Course Objectives: The purpose of the course is to provide the students for basic knowledge in material behavior, stress-strain relations and their analysis. During the course, students will review on mechanics first and obtain knowledge in stress-strain relations, their types. At the end students will have basic concept on theory of flexure and column buckling.
Axial Forces, Shearing Forces and Bending Moments (8 hours)Plotting shearing force, bending moment and axial force diagrams for determinate structures (beams and frames)Concept of superposition for shear forces, bending moments and axial forces due to various combinations of loadsMaximum shear force and bending moments and their positionsRelationship between loads, shear forces, bending momentGeometrical Properties of Sections (7 hours)Axes of symmetryCentre of gravity of built-up plane figuresCentre of gravity of built-up standard steel sectionsMoment of inertia of standard and built-up sectionsPolar moment of inertiaRadius of gyrationProduct of inertiaPrinciple moment and principle axes of inertiaMoher’s circle for moment of inertiaSimple Stress and Strain (8 hours)Definitions: deformable Bodies, internal forces, stress, strain Analysis of Internal forcesSimple stress and strainHook’s law: axial and typical stress strain diagram for characteristics of mild steelPoisson’s ratioStress-strain diagramAxial stress and strainShear stress and strainShear deformation and shear angleHook’s law for shearing deformationsAllowable stresses and factor of safetyStress concentrationsRelationships between elastic constantsStress and Strain Analysis (6 hours)Stresses in inclined plane: normal and shear stressPrinciple stresses and principle planes Relationships between normal and shear stressMaximum shear stress and corresponding planeMohr’s circle for stressThin Walled Vessels (3 hours) Definition and characteristics of thin walled vesselsTypes of stresses in thin walled vesselsCalculation of stresses in thin walled vesselsTorsion (4 hours) Introduction and assumptionsDerivation of torsion formulasTorsional moments in shaftTorsional stress in shaftAngle of twistTheory of Flexure (5 hours)Coplanar and pure bendingElastic curveAngle of rotationRadius of curvature, flexural stiffnessSmall deflection theoryBending stressFlexural formula, differential equation of deflected shapeIntroduction to deflectionColumn Theory (4 hours)Theory of columns according to support systemsCritical loadLong column by Euler’s formulaLimitations of Euler’s formulaIntermediate columns; empirical formulasPractical:
Stress-Strain Curve in tensionTorsion test to determine modules of rigidityColumn behavior due to bucklingDeflection of simple beamTutorials:8 tutorials, 2 mini projects
References:
Timoshenko and Gere ‘Mechanics of Materials”, Beer F.P. and E.R. Johnston “Mechanics of Material”, E.P. Popov “Mechanics of Material”, , 2nd Edition, New Delhi, Prentice Hall of IndiaA.Pytel, F.L. Singer ‘Strength of Materials”, 4th Edition, Harper Collins, India, 1998Evaluation Scheme:The questions will cover all the chapters of the syllabus. The evaluation scheme will be as indicated in the table below:
ChaptersHours
Marks Distribution*
1
8
16
2
7
12
3
8
16
4
6
8
5
3
6
6
4
6
7
5
8
8
4
8
Total
45
80
*Note: There may be minor deviation in marks distribution.