Steel Beam Design: AISC 360-16

Choose Automatic in the section list, or the IPE, HEA and HEB family. Every size is run through the same checks with its own weight added and its own F_y, lightest first by mass per metre, and the first one whose every check is at or below 100% is the answer. The table under the result lists the lighter sizes that fail and the next ones that pass, and any of them can be taken with one press.

Braces are placed at every L_b you give from the left support, or at the supports only, or the flange is taken as continuously braced. Each unbraced segment is checked to AISC 360-16 §F2.2 with its own length and with C_b from Eq. F1-1 on that segment of the moment diagram of each load combination, so a point load, a cantilever or bracing at third points each get their own C_b. A cantilever whose free end is unbraced takes C_b = 1.0. L_p and L_r use the torsion constant J and the warping constant C_w of the section.

Because its flange is noncompact at that yield stress: b_f/2t_f of an HE 300 A is 10.7, above the limit 0.38√(E/F_y) = 9.1 of AISC 360-16 Table B4.1b. The nominal moment is then reduced by Eq. F3-1 below the plastic moment even when the beam is fully braced. IPE and HE B flanges are compact at the grades offered.

EN 10365 does not tabulate them, so they are the ArcelorMittal Orange Book values, I_T and I_w, for each size. Every value was cross-checked against I_w = I_z (h − t_f)²/4 and the torsion constant formula with the root-fillet term, and all agree within 1.1%.

The minimum yield strength of EN 10025-2 for the thickness of the flange: S355 is 355 MPa up to 16 mm and 345 MPa from 16 to 40 mm, S275 is 275 and 265 MPa, S235 is 235 and 225 MPa. So an HE 300 B, with a 19 mm flange, is checked at 345 MPa in S355. ASTM A36 is 250 MPa, and A572 Gr. 50 and A992 are 345 MPa at every thickness.

Yours: one under live load and one under dead plus live load, both at service level. They start at l/360 and l/240; IBC Table 1604.3 gives l/360 under live load for floor members, and for a cantilever l is taken as twice its length.

The engine reproduces the AISC Design Examples for a W18×50 (φ_bM_n = 379 kip-ft continuously braced, and C_b = 1.01, M_n = 4,060 kip-in. and φ_bM_n = 305 kip-ft braced at third points) and the φ_vV_n = 306 kips of a W24×62 in shear. Every step of your own beam, with its numbers and clause, is under "The calculation step by step" and in the printed report.