Structural & Materials Calculator

Divide the applied force in newtons by the cross-sectional area in square meters. A 50 kN load on a steel bar with a 500 mm squared cross section produces a stress of 100 MPa. Structural steel (A36) has a yield strength of about 250 MPa, so this bar is loaded to 40% of its capacity - well within a typical safety factor of 1.67.

Maximum deflection equals P times L cubed divided by (48 times E times I). A 3-meter W150x13 steel beam (I = 6.83 million mm to the fourth, E = 200 GPa) under a 10 kN center load deflects about 4.1 mm. Building codes typically limit deflection to L/360, which for this span is 8.3 mm - so the beam passes.

Steel has a thermal expansion coefficient of about 12 times 10 to the minus 6 per degree C. A 10-meter steel beam heated by 40 degrees C expands roughly 4.8 mm. This is why bridges have expansion joints - a 100-meter highway bridge can grow by nearly 50 mm between winter and summer temperature extremes.

Moment of inertia (I) measures how a cross section's area is distributed relative to the bending axis. A solid rectangular section b times h has I = b times h cubed over 12. Doubling the height increases I by a factor of 8, which is why I-beams concentrate material at the top and bottom flanges - a W200x46 has an I-value of 45.5 million mm to the fourth despite using far less steel than a solid rectangle of the same depth.

Young's modulus (E) measures stiffness and yield strength measures the stress at which permanent deformation begins. Steel has E = 200 GPa and yield strength around 250-350 MPa. Aluminum has E = 69 GPa (about one-third as stiff) but with 6061-T6 alloy reaches 276 MPa yield - comparable strength at one-third the weight, which is why aircraft use aluminum extensively.