Strength of Materials
Every design check in mechanics of solids compares a stress you calculated with a stress the material can take. These topics animate both halves: where the stress comes from, and where the limit comes from.
Start from the beginning →9 topics you can watch now, 12 still to come.
Stress and strain
The two quantities the rest of the subject is written in.
- Stress, Strain and the Tensile TestStart here. Load a specimen step by step and watch elastic, yield, hardening and necking arrive in order.
- Hooke's Law and the Elastic ConstantsFour constants, and only two of them are independent — plus the reason Poisson's ratio can never exceed a half.
- Thermal Stress and Composite BarsThe one place a large stress appears with no load at all. A 50 °C rise in a restrained steel bar produces 120 MPa, and the bar's length does not enter the formula.
- Strain energy and impact loading
- Bars of varying section in detail
Shear force and bending moment
Where along the beam the load is actually being carried.
- Overhanging and continuous beams
- Moving loads and influence lines
Bending and shear stresses
Turning a bending moment into a stress at a point.
- Shear stress distribution across a section
- Beams of composite section
- Plastic bending and the shape factor
Deflection of beams
Not breaking is not enough — it also has to stay put.
- Conjugate beam method
- Deflection of frames by strain energy
Torsion, columns and combined stress
Twisting, buckling, and the states in between.
- Torsion of Circular ShaftsThe bending argument, one dimension over — and the reason shafts are hollow, and the reason the formula works only for circles.
- Columns and BucklingThe one failure mode that is not about strength at all. Euler's formula contains no yield stress, which is why a stronger steel buys you nothing.
- Principal Stresses and Mohr's CircleStress at a point depends on the plane you ask about. One circle answers every plane at once — and then two failure theories disagree by fifteen per cent.
- Springs
- Thin and thick cylinders
- Rankine's formula and code column curves
About Strength of Materials
Strength of materials moves attention from whether a structure balances to whether the material inside it can take what balance requires. Statics gives forces; this subject converts those forces into stress at a point and asks whether the material will yield, buckle or break.
Stress and strain must be understood as point quantities before anything else works. Load is external and global; stress is internal and local, and it varies across a cross-section — which is precisely why a beam's shape matters as much as the amount of material in it.
Two results reward the effort most. Mohr's circle shows that the stress at a point depends on the plane you examine, so a component can be safe in one direction and failing in another. Buckling shows that a slender column fails by going sideways at a load well below its crushing strength — a geometric failure, not a material one.
What to know first
- Statics — equilibrium, free-body diagrams, reactions
- Comfort with a second moment of area
Where it gets used
- Choosing a beam section that meets both stress and deflection limits
- Understanding why slender columns are braced rather than merely thickened
- Reading a stress analysis and knowing which failure mode it addresses