bending of beams having symmetrical and non-symmetrical cross-section
Week 10: Shear center, Shear flow in thin and open cross-section beams; Euler Bernouli and Timoshenko beam theories; beam buckling
Week 11: Energy methods, Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
Week 12: Various theories of failure and their application
Taught by
Prof. Ajeet Kumar
