JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-Requisites

Engineering Mechanics

Course Objectives

The objective of this Course is

• To understand the nature of stresses developed in simple geometries such as bars, cantilevers and beams for various types of simple loads.
• To calculate the elastic deformation occurring in simple members for different types of loading.
• To show the plane stress transformation with a particular coordinate system for different orientation of the plane.
• To know different failure theories adopted in designing of structural members.

Course Outcome

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

• Describe the concepts and principles, understand the theory of elasticity including strain/displacement and Hooke’s law relationships; and perform calculations, related to the strength of structured and mechanical components.
• Recognize various types loads applied on structural components of simple framing geometries and understand the nature of internal stresses that will develop within the components.
• To evaluate the strains and deformation that will result due to the elastic stresses developed within the materials for simple types of loading.
• Analyze various situations involving structural members subjected to plane stresses by application of Mohr’s circle of stress.

UNIT - I

Simple Stresses and Strains: Concept of stress and strain- St. Venant’s Principle-Stress and Strain Diagram - 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 – Pure shear and Complementary shear - Elastic modulii, Elastic constants and the relationship between them – Bars of varying section – composite bars – Temperature stresses. Strain Energy – Resilience – Gradual, sudden, and impact loadings – simple applications.

UNIT - II

Shear Force and Bending Moment: Types of beams – Concept of shear force and bending moment – S.F and B.M diagrams for cantilever, simply supported including overhanging beams subjected to point loads, uniformly distributed load, uniformly varying load, couple and combination of these loads – Point of contraflexure – 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- Section Modulus Determination of flexural/bending stresses of rectangular and circular sections (Solid and Hollow), I,T, Angle and Channel sections – Design of simple beam sections. Shear Stresses: Derivation of formula for shear stress distribution – Shear stress distribution across various beam sections like rectangular, circular, triangular, I, T angle and channel sections.

UNIT - IV

Deflection of Beams: 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 and couple -Mohr’s theorems – Moment area method – Application to simple cases.

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: Introduction – Stresses on an oblique plane 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 –Principal stresses – Mohr’s circle of stresses – ellipse of stress - 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 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 material by R.C. Hibbeler, Prentice Hall publications
• 2. Engineering Mechanics of Solids by Egor P. Popov, Prentice Hall publications
• 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. Strength of Materials by B.S.Basavarajaiah and P. Mahadevappa, 3rd Edition, Universities Presss