Worked engineering examples
Coursework-style problems, solved step by step in ProveCalc. Every number on these pages comes from its compute engine, with units checked on every line.
Structural engineering
ProveCalc for structural engineering →Simply supported beam: reactions, maximum moment and bending stress
Worked example: a 6 m W310×39 steel beam with a 12 kN/m uniform load and a 30 kN point load. Reactions, location of zero shear, maximum moment and bending stress checked against 0.6·Fy.
Cantilever beam: tip deflection under a point load
Worked example: tip deflection and fixed-end moment of a 2.5 m steel cantilever with a 5 kN point load, using δ = PL³/3EI with units checked.
Euler buckling load of a pinned column
Worked example: the Euler critical load of a 3 m pinned-pinned steel column, and its factor of safety against a 120 kN service load.
Mechanical engineering
ProveCalc for mechanical engineering →Simply supported beam: reactions, maximum moment and bending stress
Worked example: a 6 m W310×39 steel beam with a 12 kN/m uniform load and a 30 kN point load. Reactions, location of zero shear, maximum moment and bending stress checked against 0.6·Fy.
Cantilever beam: tip deflection under a point load
Worked example: tip deflection and fixed-end moment of a 2.5 m steel cantilever with a 5 kN point load, using δ = PL³/3EI with units checked.
Euler buckling load of a pinned column
Worked example: the Euler critical load of a 3 m pinned-pinned steel column, and its factor of safety against a 120 kN service load.
Solid shaft in torsion: torque, shear stress and angle of twist
Worked example: a 30 mm solid steel shaft transmitting 15 kW at 1450 rpm. Torque from power, polar moment, maximum shear stress τ = Tc/J and angle of twist.
Hydrostatic force on a vertical gate
Worked example: the resultant water force on a 3 m deep, 2 m wide vertical gate and where it acts, from the triangular pressure distribution.
Heat loss by conduction through a plane wall
Worked example: steady conduction through a 200 mm brick wall of 20 m² with a 25 K temperature difference, from Fourier's law, with the thermal resistance.
Aerospace engineering
ProveCalc for aerospace engineering →Euler buckling load of a pinned column
Worked example: the Euler critical load of a 3 m pinned-pinned steel column, and its factor of safety against a 120 kN service load.
Solid shaft in torsion: torque, shear stress and angle of twist
Worked example: a 30 mm solid steel shaft transmitting 15 kW at 1450 rpm. Torque from power, polar moment, maximum shear stress τ = Tc/J and angle of twist.
Lift coefficient needed at cruise
Worked example: the lift coefficient a 1200 kg light aircraft needs for level flight at 65 m/s at 3000 m, from L = ½ρV²S·CL.
Civil engineering
ProveCalc for civil engineering →Simply supported beam: reactions, maximum moment and bending stress
Worked example: a 6 m W310×39 steel beam with a 12 kN/m uniform load and a 30 kN point load. Reactions, location of zero shear, maximum moment and bending stress checked against 0.6·Fy.
Hydrostatic force on a vertical gate
Worked example: the resultant water force on a 3 m deep, 2 m wide vertical gate and where it acts, from the triangular pressure distribution.
Heat loss by conduction through a plane wall
Worked example: steady conduction through a 200 mm brick wall of 20 m² with a 25 K temperature difference, from Fourier's law, with the thermal resistance.
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