Unit 1 Stress

6 lecture hours

• Surface forces and body forces
• Cartesian components of stress on small cubic element
• Stress at a point
• Stress equations of equilibrium
• Principal stresses
• Maximum shear stress
• Two dimensional state of stress
• Special cases: Pure shear stress
• Hydrostatic state of stress
• Strain equations of transformations
• Principal strain
• Energy method for analysis of stress
• strain and deflection
• three theorem’s -theorem of virtual work
• theorem of least work
• Castiglioni’s theorem
• Rayleigh Ritz method
• Galerkin’s method

Unit 2 Theory of Elasticity

12 lecture hours

• Elasticity problems in two dimensions - stress strain relationship for brittle materials
• ductile materials
• Compatibility equations in two and three dimensions
• Airy’s stress function
• Polar component of stress in terms of stress function free body diagram of complicated structures and stress calculations
• stress functions in rectangular and cylindrical coordinate systems
• evaluation of stresses in flat rectangular plates with different clamp and load conditions evaluation of the stresses in the flat and circular plate with center hole/holes using stress function

Unit 3 Theory of Plasticity

11 lecture hours

• Different criterions for three-dimensional stress analysis using plasticity
• evaluation of stress concentration factors in different geometries using plasticity theorem
• practical problems on stress analysis for plasticity
• stress in the sharp groove of the shaft
• stress in the L shaped bracket under cantilever load
• strain rate effects on highly deformable materials and stress calculations

Unit 4 Plate bending

8 lecture hours

• Bending of plate to cylindrical surface
• bending of a long uniformly loaded rectangular plate
• pure bending in two perpendicular directions
• bending of circular plates loaded symmetrically w.r.t. center
• bending of circular plates of variable thickness
• circular plate with circular hole at center symmetrically loaded and load distributed along inner and outer edges

Unit 5 Contact stresses

17 lecture hours

• 08 Program Name: Master of Engineering Level: PG Branch: Machine Design Course / Subject Code : ME01078031 Course / Subject Name : Advanced stress analysis Geometry of contact surfaces
• method of computing contact stresses and deflection of bodies in point contact
• stress for two bodies in line contact with load normal to contact area and load normal and tangent to contact area
• gear contacts
• contacts between cam and follower
• ball bearing contacts

Unit 6 Experimental stress analysis

• Dimensional analysis
• analysis techniques
• strain gauges
• types of strain gauges
• characteristics of strain gauge measurement
• theory of photoelasticity
• elements of polariscope
• simple and circular polariscope
• fringes in dark and white field
• isoclinic and isochromatic fringe patterns
• evaluation of stresses from these fringe patterns ** 12