This structural engineering tool allows you to calculate the critical forces and deflection for a simply supported beam. A simply supported beam is a beam supported at both ends, which is a fundamental concept in civil and mechanical engineering.
Key Parameters Explained
Beam Span (L): The horizontal distance between the two supports.
Uniform Distributed Load (w): A constant force applied along the entire length of the beam (e.g., the weight of a floor).
Point Load (P): A single force applied exactly at the center of the beam.
Modulus of Elasticity (E): A measure of the material's stiffness (e.g., Steel is typically 200-210 GPa).
Moment of Inertia (I): A geometric property of the beam's cross-section that represents its resistance to bending.
Example Calculation
If you have a steel beam (E = 210 GPa) with a span of 4 meters, a uniform load of 5 kN/m, and a moment of inertia of 4500 cm⁴, the calculator will determine the maximum bending moment occurring at the center and the total deflection in millimeters. This ensures the beam can safely carry the intended load without excessive sagging or structural failure.
Physics Formulas Used
For a simply supported beam with UDL and Center Point Load:
Max Bending Moment (M) = (w * L²) / 8 + (P * L) / 4
Max Deflection (Δ) = (5 * w * L⁴) / (384 * E * I) + (P * L³) / (48 * E * I)
Shear Force (V) = (w * L + P) / 2
function calculateBeam() {
var L = parseFloat(document.getElementById('beamLength').value);
var w = parseFloat(document.getElementById('uniformLoad').value) || 0;
var P = parseFloat(document.getElementById('pointLoad').value) || 0;
var E_GPa = parseFloat(document.getElementById('elasticity').value);
var I_cm4 = parseFloat(document.getElementById('inertia').value);
if (isNaN(L) || L <= 0 || isNaN(E_GPa) || isNaN(I_cm4) || E_GPa <= 0 || I_cm4 <= 0) {
alert("Please enter valid positive numbers for Length, Elasticity, and Moment of Inertia.");
return;
}
// Calculations for Moment and Shear (in kN and m)
var maxM = (w * Math.pow(L, 2) / 8) + (P * L / 4);
var reaction = (w * L + P) / 2;
var maxV = reaction;
// Unit Conversion for Deflection (SI units: N, m)
// E: GPa to N/m^2 (1 GPa = 10^9 N/m^2)
var E = E_GPa * 1e9;
// I: cm^4 to m^4 (1 cm^4 = 1e-8 m^4)
var I = I_cm4 * 1e-8;
// w: kN/m to N/m (1 kN = 1000 N)
var w_N = w * 1000;
// P: kN to N
var P_N = P * 1000;
// Deflection Calculation (result in meters)
var deflectionUDL = (5 * w_N * Math.pow(L, 4)) / (384 * E * I);
var deflectionPoint = (P_N * Math.pow(L, 3)) / (48 * E * I);
var totalDeflectionM = deflectionUDL + deflectionPoint;
var totalDeflectionMM = totalDeflectionM * 1000; // convert to mm
// Display results
document.getElementById('maxMoment').innerText = maxM.toFixed(2) + " kNm";
document.getElementById('maxShear').innerText = maxV.toFixed(2) + " kN";
document.getElementById('reactionForce').innerText = reaction.toFixed(2) + " kN";
document.getElementById('maxDeflection').innerText = totalDeflectionMM.toFixed(2) + " mm";
document.getElementById('results').style.display = "block";
}