Credits : 3

Prerequisites : GP110

Compulsory/Optional : Compulsory

Aim(s)
To introduce the fundamental concepts of mechanics of materials to provide basic approaches for analysis of various types of structural members subject to different loadings and their load combinations.
Intended Learning Outcomes
On successful completion of the course, the students should be able to; Identify different types of structural/machine components along with corresponding boundary conditions and loading. Apply the fundamental concepts of equilibrium, compatibility and constitutive relationships to analyse various elements subjected to external loads. Evaluate internal resultant forces, stresses, displacements and strains of such elements. Determine the state of stress and strain at a point under 2D plane stress conditions on any inclined plane and to determine the principal stresses and strains.
Course content/Course description
Introduction to mechanics of materials: Concepts of stress and strain in 1D, normal and shear components, stress-strain relations, material constants: Young’s modulus E, shear modulus G and Poisson’s ratio v; strain energy Basic sectional properties: First moment of area, centroid, centroidal axes, second moments of area, radii of gyration, section moduli and polar moment of area; transformation of axes for second moment of area Derivation of simple bending formula for a prismatic beam and estimation of direct stresses induced by bending Composite sections, transformed section approach. Calculation of deflection in statically determinate beams: Differential equation approach and moment-area theorems of Mohr; statically indeterminate beam analysis Estimation of shear stress variation in a beam section: Jourawski’s theory and Timoshenko beam theory; Shear flow and shear centre, compound beams, shear connectors Derivation of torsion formula for circular shaft. Transformation of 2D stress and strain: Equilibrium equations and concept of Mohr’s circle; Introduction to principal stresses, principal strains, maximum shear stress and strain, introduction to failure criteria. 2D stress-strain relationship for isotropic linear elastic materials: Relationship among Young’s modulus E, shear modulus G and Poisson’s ratio v, application of concept of 2D stress-strain Introduction to 3D stress-strain relationship for isotropic linear elastic materials: Bulk modulus K; relationship among Young’s modulus E, shear modulus G, bulk modulus K and Poisson’s ratio v Buckling of ideal struts.
Recommended Texts
Gere, JM, Goetsch, DE & Goodno, BJ 2010, Strength of Materials, 6th edn. Hibbler, RC 2011, Mechanics of Material’s 8th edn, Prentice Hall, London. Timoshenko, SP and Young DH 2011. Elements of Strength of Materials, 5th edn, East-West Press. Timoshenko, SP 2002, Strength of Materials Part 1 and 2, 3rd edn, CBS Publisher.