Rectangular Hollow Section Weight Calculation

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Accurately calculate the weight per meter and total weight of rectangular hollow sections.

Rectangular Hollow Section Weight Calculator

Weight vs. Length Analysis

Weight of Rectangular Hollow Section at Varying Lengths

Weight Calculation Details

Detailed Breakdown of Weight Calculation

Parameter	Value	Unit
Outer Width	—	mm
Outer Height	—	mm
Wall Thickness	—	mm
Length	—	m
Material Density	—	kg/m³
Inner Width	—	mm
Inner Height	—	mm
Cross-Sectional Area	—	mm²
Weight per Meter	—	kg/m
Total Weight	—	kg

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What is Rectangular Hollow Section Weight Calculation?

Rectangular hollow section weight calculation is the process of determining the mass of a structural steel tube with a rectangular cross-section. These sections, often referred to as RHS (Rectangular Hollow Sections) or CHS (Circular Hollow Sections, though we focus on rectangular here), are fundamental building blocks in various industries, including construction, manufacturing, and engineering. Accurately calculating their weight is crucial for several reasons: efficient material procurement, cost estimation, structural load calculations, transportation logistics, and ensuring project budgets remain on track. Without precise weight calculations for rectangular hollow sections, projects can suffer from overspending on materials, structural instability due to underestimated loads, or logistical nightmares.

Who should use it? This calculator and its underlying principles are essential for structural engineers, architects, steel fabricators, construction managers, quantity surveyors, procurement specialists, and DIY enthusiasts working with steel structures. Anyone involved in designing, specifying, purchasing, or installing rectangular hollow sections will benefit from understanding how to calculate their weight.

Common misconceptions often revolve around assuming all steel has the same density, or oversimplifying the calculation by ignoring wall thickness. For instance, many might mistakenly think that two sections with the same outer dimensions will weigh the same, regardless of wall thickness. This is incorrect; a thicker wall means more material, hence more weight. Another misconception is the unit conversion; failing to convert between millimeters (mm) for dimensions and meters (m) for density and length can lead to drastically incorrect results. Understanding the precise formula and units is key to avoiding these pitfalls.

Rectangular Hollow Section Weight Formula and Mathematical Explanation

The fundamental principle behind calculating the weight of a rectangular hollow section is to determine its volume and then multiply it by the material’s density. Since we’re dealing with hollow sections, we must account for the material only, not the empty space inside.

The volume of the material in a rectangular hollow section can be found by calculating the volume of the outer rectangular prism and subtracting the volume of the inner rectangular prism (the hollow space).

Volume of Outer Rectangular Prism = Outer Width × Outer Height × Length

Volume of Inner Rectangular Prism = Inner Width × Inner Height × Length

Where:

• Inner Width = Outer Width – (2 × Wall Thickness)
• Inner Height = Outer Height – (2 × Wall Thickness)

Therefore, the Volume of Material = (Outer Width × Outer Height × Length) – (Inner Width × Inner Height × Length)

This can be simplified by factoring out Length:

Volume of Material = [ (Outer Width × Outer Height) – (Inner Width × Inner Height) ] × Length

The term `(Outer Width × Outer Height) – (Inner Width × Inner Height)` represents the Cross-Sectional Area of the material.

Cross-Sectional Area (A) = (Outer Width × Outer Height) – ( (Outer Width – 2 × Wall Thickness) × (Outer Height – 2 × Wall Thickness) )

Then, the Weight = Volume of Material × Density

Weight = [ Cross-Sectional Area × Length ] × Density

Important Unit Considerations:

• Dimensions (Width, Height, Thickness) are typically given in millimeters (mm).
• Length is often given in meters (m).
• Density is usually given in kilograms per cubic meter (kg/m³).

To ensure accurate calculations, all measurements must be converted to consistent units. A common approach is to convert all linear dimensions to meters before calculating volume or area in square meters.

• 1 mm = 0.001 m
• 1 mm² = 0.000001 m²

Let’s use meters for calculation:

• Outer Width (m) = Outer Width (mm) / 1000
• Outer Height (m) = Outer Height (mm) / 1000
• Wall Thickness (m) = Wall Thickness (mm) / 1000

Then:

• Inner Width (m) = Outer Width (m) – (2 × Wall Thickness (m))
• Inner Height (m) = Outer Height (m) – (2 × Wall Thickness (m))

Cross-Sectional Area (m²) = (Outer Width (m) × Outer Height (m)) – (Inner Width (m) × Inner Height (m))

Volume (m³) = Cross-Sectional Area (m²) × Length (m)

Weight (kg) = Volume (m³) × Density (kg/m³)

Alternatively, and often simpler:

Weight per Meter (kg/m) = Cross-Sectional Area (mm²) × Density (kg/m³) / 1,000,000

Then, Total Weight (kg) = Weight per Meter (kg/m) × Length (m)

Variables Table

Variable	Meaning	Unit	Typical Range / Notes
Outer Width (W_o)	The larger external dimension of the rectangular section.	mm	50 mm to 1000 mm (and above)
Outer Height (H_o)	The smaller external dimension of the rectangular section.	mm	25 mm to 1000 mm (and above)
Wall Thickness (t)	The thickness of the material forming the walls.	mm	1 mm to 20 mm (and above)
Length (L)	The total length of the hollow section being considered.	meters (m)	1 m to 12 m (standard lengths) or custom
Material Density (ρ)	Mass per unit volume of the material.	kg/m³	Steel: ~7850 kg/m³; Aluminum: ~2700 kg/m³
Inner Width (W_i)	The internal width dimension.	mm	Calculated: W_o – 2t
Inner Height (H_i)	The internal height dimension.	mm	Calculated: H_o – 2t
Cross-Sectional Area (A)	The area of the material in the cross-section.	mm²	Calculated: (W_o × H_o) – (W_i × H_i)
Weight per Meter (WPM)	The mass of a 1-meter length of the section.	kg/m	Calculated: (A × ρ) / 1,000,000
Total Weight (W_total)	The total mass for the specified length.	kg	Calculated: WPM × L

Practical Examples (Real-World Use Cases)

Here are a couple of scenarios demonstrating the use of the rectangular hollow section weight calculation.

Example 1: Steel Frame Construction

A construction company is building a small commercial steel frame. They need to order rectangular hollow sections for the main support columns.

• Section: Rectangular Hollow Section
• Outer Width: 150 mm
• Outer Height: 100 mm
• Wall Thickness: 6 mm
• Length: They need 8 columns, each 4 meters long. Total Length = 8 * 4 = 32 meters.
• Material Density: Standard steel, 7850 kg/m³.

Calculation using the tool/formula:

1. Inner Width = 150 mm – (2 * 6 mm) = 138 mm
2. Inner Height = 100 mm – (2 * 6 mm) = 88 mm
3. Cross-Sectional Area = (150 * 100) – (138 * 88) = 15000 – 12144 = 2856 mm²
4. Weight per Meter = (2856 mm² * 7850 kg/m³) / 1,000,000 = 22.43 kg/m
5. Total Weight = 22.43 kg/m * 32 m = 717.76 kg

Interpretation: The company needs to procure approximately 718 kg of this specific steel section for the columns. This allows for accurate ordering, preventing shortages or excess material, and aids in transportation planning. This calculation is fundamental for accurate cost estimation in structural projects.

Example 2: Industrial Machinery Frame

A manufacturer is designing a frame for industrial machinery. They need to select appropriate RHS members and estimate material costs.

• Section: Rectangular Hollow Section
• Outer Width: 80 mm
• Outer Height: 80 mm (a square hollow section, a subset of rectangular)
• Wall Thickness: 4 mm
• Length: The design requires a total of 15 meters of this section.
• Material Density: Standard steel, 7850 kg/m³.

Calculation using the tool/formula:

1. Inner Width = 80 mm – (2 * 4 mm) = 72 mm
2. Inner Height = 80 mm – (2 * 4 mm) = 72 mm
3. Cross-Sectional Area = (80 * 80) – (72 * 72) = 6400 – 5184 = 1216 mm²
4. Weight per Meter = (1216 mm² * 7850 kg/m³) / 1,000,000 = 9.54 kg/m
5. Total Weight = 9.54 kg/m * 15 m = 143.1 kg

Interpretation: For this machine frame, approximately 143 kg of the 80x80x4 RHS is required. This information is vital for budgeting the raw materials and ensuring the structural integrity and final weight of the machinery meet design specifications. This aids in assessing the overall structural load calculations.

How to Use This Rectangular Hollow Section Weight Calculator

Using our calculator is straightforward. Follow these simple steps to get accurate weight estimations for your rectangular hollow sections.

1. Input Dimensions: Enter the ‘Outer Width’ (mm), ‘Outer Height’ (mm), and ‘Wall Thickness’ (mm) of the rectangular hollow section. Ensure you use the correct dimensions as per your specifications.
2. Enter Length: Input the total ‘Length’ (in meters) for which you need to calculate the weight. If you have multiple pieces of the same section, sum their lengths.
3. Specify Density: The calculator defaults to the density of steel (7850 kg/m³). If you are working with a different material (e.g., aluminum, stainless steel), update the ‘Material Density’ field accordingly.
4. Calculate: Click the “Calculate Weight” button. The calculator will process your inputs and display the results.

How to read results:

• Main Result (Total Weight): This is the most prominent number, displayed in kilograms (kg), representing the total estimated weight for the specified length and section dimensions.
• Intermediate Values:
  • Inner Dimensions: Shows the calculated internal width and height in mm.
  • Cross-Sectional Area: Displays the area of the steel material in the cross-section, in mm².
  • Weight per Meter: Indicates the weight of a single meter of the section in kg/m. This is a useful metric for comparing different sections.
• Key Assumptions: Confirms the material density value used in the calculation.
• Data Table & Chart: The table provides a detailed breakdown of all input parameters and calculated values. The chart visually represents how the total weight changes with varying section lengths.

Decision-making guidance:

• Procurement: Use the ‘Total Weight’ to order the correct amount of material.
• Logistics: The ‘Total Weight’ helps in planning transportation capacity and costs.
• Structural Design: ‘Weight per Meter’ is useful for calculating dead loads on supporting structures.
• Costing: Estimate material costs based on the ‘Total Weight’ and current steel prices. This ties into overall cost estimation for projects.

Key Factors That Affect Rectangular Hollow Section Weight Results

Several factors influence the calculated weight of a rectangular hollow section. Understanding these helps in refining accuracy and making informed decisions:

1. Wall Thickness: This is arguably the most significant factor after dimensions. Even a small change in wall thickness drastically alters the amount of material used, directly impacting the weight. Thicker walls mean significantly heavier sections.
2. Outer Dimensions (Width & Height): Larger outer dimensions naturally lead to a greater volume of material, provided the wall thickness and length remain constant. The combined effect of width and height dictates the overall size of the section.
3. Material Density: Different metals have different densities. Steel is denser than aluminum, meaning an aluminum section of the same dimensions will be considerably lighter. Accurate density input is critical for correct weight calculation, especially when using non-standard materials. This impacts material procurement strategies.
4. Length of Section: The total weight is directly proportional to the length. Doubling the length will double the weight, assuming all other parameters are constant. This is crucial for calculating total project material needs.
5. Manufacturing Tolerances: Real-world steel sections may have slight variations in dimensions and wall thickness due to manufacturing tolerances. While standard calculations assume precise measurements, actual weight might deviate slightly. For critical applications, consider tolerances specified by standards like EN 10210 or ASTM A500.
6. Surface Coatings/Treatment: Processes like galvanizing (zinc coating) add a small amount of weight to the section. While often negligible for large projects, it can be a factor in highly precise calculations or for smaller quantities.
7. Internal Structure (Less Common): While standard RHS is hollow, some specialized sections might have internal ribs or structures. This calculator assumes a simple hollow tube. Complex internal geometries would require different calculation methods.

Frequently Asked Questions (FAQ)

What is the standard density of steel for RHS calculations?

The standard density of steel is approximately 7850 kg/m³. This value is commonly used for carbon steel and is the default in our calculator. Stainless steel might have a slightly different density, typically around 7900-8000 kg/m³.

Can I calculate the weight of a non-rectangular hollow section?

This calculator is specifically designed for rectangular hollow sections. For circular, oval, or other shapes, different geometric formulas would be required to calculate the cross-sectional area.

Does wall thickness affect weight significantly?

Yes, wall thickness has a very significant impact on weight. Since the weight is calculated based on the volume of material, increasing the wall thickness increases the material volume and thus the weight, often disproportionately compared to outer dimension changes.

What units should I use for the input dimensions?

Please use millimeters (mm) for Width, Height, and Wall Thickness, and meters (m) for Length. The calculator handles the necessary conversions internally.

How accurate is this calculator?

The calculator provides a highly accurate theoretical weight based on the provided dimensions and material density. Actual weight may vary slightly due to manufacturing tolerances and coatings.

What is ‘Weight per Meter’ used for?

‘Weight per Meter’ (kg/m) is a standard industry metric. It allows for easy comparison between different sizes of RHS and is useful for quick estimations and understanding the material intensity of a section.

Can I calculate the weight of a hollow section with different wall thicknesses on different sides?

This calculator assumes a uniform wall thickness for all sides of the rectangular hollow section. Sections with variable wall thicknesses require more complex calculations or specific manufacturer data.

How do I account for cuts or joins in the steel?

This calculator determines the weight based on the theoretical dimensions provided. For precise project costing, you might add a small percentage (e.g., 5-10%) to account for material waste from cuts, weld preparations, and potential offcuts.

What is the difference between Rectangular Hollow Section (RHS) and Square Hollow Section (SHS)?

A Square Hollow Section (SHS) is a specific type of Rectangular Hollow Section (RHS) where the width and height are equal. Our calculator can handle both, as a square is simply a rectangle with equal sides.

Related Tools and Resources

• Steel Beam Weight Calculator: Calculate weights for I-beams, H-beams, and channels.
• Circular Hollow Section Weight Calculator: Determine the weight of steel tubes and pipes.
• Material Density Chart: A reference for densities of various metals and materials.
• Structural Engineering Formulas: A collection of essential formulas for structural design.
• Steel Grade Comparison: Understand the properties of different steel grades.
• Construction Cost Estimation Guide: Learn how to estimate costs for building projects.

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} catch (err) {
console.log('Unable to copy results.', err); // In a real app, show user feedback
}
document.body.removeChild(textArea);
}

// Charting Functionality
function updateChart(currentLength, currentTotalWeight, currentWeightPerMeter) {
var canvas = document.getElementById('weightLengthChart');
var ctx = canvas.getContext('2d');

// Destroy previous chart instance if it exists
if (chartInstance) {
chartInstance.destroy();
}

// Generate data points for the chart
var lengths = [];
var weights = [];
var weightsPerMeterData = []; // For the second series

// Generate data for lengths from 1m up to a reasonable max (e.g., 12m or currentLength * 1.5)
var maxLengthForChart = Math.max(12, currentLength * 1.5);
var step = maxLengthForChart / 10; // Number of points

var baseOuterWidth = parseFloat(document.getElementById('outerWidth').value) || 50;
var baseOuterHeight = parseFloat(document.getElementById('outerHeight').value) || 100;
var baseWallThickness = parseFloat(document.getElementById('wallThickness').value) || 5;
var baseDensity = parseFloat(document.getElementById('materialDensity').value) || 7850;

// Recalculate base values to ensure consistency
var baseInnerWidth = baseOuterWidth – (2 * baseWallThickness);
var baseInnerHeight = baseOuterHeight – (2 * baseWallThickness);
if (baseInnerWidth <= 0 || baseInnerHeight <= 0) {
baseInnerWidth = 1; // Prevent errors if inputs are bad
baseInnerHeight = 1;
}
var baseOuterArea = baseOuterWidth * baseOuterHeight;
var baseInnerArea = baseInnerWidth * baseInnerHeight;
var baseCrossSectionalAreaValue = baseOuterArea – baseInnerArea; // in mm²
var baseWeightPerMeterValue = (baseCrossSectionalAreaValue * baseDensity) / 1000000; // kg/m

for (var i = 1; i <= 10; i++) {
var len = (maxLengthForChart / 10) * i;
lengths.push(len.toFixed(1));
weights.push((baseWeightPerMeterValue * len).toFixed(2));
weightsPerMeterData.push(baseWeightPerMeterValue.toFixed(2)); // Constant for all points
}
// Add current length point if not already included
if (!lengths.includes(currentLength.toFixed(1))) {
lengths.push(currentLength.toFixed(1));
weights.push(currentTotalWeight.toFixed(2));
}

chartInstance = new Chart(ctx, {
type: 'line',
data: {
labels: lengths,
datasets: [{
label: 'Total Weight (kg)',
data: weights,
borderColor: 'var(–primary-color)',
backgroundColor: 'rgba(0, 74, 153, 0.2)',
fill: true,
tension: 0.1
}, {
label: 'Weight per Meter (kg/m)',
data: weightsPerMeterData, // Show constant WPM
borderColor: 'var(–success-color)',
backgroundColor: 'rgba(40, 167, 69, 0.2)',
fill: false,
tension: 0.1,
yAxisID: 'y-axis-wpm' // Assign to secondary axis
}]
},
options: {
responsive: true,
maintainAspectRatio: true,
scales: {
x: {
title: {
display: true,
text: 'Length (meters)'
}
},
y: {
title: {
display: true,
text: 'Total Weight (kg)'
},
beginAtZero: true
},
'y-axis-wpm': { // Configuration for the secondary y-axis
type: 'linear',
position: 'right',
title: {
display: true,
text: 'Weight per Meter (kg/m)'
},
grid: {
drawOnChartArea: false, // Only want the grid lines for primary y-axis
},
beginAtZero: true
}
},
plugins: {
tooltip: {
callbacks: {
label: function(context) {
var label = context.dataset.label || '';
if (label) {
label += ': ';
}
if (context.parsed.y !== null) {
label += context.parsed.y;
if (context.dataset.label === 'Total Weight (kg)') {
label += ' kg';
} else if (context.dataset.label === 'Weight per Meter (kg/m)') {
label += ' kg/m';
}
}
return label;
}
}
}
}
}
});
}

// Initialize chart on page load with default values
document.addEventListener('DOMContentLoaded', function() {
// Trigger calculation with default values on load
calculateWeight();

// Setup FAQ toggles
var faqQuestions = document.querySelectorAll('.faq-question');
faqQuestions.forEach(function(question) {
question.addEventListener('click', function() {
var faqItem = this.parentElement;
faqItem.classList.toggle('open');
});
});
});