JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Overview

Course Pre-Requisites: Engineering Mechanics

Course Objectives

The objectives of this course are to:

• 1. Understand the concepts of internal forces, moments, stress, strain, and deformation of solids with applications to bars, beams, and columns.
• 2. Learn the fundamentals of applying equilibrium, compatibility, and force-deformation relationships to structural elements.
• 3. Study twisting of circular bars and hollow shafts acted on by torsional moments.
• 4. Define the state of stress at a point on a body and to develop stress transformations.
• 5. Introduce the concept of theories of elastic failure and their significance in the design.

Course Outcomes

At the end of the course, students will be able to:

• 1. Evaluate the internal forces, moments, stresses, strains, and deformations in structures made of various materials acted on by a variety of loads.
• 2. Draw axial force, shear force and bending moment diagrams for beams and frames.
• 3. Develop the Bending and Torsion formula and apply to the design of beams and shafts.
• 4. Use the stress transformation equations to find the state of stress at a point for various rotated positions of the stress element and display the same in graphical form as Mohr’s circle.
• 5. Understand the different criteria for the safety of the component by applying the theories of elastic failure.

UNIT - I

Simple Stresses & Strains: Elasticity and plasticity – Types of stresses & strains–Hooke’s law– stress – strain diagram for mild steel – Working stress – Factor of safety – Lateral strain, Poisson’s ratio & volumetric strain – Elastic moduli & the relationship between them – Bars of varying section – composite bars – Temperature stresses. Strain energy – Resilience – Gradual, sudden, impact and shock loadings.

UNIT - II

Shear Force and Bending Moment: Definition of beam – Types of beams – Concept of shear force and bending moment – S.F and B.M diagrams for cantilever, simply supported and overhanging beams subjected to point loads, u.d.l., uniformly varying loads and combination of these loads – Point of contra flexure – Relation between S.F., B.M and rate of loading at a section of a beam.

UNIT - III

Flexural Stresses: Theory of simple bending – Assumptions – Derivation of bending equation: M/I = f/y = E/R Neutral axis – Determination bending stresses – section modulus of rectangular and circular sections (Solid and Hollow), I,T, Angle and Channel sections – Design of simple beam sections. Shear Stresses: Derivation of formula – Shear stress distribution across various beams sections like rectangular, circular, triangular, I, T angle sections.

UNIT - IV

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 Failure: Introduction – Various theories of failure - Maximum Principal Stress Theory, Maximum Principal Strain Theory, Strain Energy and Shear Strain Energy Theory (Von Mises Theory).

UNIT - V

Torsion of Circular Shafts: Theory of pure torsion – Derivation of Torsion equations: T/J = q/r = Nθ/L – 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.

Columns and Struts: Euler’s Theory, Limitations of Euler’s theory, Equivalent Length, Rankine’s Formula, Secant Formula.

TEXT BOOKS:

• 1. Barry J. Goodno and James M. Gere, “Mechanics of Materials” Ninth Edition, Cengage Learning,2018.
• 2. S. S. Rattan, “Strength of Materials”, Second Edition Tata McGraw Hill Education Pvt. Ltd, New Delhi,2011

REFERENCE BOOKS:

• 1. U. C. Jindal, “Strength of Materials”, Pearson Education India,2012
• 2. Egor P. Popov, Toader A. Balan, “Engineering Mechanics of Solids”, PHI Learning, 2010
• 3. G. H. Ryder, “Strength of Materials”, Macmillan Long Man Publications, 1961
• 4. W. A. Nash and M. C. Potter, “Strength of Materials”, Fifth Edition, Schaum’s Outline Series, 2011