JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives

This course is concerned with the development of analytical methods for solving

problems in mechanics of materials that are generally considered beyond the scope of basic course in the discipline.

Course outcomes: After completing this course, the student should be able to

• Determined the point of location of applied load to avoid twisting in thin sections used in aerospace applications.
• Understand the concept of distinguish between neutral and centroidal axes in curved beams.
• Understanding the analogy models developed for analyzing the non-circular bars subjected to torsion, and also analyzing the stresses developed between rolling bodies and stress in three dimensional bodies.

UNIT - I

Analysis of Stress: The State of Stress at a Point, Stress Components on an Arbitrary Plane, Principal Stresses, Stress Invariants, Mohr’s Circle, Planes of Maximum Shear, Octahedral Stresses, The Plane State of Stress, Differential Equations of Equilibrium, Boundary Conditions. Analysis of Strain: Deformation in the Neighborhood of a Point, The State of Strain at a Point, Interpretation of Shear Strain Components, Transformation of Strain, and Principal Strains, Compatibility Conditions. The Plane State of Strain. Linear Stress-Strain-Temperature Relations: Internal-Energy Density, and Complementary Internal- Energy Density. Hooke’s Law for Anisotropic, Orthotropic and Isotropic Elasticity. Equations of Thermo elasticity for Isotropic Materials

UNIT - II

Shear center: Bending axis and shear center-shear center for axi-symmetric and unsymmetrical sections. Shear Stresses in Thin-Walled Sections, Shear Center of Box Beams Unsymmetrical bending: Bending stresses in Beams subjected to Nonsymmetrical bending, Deflection of straight beams due to nonsymmetrical bending.

UNIT - III

Curved beam theory: Winkler Bach formula for circumferential stress – Limitations – Correction factors –Radial stress in curved beams – closed ring subjected to concentrated and uniform loads-stresses in chain links.

UNIT - IV

Torsion: Linear elastic solution, General Prismatic Bars–Solid Sections like circular, elliptical, triangular and rectangular, Prandtl elastic membrane (Soap-Film) Analogy; Narrow rectangular cross Section, Hollow thin wall torsion members, Multiply connected Cross Section.

UNIT - V

Contact stresses: Introduction, problem of determining contact stresses, Assumptions on which a solution for contact stresses is based; Expressions for principal stresses; Method of computing contact stresses, Deflection of bodies in point contact; Stresses for two bodies in contact over narrow rectangular area (Line contact) Loads normal to area, Stresses for two bodies in line contact, loads normal and Tangent to contact area.

TEXT BOOKS:

• 1. Advanced Mechanics of materials by Boresi & Sidebottom, Wiely International.
• 2. Advanced Mechanics of Solids by L S Srinath, Tata McGraw-Hill Publishing Company Limited

REFERENCE BOOKS:

• 1. Advanced strength of materials by Den Hortog J.P.
• 2. Theory of elasticity by Timoschenko S.P. and Goodier J.N. McGraw, Hill Publishers.
• 3. Advanced Mechanics of Materials and Applied Elasticity by Ansel C. Ugural, Saul K. Fenster
• 4. Strength of materials by Sadhu singh M. TECH. I Year I Sem. (ENGG. DESIGN)