Section outline

  • I. STATICS:

       Force Systems

    • Introduction to Engineering Mechanics
    • Principles of Mechanics
    • Characteristics of a force
    • Types of forces
    • Moment of a force

       Equilibrium of a particle

    • Equilibrium of a particle
    • Equilibrium of a particle in two and three dimensions
    • Equilibrium of a rigid body
    • Equations of equilibrium or conditions of equilibrium
    • Lami’s theorem

      Plane truss analysis

    • Type of supports and reaction
    • Static determinacy
    • Plane trusses
    • Solution of plane trusses with method of joints and method of sections
    • Frames and machines

      Properties of areas

    • Centroid or centre of gravity
    • First moment of area or statical moment of area
    • Second moment of area or moment of inertia
    • Polar moment of inertia (perpendicular axis theorem)
    • Parallel axis theorem
    • Section modulus
    • Radius of gyration

      Friction

    • Theory of friction.
    • Types of friction
    • Applications of friction

     

    II. DYNAMICS:

    • Kinematics: Rectilinear and curvilinear motion of particle.
    • Kinetics: Equation of motion, angular momentum, work and energy, and impulse and momentum.

     

    III. STRENGTH OF MATERIALS:

    • Mechanical properties of materials: introduction, various definition, properties of materials, behaviour of ductile and brittle materials.
    • Simple stresses and strains: introduction, simple stresses, types of stresses, simple strains, types of strains, stress-strain diagram, thermal stresses, thermal stresses in bars of varying section, and thermal stresses in composite bars. Numerical problems.
    • Elastic constant: types, modulus of elasticity, Hooke’s law, modulus of rigidity (shear modulus), bulk modulus, Poisson’s ratio,  relationship between three moduli, derivation of various formulae, typical elastic constant for different engineering materials, load and stress limit,  allowable load/allowable stress, and selection of factor of safety. Numerical problems.
    • Strain energy: introduction, strain energy due to gradually applied load, strain energy due to suddenly applied load, and strain energy due to shear stress. Numerical problems.
    • Compound stresses and strains: state of stress at a point (general 2D system), principal planes and principal stresses, biaxial direct stress, uniaxial direct stress, case of pure shear stress, Mohr’s cycle for stresses, construction of Mohr’s cycle, and principal strains and strain energy due to principal stresses. Numerical problems.
    • Equilibrium of beams-Shear force (SF) and bending moment (BM): introduction, types of loading, types of beams, shear force and bending moment diagrams, sign convention for shear force and bending moment, important points for drawing shear force (SF) and bending moment (BM) diagrams, methods for constructing shear force and bending moment diagrams, shear force (SF) and bending moment (BM) diagrams for various types of beams with different loading conditions, numerical examples, relationships between load, shear force and bending moment.
    • Bending and shear stresses in beams: introduction, theory of simple bending with assumptions made, theory of simple bending, expression for bending stress, moment of resistance, bending stresses in symmetrical sections, section modulus, bending stresses in unsymmetrical sections, shear stresses, shear stress formula. Numerical problems.
    • Combined direct and bending stresses: introduction, resultant stress when a column of rectangular section is subjected to an eccentric load, stress distribution due to the position of the applied load, and resultant stress when a column of rectangular section is subjected to a load which is eccentric on both axes. Numerical problems.
    • Deflection of beams: introduction, relationships between loading, shear force (SF), bending moment (BM), slope and deflection of beam, methods for deflection of beams, and formulae for slope and deflection of beams. Numerical problems.
    • Torsion: introduction, pure torsion, polar moment of inertia, torsion rigidity, power transmitted by a shaft, and composite shafts. Numerical problems.