Warehouse Structural Racking, ANSI/RMI MH16.1 Beam Deflection & Material Storage
Selective Pallet-Rack Beam Deflection (L/180) Formula
Calculate Uniform Load Per Front/Rear Step Beam (kN), Midspan Elastic Beam Deflection delta (mm), ANSI/RMI MH16.1 L/180 Serviceability Limit (mm), and Deflection Utilization (%).
Pallet-rack step beams are often governed by RMI L/180 midspan bow—before steel yield stress is ever reached!
Under ANSI/MH16.1 (Rack Manufacturers Institute, RMI) and EN 15512, two parallel roll-formed box/step beams spanning clear bay width `L` (mm, e.g. `2,700` mm for two Euro/GMA pallets) share total level payload equally (`W_beam = (N_pallets * m_pallet * g) / 2` N per beam, assuming symmetric front-to-back pallet overhang!). Treating end-connector clip stiffness conservatively as a simply supported uniform load gives Midspan Vertical Deflection `delta = (5 * W_beam * L^3) / (384 * E * I_y)` mm, which RMI caps strictly at `delta_max = L / 180` (`15.00` mm on a `2,700` mm span; `L / 200` in automated AS/RS racks!) so pallets never tilt dangerously toward the aisle or snag reach-truck fork tips!
Verify on a 2,700 mm Clear-Span Selective Rack Level Supporting Two 1,100 kg Pallets—Clear_Beam_Span `L` = 2,700.0 mm (B2 -> RMI `L/180` Limit = `15.00` mm in E4), Unit_Pallet_Mass = 1,100.0 kg (B3), Pallets_Per_Pair_Level = 2 (B4 -> Load Per Single Beam = `10.79` kN in E2), Single_Box_Beam_Moment_of_Inertia `I_y` = 215.0 cm⁴ (`2,150,000` mm⁴, B5), and Cold-Formed_Steel_Modulus `E` = 200.0 GPa (`200,000` MPa, B6): Midspan Deflection equals `6.43` mm (E3), utilizing `42.86%` of the RMI `L/180` ceiling (E5)!
| ANSI/RMI MH16.1 Rack Beam KPI (L=2,700 mm, 2x 1,100 kg Pallets, Iy=215 cm⁴) | Formula | Verified Output |
|---|---|---|
| Load Per Single Beam W_beam (kN) | (Pallet_kg * Pallets * 9.80665 / 2) / 1000 | 10.79 kN |
| Midspan Elastic Deflection (mm) | (5 * W_N * (L^3)) / (384 * E_MPa * Iy_mm4) | 6.43 mm (12.57 mm @ light 110 cm⁴ beam) |
| RMI MH16.1 L/180 Ceiling (mm) | Beam_Clear_Span_L_mm / 180 | 15.00 mm |
| Serviceability Deflection Used (%) | (Deflection_mm / RMI_Limit_mm) * 100 | 42.86% (83.78% @ light 110 cm⁴ beam) |
RMI MH16.1 Simply-Supported Pair-Beam Elastic Deflection Formula
Validate `Beam_Span L >= 900` mm, `Pallet_Mass > 0` kg, `Pallets_Per_Level >= 1`, `Single_Beam_Iy > 10` cm⁴ (convert `1` cm⁴ = `10,000` mm⁴!), and `Steel_Modulus E` in `[180, 220]` GPa (`1` GPa = `1,000` MPa)!
=LET(ln_m, B2, mp_k, B3, np_l, B4, iy_c, B5, em_g, B6, IF(OR(ln_m < 900, mp_k <= 0, np_l < 1, iy_c <= 10, em_g < 180, em_g > 220), "Invalid Rack Input", LET(wb_n, (mp_k * np_l * 9.80665) / 2, df_m, (5 * wb_n * (ln_m ^ 3)) / (384 * (em_g * 1000) * (iy_c * 10000)), lm_r, ln_m / 180, ROUND((df_m / lm_r) * 100, 2))))Light-Gauge 110 cm⁴ Step-Beam Substitution Check (Set Single-Beam Iy B5 = 110.0 cm⁴)
Downsize to a shallow light-gauge step beam with `I_y` B5 = 110.0 cm⁴: Midspan Bow E3 nearly doubles from `6.43` mm to `12.57` mm, pushing RMI Serviceability Utilization E5 to `83.78%` (and exceeding stricter `L/250 = 10.8` mm AS/RS crane-fork tolerances)!
=IF(ISTEXT(E5), E5, LET(wb_n, (B3 * B4 * 9.80665) / 2, ROUND((5 * wb_n * (B2 ^ 3)) / (384 * (B6 * 1000) * (B5 * 10000)), 2)))Try the example
Use the original values or change them to test your understanding.