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SYLLABUS

UNIT-I

PRINCIPAL STRESSES AND STRAINS Introduction – Stresses on an inclined section of a bar under axial loading – Compound stresses – Normal and tangential stresses on an inclined plane for biaxial stresses – Two perpendicular normal stresses accompanied by a state of simple shear – Mohr’s circle of stresses – Principal stresses and strains – Analytical and graphical solutions. THEORIES OF FAILURES Various theories of failures like – Maximum principal stress theory – Maximum principal strain theory – Maximum shear stress theory – Maximum strain energy theory – Maximum shear strain energy theory.

UNIT-II

THIN CYLINDERS AND THICK CYLINDERS Thin seamless cylindrical shells – Derivation of formula for longitudinal and circumferential stresses – Hoop, longitudinal and Volumetric strains – Changes in dia, and volume of thin cylinders – Thin spherical shells. Introduction Lame’s theory for thick cylinders – Derivation of lame’s formulae – Distribution of hoop and radial stresses across thickness – Design of thick cylinders – Compound cylinders – Necessary difference of radii for shrinkage – Thick spherical shells.

UNIT-III

TORSION OF CIRCULAR SHAFTS Theory of pure torsion – Derivation of Torsion equations – Assumptions made in the theory of pure torsion – Torsional moment of resistance – Polar section modulus – Power transmitted by shafts – Combined bending and torsion and end thrust – Design of shafts according to theories of failure. SPRINGS Introduction – Types of springs – Deflection of close and open coiled helical springs under axial pull and axial couple – Springs in series and parallel – Carriage or leaf springs.

UNIT-IV

COLUMNS AND STRUTS Introduction – Types of columns – Short, medium and long columns – Axially loaded compression members – Crushing load – Euler’s theorem for long columns – Assumptions – Derivation of Euler’s critical load formulae for various end conditions – Equivalent length of a column – Slenderness ratio – Euler’s critical stress – Limitations of Euler’s theory – Rankine – Gordon formula – Long columns subjected to effentric loading – Secant formula – Empirical formulae – Straight line formula – Prof. Perry’s formula. 

UNIT-V

UNSYMETRICAL BENDING Introduction – Centroidal principal axes of section – Graphical method for locating principal axes – Moments of inertia referred to any set of rectangular axes – Stresses in beams subjected to unsymmetrical bending – Principal axes – Resolution of bending moment into two rectangular axes through the centroid - Location of neutral axis – Deflection of beams under unsymmetrical bending. BEAMS CURVED IN PLAN Introduction – Circular beams loaded uniformly and supported on symmetrically placed columns – Semicircular beam simply supported on three equally spaced supports