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Beam section selection online: I-beam, channel, round, timber by strength and deflection

Set the beam layout and loads (or enter M_max and Q_max directly), pick a material and a section type. The calculator finds the smallest I-beam to GOST 8239-89, channel to GOST 8240-97 or the size of a round bar, tube, rectangle or timber, checks strength by sigma and tau and stiffness by deflection, and shows the margins, the diagrams, the elastic line and a step-by-step solution. Free, no sign-up.

Loads
Section
Standard I-beams No. 10-60 to GOST 8239-89 are tried in order; bending in the plane of the web.
Material
Loads are entered as characteristic values: for strength they are multiplied by gamma_f (usually 1.1-1.4 for dead and live loads), deflection uses the characteristic loads. R and Rs are design strengths of steel (Ry, Rs = 0.58 Ry) or timber; the values are for reference and for steel depend on the plate thickness, check them against SP 16.13330. If your loads are already design values, set gamma_f = 1.
Allowable deflection f ≤ l / n
Calculate

How to select a beam section

Section selection is the second half of a beam bending calculation after the shear and moment diagrams. You look for the smallest profile that satisfies three conditions.

  1. Strength in normal stress. sigma = M / W ≤ R. It gives the required section modulus W_req = M_max / R, and you take the nearest profile with a W not smaller.
  2. Strength in shear stress. tau = Q·S / (I·b) ≤ R_s, where S is the first moment of the cut-off part and b is the width of the section at the neutral axis (the web thickness for an I-beam or a channel). For rolled profiles on long spans the margin in tau is large; the condition decides for short, heavily loaded beams.
  3. Stiffness. The largest deflection f must not exceed the limit f_u = l / n. The calculator integrates the curvature EI·y″ = M(x) segment by segment and gets the exact deflection for any load; formulas such as 5qL⁴/(384EI) and PL³/(48EI) are special cases and are used in the tests.

Strength or stiffness: which governs

For long spans and floors deflection almost always governs: a profile chosen by W fails the stiffness check, and a larger number is needed. The calculator shows both intermediate results, by W and by I, and the final profile after all checks.

Deflection limit

The value of n depends on the purpose of the structure: for floors and roof beams usually from L/200 to L/250 depending on the span, stricter for structures with finishes and glazing (L/300 and more). Exact values are in the deflection-limit table of SP 20.13330 (check the current edition). For a cantilever the design length l is twice the overhang.

Method and factors

The limit-states mode is simplified after SP 16.13330 (steel) and SP 64.13330 (timber): elastic behaviour (no plastic factor c1), loads multiplied by the load factor gamma_f, design strength multiplied by the working-conditions factor gamma_c. Deflection uses characteristic loads. The allowable-stress mode is for coursework: sigma ≤ [sigma], tau ≤ [tau], no factors. Reference values: steel St3 (C235) Ry = 230 MPa, C245 and C255 240 MPa, Rs = 0.58 Ry, E = 206 000 MPa; pine grades 1, 2, 3 bending 14, 13 and 8.5 MPa, shear 1.8, 1.6 and 1.6 MPa, E = 10 000 MPa. These numbers depend on the plate thickness, moisture, importance class and edition of the codes, so for a real project check the codes and enter your own values.

Catalogue sources

Profile properties h, b, s, t, A, I_x, W_x, S_x and mass per metre are taken from GOST 8239-89 (hot-rolled steel I-beams, standard I-beams No. 10-60) and GOST 8240-97 (hot-rolled steel channels, series U, No. 5-40). I-beams to GOST 26020 (B, Sh, K series) are not included yet.

Round, tube, rectangle and timber

For sections without a catalogue the size is found by trying sizes with a given step. For a rectangle you can set the ratio h/b (usually 1.5-2 for timber) or a fixed width b; for a tube the ratio of the inner to the outer diameter d/D. Section moduli: round pi d³/32, rectangle bh²/6, tube pi (D⁴ - d⁴)/(32D).

What the calculator ignores

  • Self-weight of the beam: add it to the load as a uniform q (mass per metre × 9.81).
  • Local and lateral-torsional buckling, support details and welds.
  • Plastic behaviour of steel, creep of timber, load duration.
  • Biaxial bending and torsion: the load is assumed to act in the plane of the web through the shear centre.

The result is an estimate for coursework and preliminary sizing; for building structures the final design must be done by a qualified engineer according to the current codes.

FAQ

How do I select an I-beam for a beam?
Draw the diagrams and find M_max, then W_req = M_max / R. Pick the nearest I-beam in GOST 8239-89 with W_x not smaller than W_req, then check the shear stress and deflection. The calculator does it in one step and shows the neighbouring numbers.
Which I-beam is needed for a 6 metre floor span?
It depends on the load. For example, with a uniform characteristic load of 10 kN/m and C245 steel, I-beam No. 22 is enough for strength but L/250 deflection requires No. 24. Enter your own layout and load to get the answer for your case.
What is the deflection limit L/250?
It is the allowable sag equal to one 250th of the span: for a 6 m span 24 mm is allowed. The value of n is chosen from the codes according to the purpose of the structure; for a cantilever l is taken as twice the overhang.
What is the difference between limit-state and allowable-stress design?
In limit-state design the loads are multiplied by a load factor and the material strength is the design value from the codes. In textbook allowable-stress design sigma is compared with [sigma] = yield stress / n without such factors. The results can differ by 10-20 percent.
Can I size a timber beam?
Yes. Choose Rectangle / timber and pine of the required grade, then set the ratio h/b or the beam width. The R values for timber are for reference and depend on the size, moisture and service conditions in SP 64.13330, so enter your own if needed.