JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-Requisites

Strength of Materials - I

Course Objectives

The objective of this Course is

• To understand the nature of stresses developed in simple geometries shafts, springs, columns &cylindrical and spherical shells for various types of simple loads.
• To calculate the stability and elastic deformation occurring in various simple geometries for different types of loading.
• To understand the unsymmetrical bending and shear center importance for equilibrium conditions in a structural member of having different axis of symmetry.

Course Outcome

On completion of the course, the student will be able to:

• Describe the concepts and principles, understand the theory of elasticity, and perform calculations, relative to the strength of structures and mechanical components in particular to torsion and direct compression.
• To evaluate the strains and deformation that will result due to the elastic stresses developed within the materials for simple types of loading.
• Analyze strength and stability of structural members subjected to Direct, and Direct and Bending stresses.
• Understand and evaluate the shear center and unsymmetrical bending.

UNIT - I

Torsion of Circular Shafts: Theory of pure torsion – Derivation of Torsion equation -Assumptions made in the theory of pure torsion – Polar section modulus – Power transmitted by shafts – Combined bending and torsion – 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.

UNIT - II

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– Long columns subjected to eccentric loading – Secant formula – Empirical formulae –– Rankine – Gordon formula- Straight line formula – Prof. Perry’s formula. BEAM COLUMNS: Laterally loaded struts – subjected to uniformly distributed and concentrated loads.

UNIT - III

Direct and Bending Stresses: Stresses under the combined action of direct loading and bending moment, core of a section – determination of stresses in the case of retaining walls, chimneys and dams – conditions for stability-Overturning and sliding – stresses due to direct loading and bending moment about both axis.

UNIT - IV

Thin Cylinders: Thin seamless cylindrical shells – Derivation of formula for longitudinal and circumferential stresses – hoop, longitudinal and Volumetric strains – changes in diameter, and volume of thin cylinders – Thin spherical shells. Thick Cylinders: 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.

UNIT - V

Unsymmetrical Bending: Introduction – Centroidal principal axes of section –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. Shear Centre: Introduction - Shear center for symmetrical and unsymmetrical (channel, I, T and L) sections.

TEXT BOOKS:

• 1. Strength of Materials by R.K Rajput, S. Chand & Company Ltd.
• 2. Mechanics of Materials by Dr. B. C Punmia, Dr. Ashok Kumar Jain and Dr. Arun Kumar Jain
• 3. Strength of Materials by R. Subramanian, Oxford University Press.

REFERENCE BOOKS:

• 1. Mechanics of Materials by R.C. Hibbeler, Pearson Education
• 2. Engineering Mechanics of Solids by Popov E.P. Prentice-Hall Ltd
• 3. Strength of Materials by T.D.Gunneswara Rao and M.Andal, Cambridge Publishers
• 4. Strength of Materials by R. K. Bansal, Lakshmi Publications House Pvt. Ltd.
• 5. Fundamentals of Solid Mechanics by M. L. Gambhir, PHI Learning Pvt. Ltd