Steel theoretical mass calculation formula

**Steel Theoretical Mass Calculation Formula** Understanding the theoretical mass of steel is essential for engineering, construction, and material estimation. These formulas provide a way to calculate the weight per meter or per square meter of various steel sections based on their dimensions. While these calculations are widely used for preliminary estimations, it’s important to note that they may have a small margin of error (typically around 0.2% to 0.7%) compared to actual measurements. Always cross-check with real-world data when precision is critical. --- ### **1. Round Steel Wire Rod** - **Unit:** kg/m - **Formula:** $ w = 0.006165 \times d^2 $ - Where $ d $ is the diameter in mm - **Example:** A round steel rod with a diameter of 80 mm has a mass per meter of: $$ 0.006165 \times 80^2 = 39.46\, \text{kg} $$ --- ### **2. Rebar** - **Unit:** kg/m - **Formula:** $ w = 0.00617 \times d^2 $ - Where $ d $ is the section diameter in mm - **Example:** A rebar with a diameter of 12 mm has a mass per meter of: $$ 0.00617 \times 12^2 = 0.89\, \text{kg} $$ --- ### **3. Square Steel** - **Unit:** kg/m - **Formula:** $ w = 0.00785 \times d^2 $ - Where $ d $ is the edge width in mm - **Example:** A square steel bar with an edge width of 30 mm has a mass per meter of: $$ 0.00785 \times 30^2 = 7.07\, \text{kg} $$ --- ### **4. Flat Steel** - **Unit:** kg/m - **Formula:** $ w = 0.00785 \times d \times b $ - Where $ d $ is the side width and $ b $ is the thickness in mm - **Example:** A flat steel plate with a width of 40 mm and thickness of 5 mm has a mass per meter of: $$ 0.00785 \times 40 \times 5 = 1.57\, \text{kg} $$ --- ### **5. Hexagonal Steel** - **Unit:** kg/m - **Formula:** $ w = 0.006798 \times d^2 $ - Where $ d $ is the distance between opposite sides in mm - **Example:** A hexagonal steel bar with a side distance of 50 mm has a mass per meter of: $$ 0.006798 \times 50^2 = 17.0\, \text{kg} $$ --- ### **6. Octagonal Steel** - **Unit:** kg/m - **Formula:** $ w = 0.006798 \times d^2 $ - Where $ d $ is the distance between opposite sides in mm - **Example:** An octagonal steel bar with a side distance of 80 mm has a mass per meter of: $$ 0.006798 \times 80^2 = 43.5\, \text{kg} $$ --- ### **7. Equal Angle Steel** - **Unit:** kg/m - **Formula:** $$ w = 0.00785 \times [d(2b - d) + 0.215(R^2 - 2r^2)] $$ - Where $ b $ is the side width, $ d $ is the edge thickness, $ R $ is the inner arc radius, and $ r $ is the end arc radius - **Example:** For a 4mm x 20mm equal angle steel, with $ R = 3.5 $, $ r = 1.2 $: $$ 0.00785 \times [4(2 \times 20 - 4) + 0.215(3.5^2 - 2 \times 1.2^2)] = 1.15\, \text{kg} $$ --- ### **8. Unequal Angle Steel** - **Unit:** kg/m - **Formula:** $$ w = 0.00785 \times [d(B + b - d) + 0.215(R^2 - 2r^2)] $$ - Where $ B $ is the long side width, $ b $ is the short side width, $ d $ is the edge thickness, $ R $ is the inner arc radius, $ r $ is the end arc radius - **Example:** For a 30mm x 20mm x 4mm unequal angle steel, with $ R = 3.5 $, $ r = 1.2 $: $$ 0.00785 \times [4(30 + 20 - 4) + 0.215(3.5^2 - 2 \times 1.2^2)] = 1.46\, \text{kg} $$ --- ### **9. Channel Steel** - **Unit:** kg/m - **Formula:** $$ w = 0.00785 \times [hd + 2t(b - d) + 0.349(R^2 - r^2)] $$ - Where $ h $ is height, $ b $ is leg length, $ d $ is waist thickness, $ t $ is average leg thickness, $ R $ is inner arc radius, $ r $ is end arc radius - **Example:** For an 80mm x 43mm x 5mm channel steel, with $ t = 8 $, $ R = 8 $, $ r = 4 $: $$ 0.00785 \times [80 \times 5 + 2 \times 8 \times (43 - 5) + 0.349(8^2 - 4^2)] = 8.04\, \text{kg} $$ --- ### **10. I-Beam** - **Unit:** kg/m - **Formula:** $$ w = 0.00785 \times [hd + 2t(b - d) + 0.8584(R^2 - r^2)] $$ - Where $ h $ is height, $ b $ is leg length, $ d $ is waist thickness, $ t $ is average leg thickness, $ R $ is inner arc radius, $ r $ is end arc radius - **Example:** For a 250mm x 118mm x 10mm I-beam, with $ t = 13 $, $ R = 10 $, $ r = 5 $: $$ 0.00785 \times [250 \times 10 + 2 \times 13 \times (118 - 10) + 0.8584(10^2 - 5^2)] = 42.2\, \text{kg} $$ --- ### **11. Steel Plate** - **Unit:** kg/m² - **Formula:** $ w = 7.85 \times t $ - Where $ t $ is the thickness in mm - **Example:** A steel plate with a thickness of 6 mm has a mass per square meter of: $$ 7.85 \times 6 = 47.1\, \text{kg} $$ --- ### **12. Steel Pipe** - **Unit:** kg/m - **Formula:** $ w = 0.02466 \times S \times (D - S) $ - Where $ D $ is the outer diameter, $ S $ is the wall thickness - **Example:** A seamless steel pipe with an outer diameter of 60 mm and a wall thickness of 4 mm has a mass per meter of: $$ 0.02466 \times 4 \times (60 - 4) = 5.52\, \text{kg} $$ --- **Note:** These formulas are based on standard steel density of 7.85 g/cm³. They are intended for reference and estimation only. Actual weights may vary slightly due to manufacturing tolerances and material composition. For precise applications, always consult official standards or perform direct measurements. *Source: Hardware Business Network Information Center | http://news.chinawj.com.cn*

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