Steel Beam Check Calculator to DBN: Bending, Shear, Stability, Deflection

Beam check calculator

Choose the I-beam and the steel grade, then enter the span, the design load q for strength, the characteristic load qn for deflection and how the load is applied. The result updates at once and no data is sent anywhere.

Example: I-beam No. 20, 6 m span

Take the conditions from the article on steel beam design: I-beam No. 20 of S255 steel (flange 8.4 mm, Ry = 250 N/mm², Ryn = 255 N/mm²), span 6 m, q = 6.2 kN/m, qn = 5.0 kN/m, γn = 1.05 for strength and 0.975 for deflection, γc = 1.0, limit deflection l/200.

Strength is satisfied: bending is used at 64 %, shear at 15 %. Deflection f·γn = 21.7 mm against an allowable 30 mm, that is 72 %. Lateral-torsional stability depends on how the load is applied:

What the calculator computes

The order is the same as in the article, and every step carries its DBN clause number:

• forces for a simply supported beam: M = q·l² / 8, Q = q·l / 2;
• design strengths from Table G.2: Ry and Ryn, for rolled sections by flange thickness; shear strength Rs = 0.58·Ryn / γm, γm = 1.025 (Tables 7.1 and 7.2);
• bending strength by formula (9.1): M·γn / (Wx·Ry·γc) ≤ 1, a class 1 section, Wn,min = Wx;
• shear strength by formula (9.2): Q·Sx·γn / (Ix·tw·Rs·γc) ≤ 1;
• lateral-torsional stability: either a continuous rigid deck (cl. 9.4.4, a) or a relative slenderness of the compression flange λ̄b = (lef / bf)·√(Ryf / E) not above the limit λ̄ub of Table 9.1: formula (9.30) for a load on the top flange, (9.31) on the bottom flange, (9.32) for a length between braces;
• deflection f = 5·qn·l⁴ / (384·E·Ix), E = 2.06·10⁵ N/mm², condition f·γn ≤ fu = l / n; you set n from Table 1 of DSTU B V.1.2-3:2006.

If bf/tf is below 15, the formulas of Table 9.1 use 15 (Note 2). If the condition of cl. 9.4.4, b is not met, the calculator does not compute the factor φb from Annex N: it only reports that the compression flange must be braced or the check to formula (9.28) made.

For an own section Ry and Ryn are taken for plate; if the steel is different, enter them by hand. The values of γn for the first and second limit-state groups are set by the designer: the example uses CC2, category B, that is 1.05 and 0.975.

What the calculator does not check

• local stresses in the web under a concentrated load or over a support (cl. 9.2.2);
• local stability of the web and flanges (cl. 9.5);
• the factor φb and the check to formula (9.28) from Annex N;
• class 2 sections with plastic deformation (formula 9.10) and weakening by bolt holes;
• non-uniform and concentrated loads, continuous beams and cantilevers, and the self-weight of the beam (include it in q and qn);
• joints, bearing stiffeners and connections.

So a “satisfied” answer only means that these separate checks are met. The full calculation to the codes in force is made by the project designer.

Codes and their validity

The formulas and the order of the check come from the article on steel beam design. The sources are DBN V.2.6-198:2014 (in force; edition with Amendment No. 1): cl. 9.2.1, 9.4.2, 9.4.4 and Tables 5.1, 7.1, 7.2, 9.1 and G.2; for the factor γn, DBN V.1.2-14:2018, Table 5; for deflection, DSTU B V.1.2-3:2006.

The numbers in the calculator are given for information, and the current edition of the codes should be checked before use in a project. The consequence class, the loads, γn and γc for a real project are set by the designer.

What comes next: I-beam geometry and the column

For the geometry of other I-beams, channels and tubes see the steel section handbook and the tables of I-beam sizes. To estimate the mass of the chosen section use the metal weight calculator, and a column in compression is checked with the steel column calculator.

What to send for agreement

We fabricate steel structures and prepare KM and KMD drawings: see KM and KMD design and steel fabrication. The beam calculation is done by the project designer, and we work from the results. Send a drawing or a sketch of the beam with its span, loads and support conditions, and we will discuss the task.