# NAAMM MBG 534-12 Metal Bar Grating Engineering Design Manual

NAAMM 5GRATINGSNAAMM—MBG534-12November4,20125GRATINGSNAAMM—MBG534-12November4,2012METAL BAR GRATING MANUAL MBG 534 -12METAL BAR GRATING ENGINEERING DESIGN MANUAL MBG Metal Bar Grating A Division of NATIONAL ASSOCIATION OF ARCHITECTURAL METAL MANUFACTURERS This manual was developed by representative members of the Metal Bar Grating Division (MBG) of the National Association of Architectural Metal Manufacturers (NAAMM) to provide their opinion and guidance on the procedures used in design calculations for metal bar grating. This manual contains advisory information only and is published as a public service by NAAMM. NAAMM disclaims all liability of any kind for the use, application or adaptation of material published in this manual. Copyright © 2012 National Association of Architectural Metal Manufacturers All Rights Reserved METAL BAR GRATING ENGINEERING DESIGN MANUALPublished and distributed by the NATIONAL ASSOCIATION OF ARCHITECTURAL METAL MANUFACTURERS 800 ROOSEVELT ROAD, BLDG. C-312.GLEN ELLYN, IL 60137 Phone (630) 942-6591 Fax (630) 790-3095 website: www.naamm.orgNAAMM MBG 543-12 ENGINEERING DESIGN MANUAL 1 METAL BAR GRATING This manual sets forth procedures used in design calculations for metal bar grating. The load bearing capabilities and deflections of grating are based on the structural properties of the bearing bars and the number of bearing bars supporting the load. Grating is designed so that the allowable stresses of the metals used are not exceeded when the design loads are applied or, if deflection governs, the specified allowances for deflection are not exceeded. Metric properties, with sample calculations, are included for metric conversions. The concentrated, uniform and partially distributed uniform loads used in the calculations are modeled as static loads. Static loads are typically used to evaluate the functionality for live loading pedestrian load applications. Examples 1 – 5 on the following pages present the formulas used for calculating the load and deflection values of static loads. Heavy rolling loads are defined as Vehicular Loads. Examples 6 – 7 present the formulas used to calculate the values for welded and pressure locked gratings when subjected to vehicular loads. Example 8 presents the formulas used to calculate the values for riveted gratings subjected to vehicular loads. The Load Criteria presented for Vehicular Loads on page 12 is intended to serve as a guide for common vehicular applications. This criteria is not intended to be all-inclusive and if your application is not clearly represented by one of these options, contact NAAMM or your nearest NAAMM MBG member company for assistance in evaluating your specific application. NOMENCLATURE a = length of partially distributed uniform load or vehicular load, parallel with bearing bars, in. b = thickness of rectangular bearing bar, in. c = width of partially distributed uniform load or vehicular load, perpendicular to bearing bars, in. d = depth of rectangular bearing bar, in. Ac = distance center to center of main bars, riveted grating, in. Ar = face to face distance between bearing bars in riveted grating, in. Aw = center to center distance between bearing bars in welded and pressure locked gratings, in. C = concentrated load at midspan, pfw Dc = deflection under concentrated load, in. Du = deflection under uniform load, in. E = modulus of elasticity, psi F = allowable stress, psi I = moment of inertia, in4IH20 = moment of inertia of grating under H20 loading, in4Ib = I of bearing bar, in4Ig = I of grating per foot of width, in4In = moment of inertia of nosing, in4K = number of bars per foot of grating width, 12“/AwL = clear span of grating, in. (simply supported) 2 ENGINEERING DESIGN MANUAL NAAMM MBG 543-12 M = bending moment, Ib-in Mb = maximum M of bearing bar, Ib-in Mg = maximum M of grating per foot of width, Ib-in N = number of bearing bars in grating assumed to carry load NbH20 = number of main bearing bars under load H20 NcH20 = number of connecting bearing bars under load H20 Pb = load per bar, Ib Pu = total partially distributed uniform load, Ib PuH20 = wheel load, H20, Ib Pw = wheel load, lb S = section modulus, in3Sb = S of bearing bar, in3Sg = S of grating per foot of width, in3SH20b = section modulus at bottom of grating under H20 loading, in3Sn = section modulus of nosing, in3U = uniform load, psf ABBREVIATIONS in. = inch ft = foot Ib = pounds Ib-in = pound-inches pfw = pounds per foot of grating width psf = pounds per square foot psi = pounds per square inch NAAMM MBG 543-12 ENGINEERING DESIGN MANUAL 3 METAL PROPERTIES Allowable Design Yield Tensile Modulus of Stress Strength Strength Elasticity Material F psi Fy psi Fu psi E psi Steel ASTM A1011 CS Type B 18,000 30,000(1) 29,000,000 ASTM A1011 SS GR36 20,000 36,000 53,000 29,000,000 ASTM A36 20,000 36,000 58,000 29,000,000 Stainless Steel ASTM A666 Type 304 20,000 30,000 75,000 28,000,000 ASTM A666 Type 304L 16,500 25,000 70,000 28,000,000 ASTM A666 Type 316 20,000 30,000 75,000 28,000,000 ASTM A666 Type 316L 16,500 25,000 70,000 28,000,000 Aluminum ASTM B221 6061-T6 12,000 35,000 38,000 10,000,000 ASTM B221 6063-T6 12,000 25,000 30,000 10,000,000 METRIC Allowable Design Yield Tensile Modulus of Stress Strength Strength Elasticity Material F MPa Fy MPa Fu MPa E MPa Steel ASTM A1011M CS Type B 124.11 205(1) 200,000 ASTM A1011M SS GR250 137.90 250 365 200,000 ASTM A36M 137.90 250 400 200,000 Stainless Steel ASTM A666 Type 304 137.90 205 515 193,000 ASTM A666 Type 304L 113.77 170 485 193,000 ASTM A666 Type 316 137.90 205 515 193,000 ASTM A666 Type 316L 113.77 170 485 193,000 Aluminum ASTM B221M 6061-T6 82.74 240 260 69,000 ASTM B221M 6063-T6 82.74 170 205 69,000 (1) Based on many years of architectural metal experience. FORMULAS 1. Number of bearing bars per foot of width for welded grating K = 12/AW2. Section modulus of rectangular bearing bar Sb = bd2/6 in34 ENGINEERING DESIGN MANUAL NAAMM MBG 543-12 3. Section modulus of grating per foot of width Sg = Kbd2/6 in3 = KSb in34. Section modulus required for given moment and allowable stress S = M/F in35. Moment of inertia of rectangular bearing bar Ib = bd3/12 in4 = Sb d/2 in46. Moment of inertia of grating per foot of width Ig = Kbd3/12 in4 = Klb in47. Bending moment for given allowable stress and section modulus M = SF Ib-in The following formulas are for simply supported beams with maximum moments and deflec- tions occurring at midspan. 8. Maximum bending moment under concentrated load M = CL/4 Ib-in per foot of grating width 9. Concentrated load to produce maximum bending moment C = 4M/L Ib per foot of grating width 10. Maximum bending moment under uniform load M = UL2/(8 x 12) = UL2/96 Ib-in per foot of grating width 11. Uniform load to produce maximum bending moment U = 96M/L2 psf 12. Maximum bending moment due to partially distributed uniform load M = Pu (2L - a)/8 Ib-in 13. Maximum deflection under concentrated load Dc = CL3/48EIg in. 14. Moment of inertia for given deflection under concentrated load Ig = CL3/48EDc in415. Maximum deflection under uniform load Du = 5UL4/(384 x 12Elg) = 5UL4/4608EIg in. 16. Moment of inertia for given deflection under uniform load Ig = 5UL4/4608EDu in417. Maximum deflection under partially distributed uniform load Du = Pu((a/2)3 + L3 - a2 L/2)/48ElbN in. NAAMM MBG 543-12 ENGINEERING DESIGN MANUAL 5 SAMPLE CALCULATIONS Example 1 These calculations show the procedures used to prepare data for metal bar grating load tables. The concentrated midspan and uniform load bearing capabilities of W-19-4 (1-1/2 x 3/16) welded A1011 CS Type B carbon steel grating and the corresponding midspan deflections will be calculated. Allowable stress, F = 18,000 psi Modulus of elasticity, E = 29,000,000 psi Span, L = 54 in. Bearing bar spacing, Aw = 1.1875 in. Number of bearing bars per foot of width K = 12/Aw = 12/1.1875 = 10.105 Section modulus of grating per foot of width Sg = Kbd2/6 = 10.105 x 0.1875 (1.5)2/6 = 0.711 in3Moment of inertia of grating per foot of width Ig = Kbd3/12 = 10.105 x 0.1875 (1 .5)3/12 = 0.533 in4Maximum bending moment for grating per foot of width Mg = FSg = 18,000 x 0.711 = 12,800 Ib-in Concentrated Load Load, C = 4Mg /L = 4 x 12,800/54 = 948 pfw Defl, Dc = CL3/48Elg = 948 x (54)3/(48 x 29,000,000 x 0.533) = 0.201 in. Uniform Load Load, U = 96Mg /L2 = 96 x 12,800/(54)2 = 421 psf Defl, Du = 5UL4/4608Elg = 5 x 421 x (54)4/(4608 x 29,000,000 x 0.533) = 0.251 in. Concentrated Mid Span Load per foot of width Uniform Load per square foot 6 ENGINEERING DESIGN MANUAL NAAMM MBG 543-12 GRATING SELECTION Example 2 - Concentrated Load Required: A welded ASTM A36 steel grating Type W-22-4 to support a concentrated load, C, of 4,000 pounds per foot of width at midspan on a clear span of 8 -0“. Deflection, D, is not to exceed the 0.25“ recommended for pedestrian comfort. Allowable stress, F = 20,000 psi Modulus of elasticity, E = 29,000,000 psi Span, L = 96in. Bearing bar spacing, Aw = 1.375 in. K = 12/Aw = 12 / 1.375 = 8.727 For a span of 8 -0“, the minimum size bearing bar to sustain a 4,000 pfw load is: 3 x 3/8 Ig = Klb = 8.727 x 0.8438 = 7.364 in4 Sg = KSb = 4.909 in3C = 4Mg/L = 4 x F x Sg/96 = 4 x 20,000 x 4.909/96 = 4,091 pfw Dc = CL3/48Elg = 4,000 x (96)3/(48 x 29,000,000 x 7.364) = 0.345 in. Since this exceeds the recommended limitation, a grating with a larger moment of inertia is needed to keep the deflection less than 0.25 in. Ig = CL3/48EDc = 4,000 x (96)3/(48 x 29,000,000 x 0.25) = 10.17 in4Using the next larger size: 3-1/2 x 3/8 Ig = 8.727 x 1.3398 = 11.693 in4Sg = 8.727 x 0.7656 = 6.682 in3C = 4 x 20,000 x 6.682/96 = 5,568 pfw D = 5,568 x (96)3/(48 x 29,000,000 x 11.693) = 0.303 in. Deflection is directly proportional to load: Dc = 0.303 x 4,000/5,568 = 0.217 in. ≤ 0.25 in. OK