WIXLIB

W/D, M/D, A/P TablesIssued: June 7, 2007

FIRE PROTECTION SYSTEMSW/D, A/P and M/D TABLES FOR STRUCTURAL STEEL SECTIONSW/D, A/P and M/D ratios provide a means of sizing structural members for the purpose of fire protection.Fire rated designs specify minimum steel sizes to which the rating information applies. The fire resistanceratings are applicable to larger structural components – those having greater W/D, A/P or M/D ratios thanthe member tested. Generally, as the W/D, A/P and M/D ratio increases, fire resistance increases and/orthe required thickness of directly applied fire protection material decreases for a given rating.For Imperial sizesFor Imperial shapesFor Metric sizes:W/D M/D x 0.017WDAPMD Weight of steel section (lb./ft)Heated perimeter of steel section in inches (in.)Cross sectional area of steel section (in2)Heated perimeter of steel section in inches (in.)Mass of steel section (kg/m)Heated perimeter of steel section in metres (m)M/D W/D / 0.017A/P W/D x 144 / 490The heated perimeter, D or P, is that portion of the perimeter of the steel cross section that could beexposed to fire. It depends on the dimensions of the steel section and its orientation to the fire. Beamssupporting a floor or roof are assumed to be exposed to fire on “three” sides - the bottom and two sides.Columns and some bracing members are assumed to be exposed to fire on “four” sides or the perimeterof round members. These tables include W/D, M/D and A/P values for both three sided (beam) and foursided (column) exposures.When required, the mass, weight or cross sectional area of steel section can be read from structural steeltables. When the cross sectional area of a steel section is known, its mass or weight can be calculated bymultiplying that area by the density of steel (7850 kg/m3 or 490 lb/ft3).ExamplesFor a W shaped section, the heated perimeter is calculated as follows:a) Beam, three sides exposed to fireD 2d 3b – 2wWhere: d depth of sectionb flange widthw web thicknessNote: Certain applications, such as the equation for “Adjustment of Thickness of SprayedProtection for Beams of Alternate Size” in ULC’s, ‘List of Equipment and Materials’, ignore theweb thickness (w) and calculate D 2d 3b.b) Column, four sides exposed to fireD 2d 4b – 2wWhere: d depth of sectionb flange widthw web thicknessValues of D and P may likewise be calculated for other shapes and orientations by considering theperimeter or surface area of the steel section and that portion of which could be exposed to fire.How May W/D, M/D and A/P Rations be Used?When the size of a structural member differs from the minimum size specified in a fire test design,compare the W/D, M/D or A/P ratios. If the W/D, M/D or A/P is greater than or equal to that of the testdesign, the fire resistance rating and method of protection (minimum thickness, etc.) are applicable to thatmember.The UL “Fire Resistance Directory” and ULC “List of Equipment and Materials” contain equations foradjusting thickness of directly applied fire resistive materials for beams and columns of alternate size. Theratios from the attached tables may be substituted directly into those equations. Some fire resistancedesigns include proprietary thickness equations that utilize W/D, M/D and/or A/P ratios.USA: 1-800-848-4645 or 314-644-1000, www.carboline.comCanada: 1-800-263-4087 or 416-292-2361, www.adfire.com1

STRUCTURAL STEEL SHAPESHeated Perimeter (D) Calculations-L (ANGLE) SHAPESColumn: D 2d 2b1h[1r Column: D 2b 2h b : 1RETANGULARBeam: D 2b htROUNDD 7t X dSQUAREColumn: D 4bBeam: D 3bHSS SHAPES/STRUCTURAL TUBINGNote: For 3-sided (beam) MID or WID, member is assumed to be oriented with longer dimension vertical.

W SHAPESSIZE(mm x kg/m)W 1100 x 499x 433x 390x 342W 1000 x 883x 748x 642x 591x 584x 554x 539x 494x 486x 483x 443x 415x 412x 393x 371x 350x 321x 314x 296x 272x 249x 222W 920 x 1188x 967x 784x 653x 585x 534x 488x 446x 417x 387x 381x 365x 345x 342x 313x 289x 271x 253x 238x 223x 201W 840 x 527x .712.702.692.972.95SIZE(in. x lb./ft.)W 44 x 335x 290x 262x 230W 40 x 593x 503x 466x 431x 397x 392x 372x 362x 331x 327x 324x 321x 297x 278x 277x 264x 249x 235x 215x 211x 199x 183x 174x 167x 149W 36 x 848x 798x 650x 527x 439x 393x 359x 328x 300x 280x 260x 256x 245x 232x 230x 210x 194x 182x 170x 160x 150x 135W 33 x 387x 354x 71061061061051051171161153

W SHAPES continued METRICColumnHeatedSIZEM/DPerimeter(mm x kg/m)(m)W 840 x 4331293.34x 3921183.31x 3591083.31x 3291003.29x 29991.43.27x 25188.02.85x 22679.22.85x 21074.22.83x 19368.42.82x 17662.62.81W 760 x 5821813.20x 4841533.15x 4341393.12x 3891253.10x 3501133.08x 3141023.07x 28493.13.05x 25784.53.04x 22084.92.59x 19675.92.58x 18571.92.57x 17367.52.56x 16163.12.55x 14757.82.54x 13452.92.53W 690 x 8022583.10x 5481852.96x 5001702.94x 4571572.91x 4191442.89x 3841332.87x 3501222.85x 3231132.84x 2891022.81x 26594.32.81x 24086.02.79x 21778.02.78W 610 x 19280.32.39x 17071.42.38x 15264.12.37x 14059.32.36x 12553.42.34x 5512012.73x 4981842.70x 4551702.67x 4151562.65x 3721412.63x 3411302.61x E(in. x lb./ft.)W33 x 291x 263x 241x 221x 201x 169x 152x 141x 130x 118W 30 x 477x 391x 357x 326x 292x 261x 235x 211x 191x 173x 148x 132x 124x 116x 108x 99x 90W 27 x 539x 448x 368x 336x 307x 281x 258x 235x 217x 194x 178x 161x 146W 24 x 129x 114x 102x 94x 84x 492x 408x 370x 335x 306x 279x 250x 229x 90.889.789.088.187.64

W SHAPES continued METRICColumnHeatedSIZEM/DPerimeter(mm x kg/m)(m)W 610 x 2851102.57x 2621022.55x 24194.52.55x 21785.42.54x 19577.32.52x 17469.62.50x 15562.22.49x 15371.82.13x 14065.72.13x 12558.92.12x 11353.52.11x 10148.02.10x 9248.41.90x 9143.72.08x 8440.32.08x 8243.31.89W 530 x 3001252.40x 2721142.38x 2481052.36x 21992.72.36x 19683.72.34x 18278.12.33x 16571.12.32x 15064.92.31x 13871.81.92x 12364.31.91x 10957.31.90x 10153.41.89x 9248.91.88x 8549.71.71x 8243.81.87x 7443.51.70x 7238.71.86x 6639.01.69W 460 x 2601222.13x 2351112.11x 2131012.09x 19392.72.08x 17785.52.07x 15876.62.06x 14470.22.05x 12862.72.04x 11355.92.02x 10662.71.69x 9757.71.68x 8953.21.67x 8249.31.66x 471.47SIZE(in. x lb./ft.)W24 x 192x 176x 162x 146x 131x 117x 104x 103x 94x 84x 76x 68x 62x 55W 21 x 201x 182x 166x 147x 132x 122x 111x 101x 93x 83x 73x 68x 62x 57x 50x 44W 18 x 311x 283x 258x 234x 211x 192x 175x 158x 143x 130x 119x 106x 97x 86x 76x 71x 65x 60x 55x 9.268.668.167.867.358.057.657.557.156.85

W SHAPES continued METRICColumnHeatedSIZEM/DPerimeter(mm x kg/m)(m)W 460 x 6844.71.52x 6740.61.65x 6137.11.64x 6039.71.51x 5234.81.49W 410 x 14978.81.89x 13270.21.88x 11461.21.86x 10054.01.85x 8555.11.54x 7448.31.53x 6744.01.52x 6039.71.51x 5436.01.50x 4634.01.35x 3928.81.35W 360 x 10863952.80x 9903652.75x 9003392.70x 8183122.66x 7442892.61x 6772672.58W 360 x 6342532.55x 5922382.52x 5512242.50x 5092092.48x 4631922.45x 4211772.42x 3821622.40x 3471482.38x 3141352.35x 2871252.34x 2621152.32x 2371042.30x 21696.22.29x 19690.52.21x 17982.92.20x 16275.32.19x 14769.12.18x 13463.12.17x 12271.71.73x 11065.01.72x 10160.21.71x 9154.41.70x 7953.61.51x 7248.61.50x 6443.81.49x 5741.01.39x 5136.91.38x 4532.81.37x 3932.21.21x 3327.71.19W 310 x 451.301.291.291.221.211.201.081.071.78SIZE(in. x lb./ft.)W 18 x 46x 40x 35W 16 x 100x 89x 77x 67x 57x 50x 45x 40x 36x 31x 26W 14 x 808x 730x 665x 605x 550x 500x 455x 426x 398x 370x 342x 311x 283x 257x 233x 211x 193x 176x 159x 145x 132x 120x 109x 99x 90x 82x 74x 68x 61x 53x 48x 43x 38x 34x 30x 26x 22W 12 x 549.247.046.946.641.441.269.36

W SHAPES continued METRICColumnHeatedSIZEM/DPerimeter(mm x kg/m)(m)W 310 x 4542202.09x 4152042.06x 3751872.03x 3421732.01x 3131601.99x 2831461.96x 2531321.94x 2261201.92x 2021081.90x 17996.71.88x 15886.11.86x 14378.31.85x 12971.51.84x 11865.41.83x 10759.51.82x 9754.11.82x 8654.31.62x 7950.11.61x 7453.11.42x 6747.91.41x 6042.91.40x 5240.31.29x 4535.11.28x 3930.71.27x 3332.31.02x 3124.61.26x 2827.71.01x 2424.01.00x 2121.01.00W 250 x 1671061.60x 14995.81.58x 13185.21.56x 11575.31.55x 10167.11.53x 8959.71.52x 8053.81.51x 7349.21.50x 6752.11.31x 5845.61.30x 4938.81.29x 4540.51.11x 3935.41.10x 3330.21.09x 2830.60.915x 2527.40.910x 2422.21.08x 2224.30.904x 1820.00.896W 200 x 10079.91.27x 8670.11.25x 7158.81.24x 5949.41.22x 5243.81.21x 1.021.011.00SIZE(in. x lb./ft.)W 12 x 305x 279x 252x 230x 210x 190x 170x 152x 136x 120x 106x 96x 87x 79x 72x 65x 58x 53x 50x 45x 40x 35x 30x 26x 22x 19x 16x 14W 10 x 112x 100x 88x 77x 68x 60x 54x 49x 45x 39x 33x 30x 26x 22x 19x 17x 15x 12W 8 x 67x 58x 48x 40x 35x .736.331.331.331.030.640.740.239.739.038.638.67

W SHAPES continued METRICColumnHeatedSIZEM/DPerimeter(mm x kg/m)(m)W 200 x 4240.01.06x 3634.81.05x 3133.80.943x 2728.90.934x 2227.20.808x 2122.60.928x 1923.60.802x 1518.90.791W 150 x 3741.00.924x 3033.30.913x 2434.30.715x 2225.40.900x 1826.10.702x 1420.10.691x 1318.80.687W 130 x 2837.70.760x 2432.20.750W 100 x ZE(in. x lb./ft.)W 8 x 28x 24x 21x 18x 15x 13x 10W 6 x 25x 20x 16x 15x 12x9x 8.5W 5 x 19x 16W 4 x .822.622.724.524.119.4M SHAPESSIZE(mm x kg/m)M 310 x 17.6x 16.1x 14.9M 250 x 13.4x 11.9x 11.2M 200 x 9.7x 9.2M 150 x 6.6x 5.5M 130 x 28.1M 100 x 730.5730.4390.4480.6190.478SIZE(in. x lb./ft.)M 12 x 11.8x 10.8x 10M 10 x 9.0x 8.0x 7.5M 8 x 6.5x 6.2M 6 x 4.4x 3.7M 5 x .027.427.427.422.222.417.017.223.918.2HP SHAPESSIZE(mm x kg/m)M/DHP 360 x 174x 152x 132x 108HP 310 x 125x 110x 94x 79HP 250 x 85x 62HP200 x 91.781.531.521.501.491.261.241.01SIZE(in. x lb./ft.)HP 14 x 117x 102x 89x 73x 84x 74x 63x 53HP 10 x 57x 42HP 8 x 58

S SHAPESSIZE(mm x kg/m)S 610 x 180X 158S 610 x 149x 134x 119S 510 x 143x 128S 510 x 112x 98.2S 460 x 104x 81.4S 380 x 74x 64S 310 x 74x 60.7S 310 x 52x 47S 250 x 52x 38S 200 x 34x 27S 150 x 26x 19S 130 x 15S 100 x 14.1x 11S 75 x 80.5530.5470.4710.4000.3980.3260.320SIZE(in. x lb./ft.)S 24 x 121x 106x 100x 90x 80S 20 x 96x 86x 75x 66S 18 x 70x 54.7S 15 x 50x 42.9S 12 x 50x 40.8x 35x 31.8S 10 x 35x 25.4S 8 x 23x 18.4S 6 x 17.25x 12.5S 5 x 10S 4 x 9.5x 7.7S 3 x 7.5x 31.731.526.025.820.420.217.314.514.411.811.6WWF SHAPESSIZE(mm x kg/m)2000 x 732x 648x 607x 5421800 x 700x 659x 617x 575x 5101600 x 622x 580x 538x 496x 4311400 x 597x 513x 471x 4.824.674.424.424.424.27SIZE(in. x lb./ft.)79 x 490x436x 408x 36471 x 470x 442x 415x 388x 34463 x 419x 388x 361x 333x 28955 x 402x 344x 316x .5W/D2.221.981.851.692.292

Jun 07, 2007 · For Metric sizes: M Mass of steel section (kg/m) . Beam: D 3b ROUND D 7t X d HSS SHAPES/STRUCTURAL TUBING t Note: For 3-sided (beam) MID or WID, member is assumed to be oriented with longer dimension vertical. 3 W SHAPES METRIC IMPERIAL Co