Mechanics of Materials – Basics

I would like to describe the process or logic or algorithm if you will in which must be followed in order to develop theories for mechanics of materials.  The process / logic / algorithm can go in either direction but you CANNOT skip steps. This idea is fact but was nicely presented in Dr. Madhukar Vable in his textbook Intermediate Mechanics of Materials.

Structural Analysis Algorithm (Logic)

1. Displacements
   • Kinematics
2. Strains
   • Material Models
3. Stresses
   • Static Equivalency
4. Internal Forces and Moments
   • Equilibrium / Energy Methods
5. External Forces and Moments

So, you may start with external forces then using equilibrium or energy methods you may determine the internal forces and moments. From here you may determine stresses by static equivalency. Then strains may be determined by the material model and finally displacements by use of kinematics. You may start at any step in the above algorithm and can proceed in any direction but you cannot skip a step. Meaning, if you know the internal forces and moments you can not determine the displacements with out considering the stresses and strains.