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.
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.
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.
Disk friction (thrust bearing); Belt friction (flat, V).
Square-threaded screw (self locking, screw jack).
Friction - II:
Journal bearings (axle friction).
Wheel friction and rolling resistance.
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.
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.
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.
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.
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).
Plane kinematics of rigid bodies - I:
Rotation; Parametric motion.
Relative velocity, instantaneous center of rotation.
