1.1 Engineering Mechanics – Statics
Free Body Diagrams – Equilibrium of forces, moments, couples; Lami's theorem; Varignon's theorem
Trusses – Method of joints, method of sections, zero-force members
Friction – Laws of dry friction, wedge friction, belt friction, ladder problems
Centroid & Moment of Inertia – First and second moment of area, composite sections, parallel axis theorem, polar moment of inertia, radius of gyration
Virtual Work – Principle of virtual work, applications to frames and mechanisms
1.2 Engineering Mechanics – Dynamics
Kinematics – Rectilinear and curvilinear motion, relative motion, projectile motion
Newton's Laws & Kinetics – Force-mass-acceleration method, D'Alembert's principle
Work-Energy Theorem – Work done by forces, kinetic energy, potential energy, conservation of energy
Impulse-Momentum – Linear impulse and momentum, conservation of momentum, impact of elastic and inelastic bodies, coefficient of restitution
1.3 Strength of Materials (Mechanics of Materials)
Stress & Strain – Normal, shear, bearing stress; Hooke's law; Poisson's ratio; stress-strain diagrams for mild steel, cast iron, aluminum; elastic constants (E, G, K) and their relationships
Axial Loading – Deformation in bars of varying cross-section, stepped bars, composite bars, thermal stresses, statically indeterminate systems
Shear Force & Bending Moment – SFD and BMD for cantilever, simply supported, overhanging beams; point loads, UDL, varying loads; relationship between load, shear, and moment
Bending Stresses – Flexure formula, neutral axis, section modulus, bending of composite/flitched beams, unsymmetrical bending
Shear Stresses in Beams – Shear stress distribution in rectangular, circular, I, T sections; shear flow
Torsion – Torsion of circular shafts (solid and hollow), power transmission, combined bending and torsion, equivalent torque and moment
Deflection of Beams – Double integration method, Macaulay's method, moment area method (Mohr's theorems), conjugate beam method, strain energy method
Columns & Struts – Euler's buckling theory, effective length, slenderness ratio, Rankine-Gordon formula, eccentrically loaded columns, secant formula, Johnson's parabolic formula
Principal Stresses – Mohr's circle for 2D stress, maximum shear stress, principal planes, combined loading problems
Theories of Failure – Maximum normal stress, maximum shear stress (Tresca), distortion energy (von Mises), maximum strain energy, Mohr-Coulomb; comparison and application
Strain Energy – Strain energy due to axial, bending, shear, torsional loads; Castigliano's theorem; impact loading; resilience and proof resilience
Thin & Thick Cylinders – Hoop and longitudinal stresses in thin cylinders and spheres; Lame's equations for thick cylinders; autofrettage