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Course

Engineering Mechanics

Indian Institute of Technology Guwahati

Course modules:

  1. Basics of Statics:
    • Fundamental principles & concepts: Vector algebra, Newton’s laws, gravitation, force (external and internal, transmissibility), couple, moment (about point and about axis), Varignon’s theorem, resultant of concurrent and non-concurrent coplanar forces, static equilibrium, free body diagram, reactions.
    • Problem formulation concept; 2-D statics, two and three force members, alternate equilibrium equations, constraints and static determinacy; 3-D statics.
  2. Analysis of Structures - I (Trusses, Frames, Machines):
    • Trusses: Assumptions, rigid and non-rigid trusses; Simple truss (plane and space), analysis by method of joints.
    • Trusses (contd): Analysis of simple truss by method of sections; Compound truss (statically determinate, rigid, and completely constrained).
    • L5 Analysis of frames and machines.
  3. Analysis of Structures - II (Beams, Cables):
    • Internal forces; Beams: types of loading and supports; shear force, bending moment, and axial force diagrams.
    • Beams (contd): shear force and bending moment diagrams and equations relating them with external load.
    • Cables (coplanar): assumptions, parabolic and catenary cables.
  4. Friction - I:
    • Coulomb dry friction laws, simple surface contact problems, friction angles, types of problems, wedges.
    • Disk friction (thrust bearing); Belt friction (flat, V).
    • Square-threaded screw (self locking, screw jack).
  5. Friction - II:
    • Journal bearings (axle friction).
    • Wheel friction and rolling resistance.
  6. Center of Mass & Area Moments of Inertia:
    • First moment of mass and center of mass, centroids of lines, areas, volumes, composite bodies.
    • Area moments- and products- of inertia, radius of gyration, transfer of axes, composite areas.
    • Rotation of axes, principal area-moments-of-inertia, Mohr’s circle.
  7. Mass Moment of Inertia:
    • Second moment of mass, Mass moments- and products- of inertia, radius of gyration, transfer of axes, flat plates (relation between area- and mass- moments- and products- of inertia), composite bodies.
    • Rotation of axes, principal mass-moments-of-inertia.
  8. Virtual Work and Energy Method - I:
    • Virtual displacements, principle of virtual work for particle and ideal system of rigid bodies, degrees of freedom.
    • Active force diagram, systems with friction, mechanical efficiency.
  9. Virtual Work and Energy Method - II:
    • Conservative forces and potential energy (elastic and gravitational), energy equation for equilibrium.
    • Applications of energy method for equilibrium.
    • Stability of equilibrium.
  10. Review of particle dynamics:
    • Rectilinear motion; Plane curvilinear motion (rectangular, path, and polar coordinates).
    • 3-D curvilinear motion; Relative and constrained motion; Newton’s 2nd law (rectangular, path, and polar coordinates).
    • Work-kinetic energy, power, potential energy.
    • Impulse-momentum (linear, angular); Impact (Direct and oblique).
  11. Plane kinematics of rigid bodies - I:
    • Rotation; Parametric motion.
    • Relative velocity, instantaneous center of rotation.
    • Relative acceleration, rotating reference frames.
  12. Plane kinematics of rigid bodies - II:
    • Rotating reference frames, 3-part velocity and 5-part acceleration relations, Coriolis acceleration.
    • Applications of rotating reference frames.
  13. Plane kinetics of rigid bodies - I:
    • Kinetics of system of particles and derivation of moment equation.
    • Translation.
    • Fixed axis rotation; General planar motion.
    • General planar motion.
  14. Plane kinetics of rigid bodies - II:
    • Work – kinetic energy, potential energy.
    • Potential energy (contd.), power; Impulse-momentum.
    • Impulse-momentum (contd.), impact; Combination problems.
  15. Introduction to vibration:
    • Free vibration (damped, undamped)
    • Forced vibration (damped, undamped)
    • Mechanical displacement meter and accelerometer; Vibration of rigid bodies
    • Vibration of rigid bodies (contd.)
    • Energy methods for undamped problems.
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