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BTech in 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.