Steel beam size calculator

Introduction

What size steel beam do you need? For a simply supported beam, find the largest bending moment, w L²/8 for a uniform load, and choose a section whose bending strength exceeds it. Then check shear at the supports and the deflection under live load. A 20 ft floor beam carrying 400 lb/ft of dead load and 800 lb/ft of live load needs a W14x22 in A992 steel: it uses 72 % of its bending strength and 75 % of the L/360 deflection allowance.

This calculator searches a table of standard rolled beams and returns the lightest one that passes all three checks, with the beam's own weight included. It offers US W-shapes designed to AISC 360 (LRFD or ASD) and European IPE beams designed to Eurocode 3. It is for engineers, builders and students making a first selection for a floor, roof or lintel beam.

Formulas

Moment and shear for a uniform load w and a point load P at midspan, span L:

M = w L² / 8 + P L / 4
V = w L / 2 + P / 2

Load combinations, with the self-weight in the dead load D (or G):

AISC LRFD:  w_u = max(1.2 D + 1.6 L, 1.4 D)
AISC ASD:   w_a = D + L
Eurocode:   w_Ed = 1.35 G + 1.5 Q

Bending strength of a compact, continuously braced section:

AISC 360 F2.1:     M_n = F_y Z_x,   LRFD φ_b M_n with φ_b = 0.90,   ASD M_n / Ω_b with Ω_b = 1.67
EN 1993-1-1 6.2.5: M_c,Rd = W_pl,y f_y / γ_M0,   γ_M0 = 1.0

Shear strength of the web:

AISC 360 G2.1:     V_n = 0.6 F_y d t_w C_v1,   φ_v = 1.00 and Ω_v = 1.50 when h/t_w ≤ 2.24 √(E/F_y)
EN 1993-1-1 6.2.6: V_pl,Rd = A_v (f_y / √3) / γ_M0

Live-load deflection, checked against L divided by the chosen limit:

δ = 5 w L⁴ / (384 E I) + P L³ / (48 E I)

• Z_x, W_pl,y — plastic section modulus; I — moment of inertia about the strong axis
• F_y, f_y — yield strength: 50 ksi (A992), 36 ksi (A36), 235, 275 or 355 MPa
• E — 29 000 ksi for AISC, 210 000 MPa for Eurocode 3
• A_v — shear area of the IPE from the catalogue; d t_w — web area of the W-shape

Assumptions and limitations

• The compression flange must be braced along its length, for example by a floor deck fixed to it. An unbraced beam can fail by lateral-torsional buckling at a much lower load, and this page does not check it.
• Only compact sections are used. A W-shape whose flange is not compact at the chosen grade, such as W8x10 in A992 steel, is skipped rather than checked for local buckling.
• Web bearing and crippling at the supports, floor vibration, fire resistance and the connections are not checked.
• Only the live-load deflection is checked. The total deflection is shown, and long spans may need a precamber.
• The table holds the light and medium W6 to W24 shapes and IPE 80 to IPE 600. Section properties come from the AISC Shapes Database v16.0 and the ArcelorMittal catalogue.

Worked example

A floor beam spans 20 ft between girders. It carries 400 lb/ft of dead load and 800 lb/ft of live load. Use A992 steel, LRFD and a live-load deflection limit of L/360.

1. The deflection limit needs I ≥ 5 × 800 × 20⁴ × 1 728 / (384 × 29 000 000 × 240/360) = 149 in⁴, so W12x19 (130 in⁴) is too flexible.
2. Try W14x22, which weighs 22 lb/ft: w_u = 1.2 × (400 + 22) + 1.6 × 800 = 1 786.4 lb/ft.
3. Design moment: M_u = 1 786.4 × 20² / 8 = 89 320 lbf·ft.
4. Bending strength: φM_n = 0.9 × 50 × 33.2 / 12 = 124.5 kip·ft, or 124 500 lbf·ft. Utilisation 72 %.
5. Shear: V_u = 17.9 kip against φV_n = 0.6 × 50 × 13.7 × 0.23 = 94.5 kip. Utilisation 19 %.
6. Live-load deflection: 0.50 in against 20 × 12 / 360 = 0.67 in. Utilisation 75 %, which governs.

W12x22 weighs the same and also works. The calculator prefers W14x22 because it has the larger plastic modulus.

FAQ

Related calculators

• Beam deflection and bending stress — other supports and load cases.
• Moment of inertia calculator — properties of built-up sections.
• Column buckling calculator — the columns that carry the beam.
• Metal weight calculator — the weight of the steel to order.