Yield Load Calculator
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"text": "Yield Load is the specific amount of force required to cause a material to transition from elastic deformation (temporary stretching) to plastic deformation (permanent bending or stretching). It is calculated by multiplying the material's Yield Strength by its Cross-Sectional Area."
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"name": "What is the formula for calculating Yield Load?",
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"text": "The formula is P = σ_y × A, where P is the Yield Load (Force), σ_y is the Yield Strength (Stress) of the material, and A is the Cross-Sectional Area."
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Yield Load Calculator
Metric (MPa, mm²)
Imperial (psi, in²)
The stress level at which the material yields.
The area of the surface carrying the load.
Please enter valid positive numbers for strength and area.
Yield Load (Base Unit):–
Yield Load (Kilo Unit):–
Calculation Formula: Load = Strength × Area
How to Calculate Yield Load
Yield Load is a critical concept in materials science and structural engineering. It represents the maximum force a material can withstand before it begins to deform plastically. Plastic deformation implies that the material will not return to its original shape once the load is removed. Calculating the yield load is essential for designing safe structures, from bridges to bicycle frames.
The Yield Load Formula
The calculation is based on the fundamental relationship between stress, force, and area. The formula to calculate yield load is:
Py = σy × A
Py = Yield Load (Force)
σy = Yield Strength (Stress limit of the material)
A = Cross-Sectional Area (Geometry of the part)
Step-by-Step Calculation Guide
To calculate the yield load manually, follow these steps:
Identify the Material's Yield Strength: Determine the yield strength of the material you are using. For example, standard A36 structural steel has a yield strength of approximately 250 MPa (Metric) or 36,000 psi (Imperial).
Calculate the Cross-Sectional Area: Measure the dimensions of the structural member perpendicular to the force. If it is a round bar, calculate the area using πr². If it is a rectangular beam, use width × height.
Multiply Strength by Area: Multiply the yield strength by the cross-sectional area to get the total force.
Convert Units (If Necessary): Ensure your units are consistent. If using MPa (N/mm²) and mm², the result is in Newtons (N). Divide by 1,000 to get kilonewtons (kN).
Example Calculation
Let's calculate the yield load for a solid round steel bar with a diameter of 20mm, made of steel with a yield strength of 300 MPa.
Parameter
Value
Yield Strength (σy)
300 MPa (N/mm²)
Diameter
20 mm
Area Calculation (πr²)
π × 10² ≈ 314.16 mm²
Yield Load Calculation
300 N/mm² × 314.16 mm² = 94,248 N
Result in kN
94.25 kN
Why is Yield Load Different from Ultimate Load?
It is important not to confuse Yield Load with Ultimate Load. Yield Load is the point where the material starts to permanently stretch. Ultimate Load is the maximum force the material can support before it physically breaks or fractures. In engineering design, we typically design parts to stay well below the Yield Load to ensure they maintain their shape and integrity over time.
function updateYieldLabels() {
var unitSystem = document.getElementById('yl_unit_system').value;
var labelStrength = document.getElementById('label_yield_strength');
var labelArea = document.getElementById('label_area');
var inputStrength = document.getElementById('yl_yield_strength');
var inputArea = document.getElementById('yl_area');
if (unitSystem === 'metric') {
labelStrength.innerText = "Yield Strength (MPa)";
labelArea.innerText = "Cross-Sectional Area (mm²)";
inputStrength.placeholder = "e.g., 250";
inputArea.placeholder = "e.g., 500";
} else {
labelStrength.innerText = "Yield Strength (psi)";
labelArea.innerText = "Cross-Sectional Area (in²)";
inputStrength.placeholder = "e.g., 36000";
inputArea.placeholder = "e.g., 0.75";
}
// Hide results when unit changes until recalculated
document.getElementById('yl_result').style.display = 'none';
}
function calculateYieldLoad() {
// Get Inputs
var strengthInput = document.getElementById('yl_yield_strength').value;
var areaInput = document.getElementById('yl_area').value;
var unitSystem = document.getElementById('yl_unit_system').value;
var errorMsg = document.getElementById('yl_error_msg');
var resultBox = document.getElementById('yl_result');
// Validation
if (strengthInput === "" || areaInput === "" || isNaN(strengthInput) || isNaN(areaInput)) {
errorMsg.style.display = 'block';
resultBox.style.display = 'none';
return;
}
var strength = parseFloat(strengthInput);
var area = parseFloat(areaInput);
if (strength <= 0 || area <= 0) {
errorMsg.innerText = "Values must be greater than zero.";
errorMsg.style.display = 'block';
resultBox.style.display = 'none';
return;
}
// Logic
errorMsg.style.display = 'none';
var load = strength * area;
var baseUnitLabel = "";
var kiloUnitLabel = "";
var baseResult = 0;
var kiloResult = 0;
if (unitSystem === 'metric') {
// Metric: MPa (N/mm^2) * mm^2 = Newtons (N)
baseResult = load;
kiloResult = load / 1000;
baseUnitLabel = "Newtons (N)";
kiloUnitLabel = "Kilonewtons (kN)";
} else {
// Imperial: psi (lb/in^2) * in^2 = Pounds (lbs)
baseResult = load;
kiloResult = load / 1000;
baseUnitLabel = "Pounds-force (lbf)";
kiloUnitLabel = "Kip-force (kips)";
}
// Formatting Output
document.getElementById('yl_result_base').innerText = baseResult.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 2}) + " " + baseUnitLabel;
document.getElementById('yl_result_kilo').innerText = kiloResult.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}) + " " + kiloUnitLabel;
resultBox.style.display = 'block';
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