Shear Center Calculator for Channel Sections
The shear center is a crucial concept in structural mechanics, particularly when dealing with thin-walled open sections like channel beams. It is the point through which the shear force must act so that the beam bends without twisting. If the shear force does not pass through the shear center, the beam will experience both bending and torsion, leading to additional stresses and deflections.
For symmetric cross-sections, the shear center lies on the axis of symmetry. For a channel section, the shear center is located outside the web, on the axis of symmetry. This calculator determines the distance of the shear center from the mid-plane of the web for a thin-walled channel section.
Calculator for Thin-Walled Channel Sections
Please enter the dimensions of your channel section below. All dimensions should be in consistent units (e.g., millimeters or inches).
Understanding the Calculation
For a thin-walled channel section, the shear center distance (e) from the mid-plane of the web can be calculated using the following formula:
e = (b² * h² * tf) / (4 * Ixx)
Where:
b = Flange Widthh = Web Heighttf = Flange ThicknessIxx = Moment of Inertia about the horizontal centroidal axis (x-axis)
The moment of inertia Ixx for a thin-walled channel section is calculated as:
Ixx = (tw * h³ / 12) + 2 * (b * tf * (h/2)²)
Where tw is the Web Thickness.
Example Calculation
Let's consider a channel section with the following dimensions:
- Flange Width (b) = 50 mm
- Web Height (h) = 100 mm
- Flange Thickness (tf) = 2 mm
- Web Thickness (tw) = 2 mm
First, calculate the Moment of Inertia (Ixx):
Ixx = (2 * 100³ / 12) + 2 * (50 * 2 * (100/2)²)
Ixx = (2 * 1,000,000 / 12) + 2 * (100 * 50²)
Ixx = 166,666.67 + 2 * (100 * 2,500)
Ixx = 166,666.67 + 500,000
Ixx = 666,666.67 mm⁴
Now, calculate the Shear Center distance (e):
e = (50² * 100² * 2) / (4 * 666,666.67)
e = (2,500 * 10,000 * 2) / 2,666,666.68
e = 50,000,000 / 2,666,666.68
e ≈ 18.75 mm
Thus, for this channel section, the shear center is approximately 18.75 mm from the mid-plane of the web.
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function calculateShearCenter() {
var flangeWidth = parseFloat(document.getElementById('flangeWidth').value);
var webHeight = parseFloat(document.getElementById('webHeight').value);
var flangeThickness = parseFloat(document.getElementById('flangeThickness').value);
var webThickness = parseFloat(document.getElementById('webThickness').value);
var resultDiv = document.getElementById('shearCenterResult');
if (isNaN(flangeWidth) || isNaN(webHeight) || isNaN(flangeThickness) || isNaN(webThickness) ||
flangeWidth <= 0 || webHeight <= 0 || flangeThickness <= 0 || webThickness <= 0) {
resultDiv.innerHTML = '
Please enter valid positive numbers for all dimensions.';
return;
}
// Calculate Moment of Inertia (Ixx) for a thin-walled channel section
// Ixx = (tw * h^3 / 12) + 2 * (b * tf * (h/2)^2)
var ixx = (webThickness * Math.pow(webHeight, 3) / 12) + 2 * (flangeWidth * flangeThickness * Math.pow(webHeight / 2, 2));
// Calculate Shear Center distance (e) from the mid-plane of the web
// e = (b^2 * h^2 * tf) / (4 * Ixx)
var shearCenterDistance = (Math.pow(flangeWidth, 2) * Math.pow(webHeight, 2) * flangeThickness) / (4 * ixx);
resultDiv.innerHTML = 'The Shear Center distance (e) from the web\'s mid-plane is:
' + shearCenterDistance.toFixed(3) + ' units.';
}