# 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.
• ##### Mod-1 Lec-1 Fundamentals Of Engineering Mechanics
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-1 Lec-2 Equations of Equilibrium
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-2 Lec-3 Truss Analysis Part-I
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-2 Lec-4 Truss Analysis Part-2
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-2 Lec-5 Analysis of Frames&Machines
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-3 Lec-6 Internal Forces
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-3 Lec-7 Internal Forces in Beams
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-3 Lec-8 Cables
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-4 Lec-9 Friction
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-4 Lec-10 Application of Friction Part-1
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-4 Lec-11 Application of Friction Part-2
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-5 Lec-12 Application of Friction Part-3
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-6 Lec-13 Centroids&Center of Mass
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-6 Lec-14 Centroids&Area of Moments
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-6 Lec-15 Product of Inertia, Rotation of Axis and Principle Moments of Inertia
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-7 Lec-16 Second Moment of Mass
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-7 Lec-17 Principle Mass Moments of Inertia
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-8 Lec-18 Virtual Work of Ideal System
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-8 Lec-19 Principle of Virtual Work
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-8 Lec-20 Systems with Friction
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-9 Lec-21 Potential Energy
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod- 9 Lec-22 Stability of Equilibrium
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-10 Lec-23 Kinematics of a Particles
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-10 Lec-24 Kinematics of a Particle Moving on a Curve
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-10 Lec-25 Relative Motion
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-10 Lec-26 Plane Kinematics of Rigid Bodies
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-11 Lec-27 Kinematics of a Particle
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-11 Lec-28 Work and Enjoy
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-11 Lec-29 Impulse and Momentum
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-11 Lec-30 Direct and Oblique Impulse
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-11 Lec-31 Plane Kinetics of Rigid Bodies
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-12 Lec-32 Kinetics of a Body
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-12 Lec-33 Method of Momentum and Analysis of Robot Manipulator
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-13 Lec-34 Kinematics in 3D
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-14 Lec-35 Kinetics in 3D
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-15 Lec-36 Free Vibration
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-15 Lec-37 Forced Vibration(Damped Undamped)
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-15 Lec-38 Vibration of Rigid Bodies Part-1
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-15 Lec-39 Vibration of Rigid Bodies Part-2
Prof. U.S. Dixit, Dr. G. Saravana Kumar
• ##### Mod-15 Lec-40 Some Problems of Vibration
Prof. U.S. Dixit, Dr. G. Saravana Kumar