(Answered): Question 56. Use tables for reference. 56. Find the least weight Douglas fir-larch, No. 1 grade, sec ...

56. Find the least weight Douglas fir-larch, No. 1 grade, section that can be used for a span of 18 ft [5.49 m] with a total uniformly distributed load of 8 kips [44.5 kN]. Investigate the deflection. TABLE A.8 Properties of Structural Lumber Bending Axis Y-YAsis Weight at Area Modulus of Inertia Modulus of Inertia Density bxh (in.2) (in3) i.)(in.) (in) (lbn) JXAxis Section Moment Section Moment 35 Dimensions (in.) Nominal Actual bxh 2x3 1.5x2.5 3.75 1.563 193 0938 0.703 0911 2x4 1.5x3.5 525 3.063 5359 1313 0984 1.276 2x6 1.5x5.5 825 7.563 20.80 2.063 1.547 2.005 2x8 1.5x7.25 10.88 13.14 47.63 2.719 2.039 2.643 2x10 1.5x9.2S 13.88 21.39 98.93 3469 2.602 3.372 2x12 1.5x 11.25 16.88 31.64 178.0 4219 3.164 4.102 2x14 1.5x13.25 19.88 43.89 290.8 4969 3.727 483 3x4 2.5x3.5 8.75 5.104 8.932 3.646 4.557 2.127 3x6 2.5x5.5 13.75 12.60 34.66 5.729 .161 3.342 x8 2.5x7.25 1813 21.90 79.39 7.552 9440 4405 3x 10 2.5x9.25 23.13 3565 1649 9635 12.04 5,621 3x12 2.5×11.25 28.13 52.73 296.6 11.72 14.65 6836 conrinied) TABLE 5.1a Reference Design Values for Visually Graded Lumber of Douglas Fir-Larch (Values in psi) Species and Commercial Member Size Tension Shear Compression Compression and Use Bending. Parallel to Parallel to Perpendicular Parallel to Modulus of Elasticity Classification F Grain, F, Grain, F, to Grain, F Grain, F Emi Dimension Lsanber 2-4 tn. thick Select structural No. 1 and better No. 1 No. 2 No. 3 Stud 2 in. and wider 1500 1200 1000 1000 180 180 180 180 1700 1,900,000 690,000 1550 1,800,000 660,000 1500 1,700,000 620,000 1350 1,600,000 580,000 775 1,400,000 510.000 850 1,400,000 10,000 625 625 575 700 180 Dense select structural Beams and stringers 1900 100 170 170 450 1300 1,700,000 620,000 1100 1.600,000 580,000 1100 1,700,000 620,000 925 ,600,000 580,000 600 1,300,000 470,000 1350 1,700,000 620,000 1150 1,600,000 580,000 1200 1.700,000 620,000 1000 1,600,000 580,000 700 1,300,000 470,000 730 Select structural Dense No. No. I No. 2 1600 1550 1350 875 950 625 425 Select structural Dense No.1 No. 1 No. 2 170 Dense select structuralPosts and timbers 1750 1150 10 170 170 170 170 1500 1000 950 750 475 Select Dex Commercial Dex 1750 1450 1,800,000 660,000 1,700,000 620,000 Source: Data adapted from National Desigs Spocification(NDSfor Wood Construction, 2005 edition (Ref.3), with permission of the publisher, American Forest nd Paper Aisociation. The tables in the reference document have data for many other spocies and also have extensive footnotes Vlus listelare for teferenic in detertrining design use values subjsct to vanious modincations See Table 3.2 for size adjustment factors for dimension lumber TABLE A.8 (Continued) X-X Axis Y-Y Axis Weight at Section Moment Section Moment 35 Ib/ft Area Modulus of Inertia Modulus of Inertia Density Dimensions (in.) Nominal Actual bxh (in2) (in.) n. (n2) (in (lb/f) 3x14 2.5x 13.25 33.13 73.15 484.6 13.80 7.2 8.051 3x 16 2.5x 15.25 38.13 96.90 738.9 15.89 1986 9.266 4x4 3.5x3.5 12.25 7.146 12.51 7.146 12.51 2977 4x6 3.5x5.5 19.25 17.65 4853 11.23 19.65 4.679 4x8 3.5×725 25.38 30.66 111.1 14.80 25.9 6.168 4x 10 3.5x 9.25 32.38 49.91 2308 18.89 33.05 7.869 4x12 3.5x11.25 39.38 73.83 415.3 2297 40.20 9.570 4x14 3,5x 13.25 46.38 1024 678.5 27.05 47.34 11.27 4x 16 3.5x 15.25 53.38 135.7 1034 5x5 4.5x4.5 20.25 15.19 34.17 15.19 34.17 4922 6x6 5.5x5.5 30.25 27.7376.26 27.73 76.26 7.352 6x8 5.5x7.5 41.25 51.56 1934 37.81 104.0 10.03 6x10 5.5×9.5 52.25 8273 393.0 47.90 131.7 12.70 6x 12 5.5x 11.5 63.25 121.2 697.1 57.98 159.415.37 6x14 5.5x 13.5 74.25 167.11128 6x16 5.5x 15.5 85.25 220.2 1707 6x18 5.5x 17.5 96.25 280.7 2456 6x20 5.5x 19.5 1073 348.6 3398 6x 22 5.5x21.5 118.3 423.7 4555 108.4 298.I 28.74 6x 24 5.5x23.5 129.3 506.2 5948 118.5 325.8 3141 8x8 7.5x7.5 56.25 70.31 263.7 70.31 263.7 13.67 8x 10 7.5x9.5 71.25 112.8 53.9 89.06 334.0 17.32 8x12 7.5x 11.5 86.25 165.3 950.5 107.8 4043 20.96 8x14 7.5x13.5 101.3 2278 1538 126.6 474.6 24.61 8x 16 7.5x 15.5 116.3 300.3 2327 145.3 544.9 28.26 8x18 7.5x17.5 1313 382.8 3350 64. 6152 31.90 8 x 20 7.5x19.5 146.3 475.3 4634 182.8 685.5 35.55 8x22 7.5x21.5 161.3 577.8 6211 201.6 755.9 39.19 8 x24 7.5x23.5 176.3 690.3 811 220.3 826.2 42.84 10x10 9.5x9.5 90.25 142.9 678.8 142.9 678.8 21.94 10x 12 9.5x 11.5 109.3 209.4 1204 173.0 821.726.55 10x14 9.5x13.5 128.3 288.6 1948 203.1 964.5 31.17 10x 16 9.5x15.5 147.3 380.4 2948 233.1 1107 10x 18 9.5x 17.5 166.3 484.94243263.2 1250 10x20 9.5x 19.5 1853 602.1 5870 293.3 1393 10×22 9.5×21.5 204.3 731.9 7868 323.41536 10x24 9.5x23.5 223.3 874.4 10270 353.5 1679 31.14 54.49 12.97 187.2 18.05 20.72 88.23 242.6 23.39 98.31 270.4 26.07 78.15 214.9 1 45.03 49.64 54.26 TABLE A.8 (Continued) X-X Axis Y-Y Axis Weight at Section Moment Section Moment 35 Tb/ft Area Modulus of Inertia Modulus of Inertia Density Dimensions (in.) Nominal Actual A bxh bxh (in.2) (in.3) (in*) (in.3) (in*) (h/ft) 12x12 11.5x11.5 132.3 253.5 1458 253.5 1458 2358 297.6 1711 12x16 11.5x15.5 178.3 460.5 3569 341.6 1964 12x18 11.5x17.5 201.3 587.0 5136 385.7 2218 12x20 11.5x19.5 224.3 728.8 7106 429.8 2471 12x22 11.5x21.5 247.3 886.0 9524 473.9 2725 12x24 11.5x23.5 270.3 1058 12440 518.0 2978 14x14 13.5x13.5 182.3 410.1 2768 410.1 2768 14x 16 13.5x15.5 209.3 540.6 4189 470.8 3178 14x 18 13.5x17.5 236.3 689.1 6029 531.6 3588 14x20 13.5x 19.5 263.3 855.6 8342 92.3 3998 14x22 13.5×21.5 290.3 1040 11180 653.14408 14x24 13.5 x 23.5 317.3 1243 14600 713.8 48s 16x 16 15.5x15.5 240.3 620.6 4810 620.6 4810 16x 18 1S.5x 17.5 271.3 791.1 6923 700.7 5431 16x20 15.5x 19.5 302.3 982.3 9578 780.8 6051 16×22 15.5×21.5 333.31194 12840 860.96672 16x24 15.5x 23.5 364.3 1427 16760 941.0 7293 18x 18 17.5x17.5 306.3 893.2 7816 893.2 7816 18 x20 17.5x 19.5 341.3 1109 10810 995.3 8709 18×22 17.5 x21.5 376.3 1348 14490 1097 9602 18×24. 17.5×23.5 411.3 1611 18930 1199 10500 20×20 19.5 × 19.5 380.3 1236 12050 1236 12050 12x 14 11.5x13.5 1S5.3 349.3 37.73 43.32 48.91 54.51 60.10 65.69 44.30 50.86 5742 63.98 70.55 58.39 73.46 81.00 74.44 82.94 91.45 99.96 92.42 20 x 22 19.5x 21.5 419.3 1502 16150 1363 13280 101.9 20x 24 19.5x23.5 458.3 1795 21090 1489 14520 22x22 21.5x21.5 462.3 1656 17810 1656 17810 22 x 24 21.5x23.5 505.3 1979 23250 1810 19460 24×24 23.5×23.5 552.3 2163 25420 2163 25420 112.4 122.8 134.2 Source: Compiled from data in the National Design Specification for Wood Construction (Ret. 3). with permission of the publisher, American Forest and Paper Association.