JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre Requisites

Engineer Mechanics

Course Objectives

The subject provide the knowledge of simple stress strains flexural

stresses in members, shear stresses and deflection in beams so that the concepts can be applied to the Engineering problems.

Course Outcomes

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

• Analyze the statically determinate and indeterminate problems.
• Determine the stresses and strains in the members subjected to axial, bending.
• Evaluate the slope and deflection of beams subjected to loads.
• Determine the principal stresses and strains in structural members.

UNIT - I

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

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, uniformly distributed load, 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 of 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 beam sections like rectangular, circular, triangular, I, T angle sections.

UNIT - IV

Deflection of Beams: Bending into a circular arc – slope, deflection and radius of curvature – Differential equation for the elastic line of a beam – Double integration and Macaulay’s methods – Determination of slope and deflection for cantilever and simply supported beams subjected to point loads, U.D.L, Uniformly varying load-Mohr’s theorems – Moment area method – application to simple cases including overhanging beams. Conjugate Beam Method: Introduction – Concept of conjugate beam method. Difference between a real beam and a conjugate beam. Deflections of determinate beams with constant and different moments of inertia.

UNIT - V

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, Maximum shear stress theory- Strain Energy and Shear Strain Energy Theory (Von Mises Theory).

TEXT BOOKS:

• 1. Strength of Materials by R. K. Bansal, Lakshmi Publications House Pvt. Ltd.
• 2. Strength of Materials by R. Subramanian, Oxford University Press.
• 3. Strength of Materials by W.A Nash, MC Graw Hills 2014 6th edition.
• 4. Mechanics of Materials by James M Gere and Barry J Goodno Cengage Learning India Pvt. Ltd Eight edition.

REFERENCES:

• 1. Strength of Materials by S. S. Bhavikatti, Vikas Publishing House Pvt. Ltd.
• 2. Mechanics of Structures Vol –I by H. J. Shah and S. B. Junnarkar, Charotar Publishing House Pvt. Ltd.
• 3. Strength of Materials by S. S. Rattan, McGraw Hill Education Pvt. Ltd.
• 4. Fundamentals of Solid Mechanics by M. L. Gambhir, PHI Learning Pvt. Ltd.
• 5. Strength of Materials and Structures by John Case et al., Butterworth-Heinemann.
• 6. Strength of Materials by Dr.Sadhu Singh Khanna Publishers 11th edition 2015.