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Mechanics of Solids

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About This Course

Mechanics of solids is one of the foundation courses in the study of structural systems. The course provides the fundamental concepts of mechanics of deformable bodies and helps students to develop their analytical and problem solving skills. The course introduces students to the various internal effects induced in structural members as well as their deformations due to different types of loading. After this course students will be able to determine the stress, strain and deformation of loaded structural elements.

Module – 1 Review of statics, Concept of stress and strain – types, Stress – strain relation - Hooke’s law, Young’s modulus of elasticity. Stress-strain diagram of mild steel. Factor of safety, working stress. Axially loaded bars with uniform cross section–stress, strain and deformation. Deformation of axially loaded bars with varying cross section and bars with varying axial loads. Statically indeterminate systems (number of unknowns restricted to two). Module – 2 Temperature effects, temperature stress in composite bars. Shear stress and shear strain, Modulus of rigidity, simple shear, punching shear. Lateral strain, Poisson’s ratio, volumetric strain. Bulk modulus of elasticity, relationships between elastic constants. Strain energy – concept. Strain energy due to normal stress. Strain energy in bars carrying axial loads. Instantaneous stress in bars due to gradual, sudden and impact loads. Strain energy due to shear stress. Stresses in thin cylinders and spheres due to internal pressure. Module – 3 Beams – different types. Types of loading on beams. Concept of bending moment and shear force. Relationship between intensity of load, shear force and bending moment. Shear force and bending moment diagrams of cantilever beams, simply supported beams and overhanging beams for different type of loads. Point of contraflexure. Module – 4 Theory of simple bending, assumptions and limitations. Calculation of normal stress in beams, moment of resistance Shear stress in beams. Beams of uniform strength. Strain energy due to bending – calculation of strain energy in beams. Differential equation for calculating the deflection of beams. (Introduction and demonstration only. Students are not expected to solve deflection problems.) Module – 5 Stresses on inclined sections for uniaxial and biaxial stress fields. Principal stresses and principal planes in 2D problems, maximum shear stress. Strains along principal directions. Mohr’s circle of stress for 2D problems. Short columns – direct and bending stress. Kern of a section. Slender columns – Euler’s buckling load, slenderness ratio, limitation of Euler’s formula. Rankines formula. Torsion of circular and hollow circular shafts, Power transmitted by circular shafts and hollow circular shafts. Strain energy due to torsion. .

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EST100 Engineering Mechanics

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