Strength of Materials - II
Definition: Strength of Materials - II extends analysis to advanced topics like curved beams, springs, thick cylinders, and unsymmetrical bending.
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Detailed Syllabus
Unit 1: Stress Tensors
- Introduction to Cartesian tensors
- Strains: Concept of strain
- derivation of small strain tensor and compatibility
- principal strain and directions
- strain invariants
- Stress: Derivation of Cauchy relations and differential equations of equilibrium and symmetry equations
- principal stresses and directions
- stress in variants
- Constitutive equations
- Generalized Hooke’s law
- stress - strain relations for Isotropic material
Unit 2: Theories of Elastic Failure
- Various theories of elastic failures with derivations and graphical representations
- applications to problems of 2-D & 3-D stress system with
- (i) Combined direct loading and bending
- (ii) combined torsional and direct loading
Unit 3: Energy Methods
- Definitions, expressions for strain energy stored in a body when load is applied
- (i) gradually
- (ii) suddenly
- (iii) with Impact
- strain energy of beams in bending, beam deflections
- strain energy of shafts in twisting
- energy methods in determining spring deflection
Unit 4: Columns and Struts
- Column under axial load
- concept of instability and buckling
- slenderness ratio
- derivation of Euler’s formulae for the elastic buckling load
- Rankine’s, Gordom’s and Johnson’s empirical formula for axial loading columns and their applications
- eccentric compression of a strut with rectangular & circular sections
Unit 5: Rotating Rings & Discs
- Stresses in uniform rotating rings & discs, rotating discs of uniform strength
- stresses in rotating cylinders, hollow cylinders & solids cylinders
Unit 6: Bending of Curved Bars
- Bending of beams with large initial curvature
- position of neutral axis for rectangular, trapezoidal and circular cross sections
- stresses in crane hooks
- stresses in circular rings subjected to tension or compression