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VTU NOTES
Subject code
21CV33
Semester
III Sem

## Module - 1

Simple Stresses and Strains: Introduction, Properties of Materials, Stress, Strain, Hook’s law, Poisson’s Ratio, Stress – Strain Diagram for structural steel, Principles of superposition, Total elongation of tapering bars of circular and rectangular cross sections. Composite section, Volumetric strain, expression for volumetric strain, Elastic constants, relationship among elastic constants (No Numerical), Thermal stress and strains Compound stresses: Introduction, Stress components on inclined planes, General two- dimensional stress system, Principal planes and stresses, maximum shear stresses and their planes (shear planes). Compound stress using Mohr’s circle method.

## Module - 2

Bending moment and shear force diagrams in beams: Definition of shear force and bending moment, Sign convention, Relationship between loading, shear force and bending moment, Shear force and bending moment equations, development of Shear Force Diagram(SFD) and Bending Moment Diagram (BMD) with salient values for cantilever, simply supported and overhanging beams for point loads, UDL(Uniformly Distributed Load), UVL(Uniformly Varying Load) and Couple.

## Module - 3

Bending stress in beams: Introduction – Bending stress in beam, Pure bending, Assumptions in simple bending theory, derivation of Simple bending equation (Bernoulli’s equation), modulus of rupture, section modulus, Flexural rigidity, Problems Shear stress in beams: Derivation of Shear stress intensity equations, Derivation of Expressions of the shear stress intensity for rectangular, triangular and circular cross sections of the beams. Problems on calculation of the shear stress intensities at various critical levels of T, I and Hollow rectangular cross sections of the beam.

## Module - 4

Torsion: Twisting moment in shafts, simple torque theory, derivation of torsion equation, tensional rigidity, polar modulus, shear stress variation across solid circular and hollow circular sections, Problems Thin cylinders: Introduction: Longitudinal, circumferential (hoop) stress in thin cylinders. Expressions for longitudinal and circumferential stresses. Efficiency of longitudinal and circumferential joints. Problems on estimation of change in length, diameter and volume when the thin cylinder subjected to internal fluid pressure. Thick cylinders: Concept of Thick cylinders Lame’s equationsapplicable to thick cylinders with usual notations, calculation of longitudinal, circumferential and radial stresses – simple numerical examples. Sketching the variation of radial stress (pressure) and circumferential stress across the wall of thick cylinder

## Module - 5

Elastic stability of columns: Introduction – Short and long columns, Euler’s theory on columns, Effective length, slenderness ratio, radii of gyration, buckling load, Assumptions, derivations of Euler’s Buckling load for different boundary conditions, Limitations of Euler’s theory, Rankine’s formula and related problems. Deflection of determinate Beams: Introduction, Elastic curve –Derivation of differential equation of flexure, Sign convention, Slope and deflection using Macaulay’s method for statically determinate beams subjected to various vertical loads, moment, couple and their combinations. Numerical problems.