Understanding the SkyCiv Beam Calculator and Structural Analysis
This calculator provides a simplified tool for analyzing basic beam behavior under common loading conditions. Structural engineers use advanced software like SkyCiv's Beam analysis tools to model complex structures, but understanding the fundamental principles is crucial. This calculator helps visualize how different loads and support types affect a beam's internal forces (shear force, bending moment) and its physical response (deflection).
Key Concepts:
Beam Length: The total span of the beam between its supports. Measured in meters (m).
Load Types:
Point Load: A concentrated force applied at a single point on the beam. Measured in Newtons (N).
Uniformly Distributed Load (UDL): A load spread evenly across a length of the beam. Measured in Newtons per meter (N/m).
Support Types:
Simply Supported: The beam rests on supports at both ends, allowing rotation but preventing vertical movement.
Cantilever: The beam is fixed at one end and free at the other. This creates a moment at the fixed support.
Shear Force: The internal force acting perpendicular to the beam's axis, caused by the tendency of one part of the beam to slide vertically relative to another. It is calculated by summing forces along the beam's cross-section.
Bending Moment: The internal force acting about the beam's axis, caused by the tendency of the beam to bend or rotate. It is calculated by summing moments about the beam's cross-section.
Deflection: The vertical displacement of the beam under load. This is a critical factor for serviceability and preventing excessive deformation.
How the Calculations Work (Simplified):
The calculations performed by this calculator are based on the principles of statics and mechanics of materials. For different load and support combinations, specific formulas are applied:
Reactions: The first step is typically to calculate the vertical reactions at the supports. These are forces that balance the applied loads.
Shear Force (V): For a section at distance 'x' from the left support:
Simply Supported with Point Load (P) at 'a': V(x) = R_A – (P if x > a)
Simply Supported with UDL (w): V(x) = R_A – w*x
Cantilever with Point Load (P) at end 'L': V(x) = P (for x < L)
Cantilever with UDL (w) over length 'L': V(x) = w * (L – x)
Where R_A is the reaction at the left support.
Bending Moment (M): For a section at distance 'x' from the left support:
Simply Supported with Point Load (P) at 'a': M(x) = R_A*x – P*(x-a) (if x > a)
Simply Supported with UDL (w): M(x) = R_A*x – (w*x^2)/2
Cantilever with Point Load (P) at end 'L': M(x) = P*(L – x)
Cantilever with UDL (w) over length 'L': M(x) = (w*(L-x)^2)/2
Deflection (δ): This is often the most complex calculation, involving integration of the moment equation and material properties (like the Modulus of Elasticity 'E' and the Moment of Inertia 'I' of the beam's cross-section, which are simplified or assumed in basic calculators). For a simply supported beam with a central point load P, the maximum deflection is (PL^3) / (48EI). For a UDL, it's (5wL^4) / (384EI). This calculator provides a qualitative indication or a simplified calculation assuming standard values.
Disclaimer: This calculator is for educational and illustrative purposes only. It uses simplified formulas and does not account for all real-world factors such as material properties (E, I), stress concentrations, shear deformation, or dynamic loads. For critical engineering applications, always use professional structural analysis software and consult with a qualified engineer.
function toggleLoadSections() {
var loadType = document.getElementById("loadType").value;
if (loadType === "point") {
document.getElementById("pointLoadSection").style.display = "block";
document.getElementById("udlSection").style.display = "none";
} else {
document.getElementById("pointLoadSection").style.display = "none";
document.getElementById("udlSection").style.display = "block";
}
}
function calculateBeam() {
var beamLength = parseFloat(document.getElementById("beamLength").value);
var loadType = document.getElementById("loadType").value;
var pointLoadValue = parseFloat(document.getElementById("pointLoadValue").value);
var pointLoadLocation = parseFloat(document.getElementById("pointLoadLocation").value);
var udlValue = parseFloat(document.getElementById("udlValue").value);
var supportType = document.getElementById("supportType").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "Results will appear here."; // Reset
// Basic validation
if (isNaN(beamLength) || beamLength <= 0) {
resultDiv.innerHTML = "Error: Please enter a valid beam length.";
return;
}
var reactionLeft = 0, reactionRight = 0;
var maxShear = 0, maxMoment = 0;
var maxDeflection = 0; // Simplified calculation / placeholder
var shearDiagram = [];
var momentDiagram = [];
// — Calculations based on Support Type —
if (supportType === "simplySupported") {
if (loadType === "point") {
if (isNaN(pointLoadValue) || pointLoadValue <= 0 || isNaN(pointLoadLocation) || pointLoadLocation = beamLength) {
resultDiv.innerHTML = "Error: Please enter valid point load details.";
return;
}
// Reactions
reactionLeft = pointLoadValue * (beamLength – pointLoadLocation) / beamLength;
reactionRight = pointLoadValue * pointLoadLocation / beamLength;
// Max Shear (absolute value)
maxShear = Math.max(Math.abs(reactionLeft), Math.abs(reactionRight), Math.abs(reactionLeft – pointLoadValue));
// Max Moment (occurs under point load for simply supported)
maxMoment = reactionLeft * pointLoadLocation; // Moment under the point load
// Max Deflection (simplified, assuming E*I=1 for illustration)
// For a general point load P at 'a' on a span L: Max deflection = P*a*(L-a)*(L + a*(L-a)/L) / (6*E*I*L)
// Simplified: Max deflection under load is approx. (P * a * (L-a)) / (k * E * I * L) where k depends on location. Central load is 48.
// Using a simplified empirical value for illustration or assuming E*I is factored out.
maxDeflection = (pointLoadValue * pointLoadLocation * (beamLength – pointLoadLocation) * (beamLength + pointLoadLocation*(beamLength – pointLoadLocation)/beamLength)) / (6 * 1 * beamLength); // Assuming E*I=1 for relative comparison
if(maxDeflection < 0) maxDeflection = -maxDeflection; // Ensure positive value for display
maxDeflection = maxDeflection / 10000; // Scale down for typical display
} else { // UDL
if (isNaN(udlValue) || udlValue <= 0) {
resultDiv.innerHTML = "Error: Please enter a valid UDL magnitude.";
return;
}
// Reactions
reactionLeft = (udlValue * beamLength) / 2;
reactionRight = (udlValue * beamLength) / 2;
// Max Shear (at supports)
maxShear = Math.abs(reactionLeft);
// Max Moment (at mid-span)
maxMoment = (udlValue * beamLength * beamLength) / 8;
// Max Deflection (at mid-span, assuming E*I=1)
maxDeflection = (5 * udlValue * Math.pow(beamLength, 4)) / (384 * 1); // Assuming E*I=1
maxDeflection = maxDeflection / 10000; // Scale down
if(maxDeflection < 0) maxDeflection = -maxDeflection; // Ensure positive value for display
}
} else { // Cantilever (Fixed Left, Free Right)
if (loadType === "point") {
if (isNaN(pointLoadValue) || pointLoadValue <= 0 || isNaN(pointLoadLocation) || pointLoadLocation beamLength) {
resultDiv.innerHTML = "Error: Please enter valid point load details for cantilever.";
return;
}
// Reactions (at fixed support)
reactionLeft = pointLoadValue; // Vertical reaction
// Moment reaction at fixed support = P * (L – a) where a is distance from fixed end
var momentReactionLeft = pointLoadValue * (beamLength – pointLoadLocation);
// Max Shear (at fixed support)
maxShear = Math.abs(pointLoadValue);
// Max Moment (at fixed support)
maxMoment = Math.abs(momentReactionLeft);
// Max Deflection (at free end, assuming E*I=1)
// For point load P at 'a' from fixed end: Max deflection = P * a^2 * (3L – a) / (6EI)
maxDeflection = (pointLoadValue * Math.pow(pointLoadLocation, 2) * (3 * beamLength – pointLoadLocation)) / (6 * 1); // Assuming E*I=1
if(maxDeflection < 0) maxDeflection = -maxDeflection; // Ensure positive value for display
} else { // UDL
if (isNaN(udlValue) || udlValue <= 0) {
resultDiv.innerHTML = "Error: Please enter a valid UDL magnitude.";
return;
}
// Reactions (at fixed support)
reactionLeft = udlValue * beamLength; // Vertical reaction
var momentReactionLeft = (udlValue * beamLength * beamLength) / 2; // Moment reaction
// Max Shear (at fixed support)
maxShear = Math.abs(reactionLeft);
// Max Moment (at fixed support)
maxMoment = Math.abs(momentReactionLeft);
// Max Deflection (at free end, assuming E*I=1)
// Max deflection = w * L^4 / (8EI)
maxDeflection = (udlValue * Math.pow(beamLength, 4)) / (8 * 1); // Assuming E*I=1
if(maxDeflection < 0) maxDeflection = -maxDeflection; // Ensure positive value for display
}
}
// — Display Results —
resultDiv.innerHTML =
"
Analysis Results:
" +
"Support Type: " + supportType.replace(/([A-Z])/g, ' $1').trim() + "" +
"Maximum Shear Force: " + maxShear.toFixed(2) + " N" +
"Maximum Bending Moment: " + maxMoment.toFixed(2) + " Nm" +
"Estimated Max Deflection: " + maxDeflection.toFixed(4) + " m (Assuming E*I = 1, relative)" +
(supportType === "simplySupported" ? "Left Support Reaction: " + reactionLeft.toFixed(2) + " N" : "") +
(supportType === "simplySupported" ? "Right Support Reaction: " + reactionRight.toFixed(2) + " N" : "");
toggleLoadSections(); // Ensure correct sections are visible if user changes load type after calculation
}
// Initial call to set the correct visibility of load sections on page load
window.onload = toggleLoadSections;