Flitch Beam Calculator

Flitch Beam Capacity Calculator

Calculation Results

Total Equivalent Stiffness (EI): lb-in²

Maximum Bending Moment: lb-ft

Calculated Deflection: in

Span/Deflection Ratio: L/

Understanding Flitch Beam Calculations

A flitch beam (or flitch plate beam) is a composite structural element consisting of a steel plate sandwiched between two or more timber beams. The components are bolted together, allowing the materials to act as a single unit. This design provides the strength of steel with the ease of fastening associated with wood.

The Mathematics of Composite Beams

To calculate the strength of a flitch beam, engineers use the Method of Transformed Sections. Because steel and wood have different stiffnesses (Modulus of Elasticity), the steel plate is "transformed" into an equivalent amount of wood by calculating a modular ratio (n):

n = E_steel / E_wood

Common Applications

  • Residential Remodeling: Used to support long spans where a standard 2×10 or 2×12 header would sag, but a full steel I-beam is too heavy or difficult to install.
  • Open Floor Plans: Ideal for removing load-bearing walls while keeping the beam depth thin enough to remain hidden within the ceiling joist space.
  • Historic Restoration: Reinforcing older timber frames without significantly altering the visual appearance of the wood.

Example Calculation

If you have a 12ft span with a total load of 400 lbs per linear foot (PLF), and you use two 2×10 Douglas Fir members (1.5″ x 9.25″) with a 1/2″ steel plate:

  1. Wood Inertia: 2 * (1.5 * 9.25³ / 12) = 197.8 in⁴
  2. Steel Inertia: (0.5 * 9.25³ / 12) = 32.9 in⁴
  3. Modular Ratio (n): 29,000,000 / 1,600,000 = 18.125
  4. Equivalent Stiffness (EI): (E_wood * I_wood) + (E_steel * I_steel)

The resulting deflection check (usually L/360 or L/240) determines if the beam is stiff enough for the intended application.

function calculateFlitch() { // Inputs var span_ft = parseFloat(document.getElementById('span_ft').value); var load_plf = parseFloat(document.getElementById('load_plf').value); var wood_depth = parseFloat(document.getElementById('wood_depth').value); var wood_count = parseFloat(document.getElementById('wood_count').value); var wood_width = parseFloat(document.getElementById('wood_width').value); var steel_thick = parseFloat(document.getElementById('steel_thick').value); var wood_e = parseFloat(document.getElementById('wood_e').value); var steel_e = parseFloat(document.getElementById('steel_e').value); if (isNaN(span_ft) || isNaN(load_plf) || isNaN(wood_depth)) { alert("Please enter valid numerical values."); return; } // Convert Span to inches var span_in = span_ft * 12; // Moment of Inertia Wood (I = bh^3 / 12) var i_wood = (wood_count * wood_width * Math.pow(wood_depth, 3)) / 12; // Moment of Inertia Steel var i_steel = (steel_thick * Math.pow(wood_depth, 3)) / 12; // Total EI (Stiffness) var total_ei = (wood_e * i_wood) + (steel_e * i_steel); // Maximum Bending Moment (M = wL^2 / 8) // Convert PLF to lb/in for the calculation if needed, but standard is lb-ft var max_moment_lbft = (load_plf * Math.pow(span_ft, 2)) / 8; // Max Deflection (Delta = 5wL^4 / 384EI) // w must be in lb/in, L in inches var load_pli = load_plf / 12; var deflection = (5 * load_pli * Math.pow(span_in, 4)) / (384 * total_ei); // Span/Deflection Ratio var ratio = span_in / deflection; // Display Results document.getElementById('results').style.display = 'block'; document.getElementById('res_ei').innerText = total_ei.toLocaleString(undefined, {maximumFractionDigits: 0}); document.getElementById('res_moment').innerText = max_moment_lbft.toLocaleString(undefined, {maximumFractionDigits: 0}); document.getElementById('res_deflection').innerText = deflection.toFixed(3); document.getElementById('res_ratio').innerText = Math.round(ratio); var status = document.getElementById('status_box'); if (ratio >= 360) { status.innerText = "PASS: Beam meets L/360 criteria for floor loads."; status.style.backgroundColor = "#d4edda"; status.style.color = "#155724"; } else if (ratio >= 240) { status.innerText = "PASS: Beam meets L/240 criteria for roof loads/general structural."; status.style.backgroundColor = "#fff3cd"; status.style.color = "#856404"; } else { status.innerText = "FAIL: Deflection exceeds standard limits (L/240). Increase member size."; status.style.backgroundColor = "#f8d7da"; status.style.color = "#721c24"; } }

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