How is the theoretical weight per meter of a Q355B I-beam calculated, and what are the permissible weight tolerances?

The theoretical weight per meter of a Q355B I-beam is calculated based on its nominal cross-sectional dimensions and the density of steel. The standard density used in Chinese standards is 7.85 g/cm³ (7850 kg/m³). The formula is: Theoretical Weight (kg/m) = Cross-Sectional Area (cm²) × 0.785 (kg/(m·cm²)) or equivalently, = Area (m²) × 7850 kg/m³. The cross-sectional area (A) for an I-beam is calculated as: A = h*t1 + 2*b*t2 - 2*(t1+2r)*t2 + 0.8584*r² (accounting for web, two flanges, subtracting the overlapping regions at the web-flange junction, and adding the area of the fillets). In practice, designers and suppliers always refer to the tabulated "theoretical weight" values provided in GB/T 706-2016 for each specific section designation (e.g., HN 400x200x8x13 has a listed weight of 66.0 kg/m). Regarding weight tolerances, GB/T 706 specifies allowable deviations. The tolerance can be expressed in two ways: 1. Single Weight Tolerance: The deviation of the weight of any single piece from its theoretical weight should generally not exceed ±5% for normal rolled sections. 2. Batch Weight Tolerance: The deviation of the total weight of a shipment (batch or lot) from the total theoretical weight calculated from the total length and nominal unit weight should not exceed a certain percentage (e.g., ±2% or ±3%). The batch tolerance is typically stricter. These tolerances account for normal variations in rolling, such as slight deviations in thickness, width, and fillet radius, as well as the density of the scale (oxide layer). For structural fabrication, where weight impacts material costing and crane capacities, monitoring batch weight is common. Positive tolerance means the fabricator receives more steel than paid for (based on theory), and negative tolerance means less.