Structural logic, then the stop
These tools share one rule: the figure is the statics or the section property you asked for. It is not a utilisation ratio.
Logic
Direct stress is force divided by area. 100 kN on 2,000 mm² is 50 N/mm². That assumes the force is axial and the area is the area that carries it. A hole, a bending moment or a buckle breaks the assumption. Use direct stress.
Modulus is stress divided by strain. 2 mm extension on a 2,000 mm bar is strain 0.001. At 200 N/mm² the modulus is 200 kN/mm². That is linear elastic. Past yield it is the wrong model. Use Young's modulus.
A rectangle uses I = bd³/12 and Z = bd²/6, about the axis parallel to the breadth. A 100 mm by 200 mm rectangle is I 66.7×10⁶ mm⁴ and Z 6.67×10⁵ mm³. A solid circle uses I = πd⁴/64. A 100 mm circle is I 4.91×10⁶ mm⁴. Neither is a steel-table section. Use the rectangle and the circle.
Simply supported deflection under a uniform load is 5wL⁴/384EI. The worked beam, 8 kN/m on 6 m with E 210 kN/mm² and I 0.0001 m⁴, deflects 6.43 mm. Reactions for that same beam are 24 kN and the moment is 36 kN·m. The moment is not a section size. Use deflection and reactions.
Pinned-pinned Euler load is π²EI/L². E 210 kN/mm², I 1×10⁻⁵ m⁴, length 3 m, is 2,303 kN. Effective length, imperfections and a buckling curve are not in that equation. Use Euler load only as that bound.
Two perpendicular components combine as the square root of the sum of squares. 3 and 4 give 5 at 53.13°. Use resultant force.
A utilisation is a later step
The structural pages stop at the statics or the section property. A 50 N/mm² axial stress is not a utilisation until a resistance is named. A 6.43 mm deflection is not a span/250 pass until someone applies that limit. A 2,303 kN Euler load is not a design resistance until a buckling curve is applied.
Write the input set beside the result. The worked beam is 8 kN/m, 6 m, E 210 kN/mm², I 0.0001 m⁴. Without those, 6.43 mm cannot be reviewed.
Last checked 3 October 2026. The logic is the textbook relationship named above. It is not a code check. See standards these tools do not replace.