Pre Requisites: Strength of Materials - I
Course Objectives:
Study of the subject provides the understanding of principal stress, strains, springs, columns, and structures.
Course Outcomes:
At the end of the course, the student will be able toÂ
-Determine stresses in the member subjected to TorsionÂ
-Analyze columns and struts
-Understand the concept of direct and bending stressesÂ
-Analyze and design springs, thin and thick cylindersÂ
-Understand the concept of unsymmetrical bending.
UNIT I
Torsion of Circular Shafts: Theory of pure torsion â?? Derivation of Torsion equations : T/J = q/r = Nθ/L Assumptions made in the theory of pure torsion â?? Torsional moment of resistance â?? Polar section modulus. Power transmitted by shafts . Combined bending and torsion and end thrust â?? Design of shafts according to theories of failure. Springs: Introduction â?? Types of springs â?? deflection of close and open coiled helical springs under axial pull and axial couple â?? springs in series and parallel â?? Carriage or leaf springs.
UNIT II
Columns and Struts: Introduction â?? Types of columns â?? Short, medium and long columns â?? Axially loaded compression members â?? Crushing load â?? Eulerâ??s theorem for long columnsassumptions- derivation of Eulerâ??s critical load formulae for various end conditions â?? Equivalent length of a column â?? slenderness ratio â?? Eulerâ??s critical stress â?? Limitations of Eulerâ??s theory â?? Rankine â?? Gordon formula â?? Long columns subjected to eccentric loading â?? Secant formula â?? Empirical formulae â?? Straight line formula â?? Prof. Perryâ??s formula. Beam Columns: Laterally loaded struts â?? subjected to uniformly distributed and concentrated loads â?? Maximum B.M. and stress due to transverse and lateral loading.
UNIT - III
Direct and Bending Stresses: Stresses under the combined action of direct loading and bending moment, core of a section â?? determination of stresses in the case of chimneys, retaining walls and dams â?? conditions for stability â?? stresses due to direct loading and bending moment about both axis.
Beams Curved In Plan: Introduction -circular beams loaded uniformly and supported on symmetrically placed Columns . Semi-circular beam simply-supported on three equally spaced supports.
UNIT IV
Thin Cylinders: Thin seamless cylindrical shells â?? Derivation of formula for longitudinal and circumferential stresses â?? hoop, longitudinal and Volumetric strains â?? changes in dia, and volume of thin cylinders â?? Thin spherical shells. Thick Cylinders: Introduction - Lameâ??s theory for thick cylinders â?? Derivation of Lameâ??s formulae â?? distribution of hoop and radial stresses across thickness â?? design of thick cylinders â?? compound cylinders â?? Necessary difference of radii for shrinkage â?? Thick spherical shells.
UNIT V
Unsymmetrical Bending: Introduction â?? Centroidal principal axes of section â?? Graphical method for locating principal axes â?? Moments of inertia referred to any set of rectangular axes â?? Stresses in beams subjected to unsymmetrical bending â?? Principal axes â?? Resolution of bending moment into two rectangular axes through the centroid â?? Location of neutral axis - Deflection of beams under unsymmetrical bending. Shear Centre: Introduction - Shear centre for symmetrical and unsymmetrical (channel, I, T and L) sections.
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