Course 8 | Core
Mechanics of Materials
Connect loads to stress, strain, stiffness, deflection, failure, and safe sizing.
Course snapshot
- Purpose
- Mechanics of Materials turns external loads into internal stress, deformation, and failure checks.
- Prerequisites
- Next in the guided sequence
How to study this course
- Define the body and load path
- Cut the member if needed
- Choose the stress or deflection model
- Apply material behavior
- Check safety, stiffness, and units
How this course is designed
Original course map
This course uses an original MechCompass module order using prerequisite logic, standard engineering practice, and evidence tasks. Suggested references are optional and listed separately.
From internal force to stress
Every module follows the same chain: statics gives the internal force, geometry turns it into stress, the material law turns stress into strain, and integration turns strain into deflection.
Models before formulas
The habit is to draw the free body and the internal force first, then reach for σ = My/I or τ = Tr/J. Numbers and a factor of safety come after the load path is clear.
The 10 modules
01 | Module
Concept of Stress and Strain
Normal, shear, and bearing stress, strain, Hooke's law, and the factor of safety.
02 | Module
Axial Loading
Elongation δ = PL/AE, statically indeterminate members, and thermal stress.
03 | Module
Torsion
Shear stress τ = Tr/J, the angle of twist, and power-transmitting shafts.
04 | Module
Pure Bending
The flexure formula σ = My/I, the moment of inertia, and section modulus.
05 | Module
Beams: Shear and Moment Diagrams
Reactions and the V and M diagrams that locate the worst section.
06 | Module
Shear Stress in Beams
The τ = VQ/It distribution across a beam section.
07 | Module
Stress Transformation and Mohr's Circle
Principal stresses, maximum shear, and rotating the stress state.
08 | Module
Combined Loadings
Superposing axial, torsion, and bending, and thin-walled pressure vessels.
09 | Module
Deflection of Beams
Slopes and deflections by integration and superposition.
10 | Module
Columns and Buckling
Euler's critical load, slenderness, and end conditions.