Worked engineering calculation examples
Each example is a complete calculation sheet. Open it, change any input, and every line, diagram and check below it works itself out again.
Buildings, foundations and connections
- Steel beam - flexure and shear (AISC 360-16): shear, moment and stress diagrams, flexure, shear and deflection checks.
- Reinforced concrete beam (ACI 318-19): flexure, minimum steel and stirrup shear.
- Pile cap punching shear (ACI 318-19): the size effect factor and all three limits.
- Spread footing: eccentric load, the kern check and the soil pressure under the footing.
- Bolt group (AISC J3): bolt shear, bearing and tearout at the end bolts.
- Lateral earth pressure on a pile: loose over dense sand, redrawn when a friction angle or layer changes.
- Welded girder section: area, neutral axis and moment of inertia read straight off a parametric drawing.
Structural analysis
- Pratt truss: reactions and every member force by joints and sections.
- Truss by the stiffness method: a short Python block solves the truss, checked by hand.
- Propped cantilever: reactions from compatibility, moments and the largest deflection.
Mechanical engineering
- Shaft in bending and torsion: torque from power and speed, von Mises stress and factor of safety.
- Pressure vessel shell (ASME VIII-1): hoop and longitudinal stress, required thickness and MAWP.