The Four Principles of Mechanics of Materials

Course subject(s) 2. Axial Loaded Members

All problems in Mechanics of Materials can be approached using the same basic four principles. These principles are:

  1. Free Body Diagram. If a part is separated or isolated from a body (ie: sectioned) or surroundings (ie: boundary conditions), appropriate reactions and/or internal forces must be added.
  2. Equilibrium of Forces. If a part or body is in equilibrium, all reactions and/or internal forces must also be in equilibrium.
  3. Displacement Compatibility. The nature of plausible deformation in a system imposes constraints on the geometry and/or deformation of structural elements in a given system (ie: two solid objects cannot occupy the same space, elements rigidly connected to each other must deform with each other).
  4. Stress-Strain (Force-Displacement) Relations. Loading and deformation in a structure are linked by material properties and structural geometry through Hooke’s Law

Be conscious of these four principles throughout the course. They will be ingrained in all of the derivations of formulas, analysis of new structural components, and solutions to problems examined throughout the course. They should become second-nature to you. Furthermore, demonstration of understanding and application of these four principles during the solution of problems (ie: in the exam!) is the primary means of assessment.

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