Dr. B. N. Rao

Structural Engineering Division

Department of Civil Engineering

Indian Institute of Technology Madras

Chennai 600 036

bnrao@iitm.ac.in

THEORY OF ELASTICITY

1. BRIEF REVIEW OF THE THEORY OF ELASTICITY

In this course, we will assume quasi-static loads and deformation,

And no body forces (e.g., weights). Unless stated otherwise, we will

Also assume small-strain theory.

2. STRESS COMPONENTS AT A POINT

STRESS COMPONENTS AT A POINT (continued)

2 Equilibrium Equations

2 Equilibrium Equations (Continued)

2 Equilibrium Equations (Continued)

2 Equilibrium Equations (Continued)

3. STRAIN COMPONENTS AT A POINT

STRAIN COMPONENTS AT A POINT (continued)

STRAIN COMPONENTS AT A POINT (continued)

4. MATERIAL CONSTITUTIVE LAW (STRESS-STRAIN

RELATIONSHIP)

4.1 Generalized Hooks Law (Isotropic Material)

Generalized Hooks Law (continued)

5. COMPATABILITY CONDITIONS/EQUATIONS

COMPATABILITY CONDITIONS/EQUATIONS( continued)

6. FUNDAMENTAL PRINCIPLES IN THEORY OF

ELASTICITY

FUNDAMENTAL PRINCIPLES IN THEORY OF

ELASTICITY (continued)

7. TWO IMPORTANT STRESS STATES IN PLANE (2D)

ELASTICITY

7.1 Plane Stress

Plane Stress (continued)

7.2 Plane Strain

Plane Strain (continued)

7.3 Compatibility Condition in Stress

Compatibility Condition in Stress (continued)