# BTech Engineering Preparatory Unit (BEPU) in Mechanical Engineering

### Syllabus

1. Introduction - Definitions; Vectors; Vectorial Law; Principle of Transmissibility; Scalar Product; Cross Product; Equilibrium of a Particle- Free Body Diagram. Moment and Equilibrium.

2. Moment of a Force - Moment of a Couple, Equilibrium of a Two-Force Body. Equilibrium of a Rigid Body in 2-D

3. Equilibrium of a Rigid Body- Statically Indeterminate System; Partial Constraints; Improper Constraints. Equilibrium of a Three-Force Body, Equilibrium of a Body in 3-D

4. Distributed Forces - Centre of Gravity of a 2-D Body, Distributed Loans on Beam

5. Analysis of Truss - Simple Trusses, Analysis of Trusses by Method of Joint, Analysis of Truss by Method of Section.

6. Friction - Dry Friction, Coefficients of Friction

7.  Deformable Bodies- Stress and Strain and Sign Convention; Linear Elastic Stress-Strain Relationships.

8. Axial Force Members- Solution of Axially-Loaded Structures; Statically Indeterminate Axially Loaded Structures.

9. Torsion of Cylindrical Shafts- Torque and Torsional Deformation (Relationships between Torque, Angle of Twist, Shear Stresses and Shear Strains); Solid and Hollow Shafts; Polar Second Moment of Area: Stepped Shafts; Torque Distribution; Composite Shafts.

10. Flexure (Bending) of Beams- Idealized Loads and Supports; Shear Force and Bending Moment Diagrams; Relationships between Load-Intensity, Shear Force and Bending Moment, Singularity Functions.

11. Normal Stresses in Beams Subjected to Bending Curvature- Longitudinal Strains; Normal Stresses; Neutral Axis; Flexural Formula; Second Moment of Area; Design of Beams for Bending.

12. Beam Deflection Induced by Bending- Equations for Deflection and Slope; Relationships between Deflection, Slope, Shear Force and Bending Moment; Macaulay's Method of Double Integration; Application to Determinate Beams.

02 October 2019