JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

Strength of Materials I & II

Course Objectives:

• 1. To define stresses, strains, equilibrium and compatibility
• 2. To derive the governing equilibrium equations in Two-dimensional & in three dimensional problems
• 3. To understand stress -strain relationships
• 4. To apply the concepts of elasticity & Plasticity to solve Structural Engineering problems

Course Outcomes

After completion of the course, students should be able to

• 1. Solve simple problems of elasticity and understanding the basic concepts
• 2. Apply numerical methods to solve continuum problems
• 3. Solve engineering problems such as thick cylinders, rotating discs
• 4. Solve engineering problems related to Torsion of shafts.

UNIT - I

Stress: Introduction to Elasticity – Definition of Kinetics and Kinematics - Notation for forces and stress - Components of stresses – Stress tensor - Differential equations of equilibrium in 2D & 3D in Cartesian coordinates and in polar coordinates - boundary conditions – Cauchy’s postulate – Stress transformation – Direction Cosines -Principal stresses – Stress invariants – Decomposition of stresses -Hydrostatic and Deviatoric stresses – Octahedral stresses – stress concentration factors

UNIT - II

Strain: Notation for strain - Components of strain – Strain tensor – Strain Components -Strain - displacement relations - Strain Compatibility Conditions - Strain transformation – Direction Cosines - Principal strains – Strain invariants - Octahedral strains – Strain Rosette

UNIT - III

Stress -Strain Relationship: Navier’s equation for stress-strain relationships – Relationship between Material constants – Stress - strain relations in 2D and 3D – Complementary conditions for shear - Material symmetry -Reduction of Material constants from anisotropic to orthotropic, monoclinic, isotropic and transversely isotropic – Plane stress, Plane strain and axi-symmetric idealizations - Mohr circle in 2D and 3D – Airy’s stress function – Potential function -

UNIT - IV

Solution of 2D and 3D elasticity problems: Problem solving using stress function approach: Beam bending problems – Symmetric stress distribution problems, Plane problems. Torsion problems in Elasticity – Membrane analogy approach – Application to non- circular thin walled sections

UNIT - V

Plasticity: Introduction to plasticity – Yield criteria for pressure dependent and independent materials - – Tresca’s criterion – Von mises criterion – Mohr-Coulomb criterion -Rankine criterion -Flow rule – Associative and Non-Associative-Hardening rules and consistency conditions -Introduction to iterative and return mapping.

REFERENCES:

• 1. Theory of Elasticity by Timeshenko, McGraw-Hill Publications
• 2. Theory of Elasticity by Y.C.Fung
• 3. Advanced Mechanics of solids by LS Srinath,
• 4. Elasticity and Plasticity for structural Engineers by Wang & Chen M. Tech in COMPUTER AIDED STRUCTURAL ENGINEERING I YEAR I – SEMESTER