Deformable bodies, external forces, internal stresses and strains
Types of stresses: Normal stress, shear stress, bearing stress
Material behavior under axial loading: Stress-strain diagram for mild steel, yield stress, proportional limit, elastic limit, Hooke's law, Young's modulus of elasticity, strain hardening, ultimate stress/strength, ductility, toughness, elastic and inelastic strains, concept of factor of safety and allowable/permissible stress
Stress-strain behavior for ductile and brittle materials, proof stress
Fatigue and creep strength
Thermal stress and strain in simple, compound, composite and indeterminate bars
Lateral strains and Poisson's ratio
Shear deformation and shear angle; Hooke's law for shearing deformations, modulus of rigidity
Multi-axial loading and generalized Hooke's law
Definitions of isotropic, anisotropic and orthotropic materials
Volumetric stress-strain, bulk modulus
Relationships between elastic constants
Saint-Venant's principle and stress concentrations
Elongation of bars under axial loadings: Uniform and varying cross sections, tapered sections, compound and composite bars
Use of compatibility equations for axially loaded indeterminate bars
Geometric Properties of Sections (5 hours)
Axes of symmetry
Centre of gravity of plane and built-up sections
Moment of inertia of standard and built-up sections
Parallel and perpendicular axis theorems
Polar moment of inertia
Radius of gyration
Product moment of inertia
Principal axes and principal moment of inertia
Mohr's circle for principal moment of inertia
Principal Stress Analysis in 2D Planes (5 hours)
Stresses in inclined plane: Normal stress under uniaxial loading, Normal and shear stress subjected to two mutually perpendicular planes
Principal planes and principal stresses
Relationships between normal and shear stresses
Maximum shear stresses
Mohr's circle diagram for principal stresses
Principal Strain Analysis (4 hours)
Plane strain: Normal and shear strains in inclined planes
Principal strains, maximum in-plane shear strains and their positions
Mohr's circle diagram for plane strain
Absolute maximum shear strain
Strain rosettes
Modes of failure for different materials
Introduction of failure theories
Thin Walled Vessels (3 hours)
Introduction and characteristics
Types of stresses and strains in cylindrical and spherical pressure vessels
Calculation of stresses and strains in pressure vessels
Torsion (5 hours)
Introduction to torsion
Stress-strain behavior in torsion
Derivation of torsion formula for a circular shaft
Torsional moments: Series and parallel combination of shafts and composite shaft
Torsional stress in shafts, torsional resilience
Comparison between solid and hollow shafts
Power transmitted by shafts
Statically indeterminate shafts
Introduction to non-circular shafts
Combined bending and torsion
Theory of Flexure (8 hours)
Introduction to flexure
Coplanar and pure bending
Derivation of bending equation
Distribution of bending stress across the different beam cross-sections
Analysis of beams for symmetric and composite sections
Shear equation, shear stress variation in rectangular, circular, I and T sections
Concept of slope and deflection in beams using double integration method: Simply supported and cantilever beams
Column Theory (5 hours)
Introduction: Buckling and stability of columns
Classification based on slenderness ratio
Effect of support conditions and effective length
Derivation of Euler's formula for different end conditions, limitations and applicability
Intermediate columns: Rankine's hypothesis
Introduction to uniaxial and biaxial eccentric loading, condition for no tension
Practicals
Tensile test and stress-strain curve for mild steel bar, HYSD bar, timber
CG of simple plane figure
Simple bending test on timber, steel, aluminum beams: Deflection, flexural relations and MoI comparisons
Torsion test on simple shaft to determine modulus of rigidity
