HW 6

HW 6 - Check for compactness. For the flange, 29, 000 50...

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Unformatted text preview: Check for compactness. For the flange, 29, 000 50 29, 000 50 lp=0.38 =9.152, Ar=l.0 =24.08 A = gif— = 9.92, 71,, < 2. < it, flange is noncompact (In the Dimensions and Properties tables, there is a footnote indicating that the flange of 3 W12 x 65 is noncompact.) The web is compact for all shapes in Part 1 of the Manual for F y 5 65 ksi. Compute the strength based on the limit state of flange local buckling. M = 52, = 50(96.8) = 4840 in.—kips M" = Mp — (Mp — outwith) A, —A,, = 4840 - (4840 — 0.7 x 50 x 87.9)(flz94958199-115522 ) = 4749 in.-kips = 395. 8 fi—kips (3.) Available strength = design strength = gin,an = 090(395. 8) = 356. 2 fi-kips Factored load moment: 311., = gm]? = gay-“(50): = 356.2 :s w” = 1.140 kips/fi . r , _1 mun—1,6(3wD) = 1.140 => WD = 0.1900 kips/fi ivé_ - .3 : 53;: 0: =96.«:;s 96k 961-: F1'_H_1'_fi ' £// f 6‘ f A 144k 48k 48k -48k Mu = 144(2) — 96(1) = 192 fi-kip From the ZJr table, 05an = ¢bM = 203 fi-kips > 192 fi-kips (OK) Check shear: i_ L _ 29,000 = W —51.6<2424 Fy _2.24{ 50 53.95 V" = 0.6FyAw = 0.6(50)(15.9 x 0.275) = 131.2 kips ¢vVn =1.0(131.2)=131ksi Vu = 144 kips > 131 kips (N .G.) Beam not adequate (¢v Vn can also be found in the Z, table.) (13) a = 60 kips [5—33] e I :r.nF3' (a) Pu = 1.2PD + 1.6PL = 1.6(18) = 28.8 kips (neglect beam wt. and check it later.) 28.8 k 1 2 l 3 4 Ffifiqfl } +++++ 4 14.4k 4Sp@2.5. 14.4k Compute CI, for center segment: MA = MC = 14.4(12.5) = 180.0ft—kips M3 = Mmax =14.4(15) = 216.0 fi-kips Cb = 12.5Mmax 2.5Mmax + 3MA + 4MB + 3MC = 12.5(216) :1 087 2.5(216)+3(180)+4(216)+3(180) ' Mu = A6— = 199 fi-kips Enter the beam de51gn charts Wlth Lb = 10 ft and Cb 1_og7 Try a W16 x 40 a5an = 229 fi-kips for C1, = 1.0. For C], = 1.087, (fian = 1.087(229) = 249 fi-kips > 216 ft-kips (OK) ¢bMp = 274 ft—kips > 249 ft-kips (OK) Check beam weight: [5—44] Mu = 216 + %(1.2 X 0.040)(30)2 = 221 ft—kips <249 fi-kips 2&8 + 1.2(0.04o (30 :15 mp5 2 . Check shear: Vu = 2 From the Zx table, div V" = 146 kips > 15.1 kips (OK) (b) Pa = P3 + PL = 18 kips (neglect beam wt. and check it later.) (OK) ...
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HW 6 - Check for compactness. For the flange, 29, 000 50...

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