Hollow Section Weight Calculator
Accurately calculate the weight of Rectangular (RHS), Square (SHS), and Circular (CHS) hollow sections using standard engineering formulas.
Formula Used: Weight = Volume × Density. Volume is calculated by subtracting the inner void volume from the outer volume based on the selected geometry.
Understanding the Hollow Section Weight Calculation Formula
In structural engineering and construction, accurately estimating the weight of materials is critical for logistics, cost estimation, and structural integrity analysis. The hollow section weight calculation formula is the mathematical foundation used to determine the mass of hollow steel profiles, including Rectangular Hollow Sections (RHS), Square Hollow Sections (SHS), and Circular Hollow Sections (CHS).
Whether you are a fabricator ordering steel or an engineer designing a truss, understanding how to apply the hollow section weight calculation formula ensures you avoid costly errors. This guide breaks down the math, variables, and practical applications of calculating hollow section weights.
What is the Hollow Section Weight Calculation Formula?
The hollow section weight calculation formula is derived from the basic physical principle that Mass equals Volume multiplied by Density ($$M = V \times \rho$$). For hollow sections, the challenge lies in accurately calculating the volume of the material itself, excluding the hollow air gap inside.
This calculation is essential for:
- Structural Engineers: To calculate dead loads on a structure.
- Quantity Surveyors: To estimate the tonnage of steel required for a project.
- Logistics Managers: To ensure transport vehicles are not overloaded.
A common misconception is that one can simply estimate weight based on outer dimensions. However, the wall thickness plays a massive role. A small change in thickness significantly impacts the final result of the hollow section weight calculation formula.
Formula and Mathematical Explanation
To calculate the weight, we first determine the Cross-Sectional Area ($$A$$) in square meters, multiply it by the Length ($$L$$) to get Volume ($$V$$), and finally multiply by the Material Density ($$\rho$$).
1. The General Formula
$$Weight (kg) = Area (m^2) \times Length (m) \times Density (kg/m^3)$$
2. Calculating Cross-Sectional Area (A)
The area formula changes based on the shape of the section:
Rectangular (RHS) & Square (SHS)
$$Area = (W \times H) – ((W – 2t) \times (H – 2t))$$
Where $$W$$ is outer width, $$H$$ is outer height, and $$t$$ is wall thickness.
Circular (CHS)
$$Area = \pi \times (R_{outer}^2 – R_{inner}^2)$$
Where $$R_{outer}$$ is half the diameter, and $$R_{inner} = R_{outer} – t$$.
Variables Table
| Variable | Meaning | Standard Unit | Typical Range |
|---|---|---|---|
| W / H | Outer Width / Height | Millimeters (mm) | 20mm – 500mm+ |
| t | Wall Thickness | Millimeters (mm) | 1.6mm – 20mm |
| L | Length | Meters (m) | 6m, 12m (Standard) |
| ρ (Rho) | Density | kg/m³ | 7850 (Steel) |
Practical Examples (Real-World Use Cases)
Example 1: Steel Column for a Carport (SHS)
Scenario: You need to install a support post using a Square Hollow Section (SHS). The post is 100mm x 100mm with a 4mm wall thickness, and it is 3 meters long. The material is Mild Steel.
- Inputs: Width=100mm, Thickness=4mm, Length=3m, Density=7850 kg/m³.
- Area Calculation: Outer Area = $$100 \times 100 = 10000 mm^2$$. Inner Area = $$(100-8) \times (100-8) = 8464 mm^2$$. Net Area = $$1536 mm^2$$ ($$0.001536 m^2$$).
- Weight Calculation: $$0.001536 m^2 \times 3m \times 7850 kg/m^3$$.
- Result: Approximately 36.17 kg.
Example 2: Stainless Steel Handrail (CHS)
Scenario: A handrail requires a Circular Hollow Section (CHS) with an outer diameter of 50mm and a thickness of 2mm. The total run is 10 meters. Material is Stainless Steel.
- Inputs: Diameter=50mm, Thickness=2mm, Length=10m, Density=8000 kg/m³.
- Area Calculation: $$R_{out} = 25mm$$, $$R_{in} = 23mm$$. Area = $$\pi \times (25^2 – 23^2) \approx 301.6 mm^2$$ ($$0.0003016 m^2$$).
- Weight Calculation: $$0.0003016 m^2 \times 10m \times 8000 kg/m^3$$.
- Result: Approximately 24.13 kg.
How to Use This Hollow Section Weight Calculator
Our tool simplifies the complex hollow section weight calculation formula into a few clicks. Follow these steps:
- Select Shape: Choose between RHS (Rectangle), SHS (Square), or CHS (Circle).
- Enter Dimensions: Input the outer dimensions (width/height/diameter) and the wall thickness in millimeters (mm).
- Set Length: Enter the total length of the section in meters (m).
- Choose Material: Select the material type (e.g., Mild Steel) to automatically apply the correct density.
- Review Results: The calculator instantly provides the total weight, weight per meter, and surface area.
Use the "Copy Results" button to save the data for your procurement list or engineering notes.
Key Factors That Affect Hollow Section Weight Results
When applying the hollow section weight calculation formula, several factors can influence the final accuracy and real-world weight:
1. Corner Radii (The "R" Factor)
In reality, cold-formed hollow sections (RHS/SHS) have rounded corners, not sharp 90-degree angles. This reduces the actual volume of material slightly compared to a theoretical sharp-corner calculation. Standard engineering tables often account for this, but pure geometric formulas may slightly overestimate weight.
2. Manufacturing Tolerances
Steel mills produce sections within specific tolerances (e.g., EN 10219 or ASTM A500). Wall thickness can vary by +/- 10%. A "5mm" thick tube might actually be 4.8mm or 5.2mm, affecting the total weight significantly over long distances.
3. Material Density Variations
While 7850 kg/m³ is the standard density for mild steel, different alloys vary. Stainless steel is denser (approx. 8000 kg/m³), while aluminum is much lighter (2700 kg/m³). Using the wrong density in the hollow section weight calculation formula will yield incorrect results.
4. Surface Coatings (Galvanization)
If the hollow section is hot-dip galvanized, zinc is added to the surface. This can add 3-5% to the total weight of the section, which is crucial for lifting and transport calculations.
5. Weld Seams
Welded hollow sections have an internal weld seam that adds a small amount of mass. While negligible for single beams, this adds up in large-scale structural steel projects.
6. Temperature
While thermal expansion affects dimensions, it rarely affects mass. However, calculating volume at extreme temperatures without adjusting for expansion coefficients can lead to minor dimensional discrepancies in precision engineering.