Steel Beam Span and Load Calculator

ANA›Life Services Authority›National Calculator Authority›Steel Beam Span and Load Calculator

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Steel Beam Span and Load Calculator

Calculate the maximum allowable uniform distributed load (UDL) or maximum safe span for a simply supported steel beam using elastic bending theory and standard steel section properties.

Beam Span, L (m)

Elastic Section Modulus, Z (cm³)

Find Z from steel section tables (e.g. UB 305×127×48 → Z ≈ 711 cm³)

Steel Yield Strength, fy (MPa)

S275 = 275 MPa, S355 = 355 MPa, S460 = 460 MPa

Safety Factor (typically 1.5 – 1.67)

Beam Self-Weight (kN/m) (optional, 0 to ignore)

Calculate

Results will appear here.

function steCalc() { const resultDiv = document.getElementById('ste-result');

const L = parseFloat(document.getElementById('ste-span').value); const Z = parseFloat(document.getElementById('ste-section-modulus').value); const fy = parseFloat(document.getElementById('ste-yield-strength').value); const SF = parseFloat(document.getElementById('ste-safety-factor').value); const sw = parseFloat(document.getElementById('ste-self-weight').value) || 0;

// --- Validation --- if (isNaN(L) || L ⚠ Please enter a valid positive beam span (L).'; return; } if (isNaN(Z) || Z ⚠ Please enter a valid positive section modulus (Z).'; return; } if (isNaN(fy) || fy 700) { resultDiv.innerHTML = '⚠ Yield strength must be between 100 and 700 MPa.'; return; } if (isNaN(SF) || SF 3.0) { resultDiv.innerHTML = '⚠ Safety factor must be between 1.0 and 3.0.'; return; } if (sw ⚠ Self-weight cannot be negative.'; return; }

// --- Core Calculations --- // Allowable bending stress // f_allow = fy / SF [MPa = N/mm²] const f_allow = fy / SF;

// Allowable moment capacity // M_allow = f_allow × Z [Z in cm³ → convert to mm³ × 1000] // M_allow [N·mm] = f_allow [N/mm²] × Z [mm³] // Z cm³ → mm³: multiply by 1000 const Z_mm3 = Z * 1000; // mm³ const M_allow_Nmm = f_allow * Z_mm3; // N·mm const M_allow_kNm = M_allow_Nmm / 1e6; // kN·m

// For a simply supported beam with UDL (w total including self-weight): // M_max = w × L² / 8 // Solving for w_total: w_total = 8 × M_allow / L² const w_total_kNm = (8 * M_allow_kNm) / (L * L); // kN/m

// Subtract self-weight to get net allowable applied load const w_applied_kNm = w_total_kNm - sw;

// Total allowable load on beam const W_total_kN = w_applied_kNm * L;

// Maximum safe span (if load is given as self-weight only, solve for L) // L_max = sqrt(8 × M_allow / w_total) — shown for reference using sw as total load let L_max_m = null; if (sw > 0) { L_max_m = Math.sqrt((8 * M_allow_kNm) / sw); }

// Deflection check (span/360 serviceability limit, elastic, EI needed) // Using E = 210,000 MPa for steel; I not directly available from Z alone // Approximate: I ≈ Z × (d/2), but d unknown — skip exact deflection, // provide span-to-depth guidance instead.

// Slenderness / span-to-depth ratio guidance const span_depth_typical = L * 1000 / 20; // typical d = L/20 for steel beams (mm)

// --- Output --- let html = '### 📊 Results ';

html += ''; html += 'ParameterValue'; html += 'Allowable Bending Stress (fallow)' + f_allow.toFixed(2) + ' MPa'; html += 'Allowable Moment Capacity (Mallow)' + M_allow_kNm.toFixed(2) + ' kN·m'; html += 'Max Total UDL (incl. self-weight)' + w_total_kNm.toFixed(3) + ' kN/m'; html += 'Beam Self-Weight' + sw.toFixed(3) + ' kN/m';

if (w_applied_kNm > 0) { html += '✅ Max Allowable Applied UDL' + w_applied_kNm.toFixed(3) + ' kN/m'; html += '✅ Max Total Applied Load on Beam' + W_total_kN.toFixed(2) + ' kN'; } else { html += '⚠ Self-weight alone exceeds beam capacity at this span. Increase section modulus or reduce span.'; }

if (L_max_m !== null) { html += 'Max Safe Span (self-weight load only)' + L_max_m.toFixed(2) + ' m'; }

html += 'Typical Min. Beam Depth (L/20 rule)' + span_depth_typical.toFixed(0) + ' mm'; html += '';

// Warnings if (w_applied_kNm > 0 && w_applied_kNm 12) { html += '⚠ Spans over 12 m: lateral torsional buckling (LTB) must be checked separately per BS EN 1993-1-1 §6.3.2.

'; } if (Z

#### Formulas Used

1. Allowable Bending Stress:

fallow = fy / SF

2. Allowable Moment Capacity (Elastic):

Mallow = fallow × Z

where Z is the elastic section modulus (cm³ → converted to mm³ × 1000)

3. Maximum UDL for Simply Supported Beam:

Mmax = w × L² / 8  →  wtotal = 8 × Mallow / L²

4. Net Allowable Applied Load:

wapplied = wtotal − wself-weight

Wtotal = wapplied × L

5. Maximum Safe Span (given self-weight as governing load):

Lmax = √(8 × Mallow / wsw)

#### Assumptions & References

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