# BTech Engineering Bridging Unit (BEBU) in Mechanical Engineering (Statics and Mechanics of Materials)

### Objectives

• Draw a free body diagram and identify unknown reaction forces and moments.

• Solve statically determinate problems involving rigid bodies, pin-jointed structures and cables with and without friction.

• Understand the concepts of engineering stress, strain and linear elastic material behaviour.

• Determine stress and deformation of axial force members.

• Determine torque distributions, shear stress and angles of twist in torsional members.

• Determine bending moment and shear force distributions in laterally-loaded beams.

• Determine normal stresses and transverse deflections in beams.

### Description

• Introduction – Definitions; Vectors; Vectorial Law; Principle of Transmissibility; Scalar Product; Cross Product;

• Equilibrium of a Particle – Free Body Diagram. Moment and Equilibrium.

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

• 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

• Distributed Forces – Centre of Gravity of a 2-D Body, Distributed Loans on Beam

• Analysis of Truss – Simple Trusses, Analysis of Trusses by Method of Joint, Analysis of Truss by Method of Section.

• Friction – Dry Friction, Coefficients of Friction

• Introduction to Mechanics of Materials Deformable Bodies – Stress and Strain and Sign Convention; Linear Elastic Stress-Strain Relationships.

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

• 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.

• 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.

• 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.

• 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.

### Assessment Component

• Tests/Quizzes: 20%

• Others (e.g. Projects, assignments, homework, class participation): 20%

• Final Examination: 60%

02 October 2019