CAE303_Solution__5_F07

CAE303_Solution__5_F07 - CAE 303 FALL 2007 STRUCTURAL...

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Problem 1 load P = 6 change th F t 1: As show 650 kips (80% he section wi Figure 2(a). the column b n in Figure % from dead ithin W14 gr 18 ft 22 ft A B C P x The deform buckles abou So 1, W 14 x 99 d load and 2 roup so that Fig A B C P y ation when ut x-axis. olution Set 9, F y = 36 ks 0% form live the column gure1 40 ft La Su Su sam we # 5 si steel shape e load). Che is able to ca STRUCTU ateral support at upport condition upport condition me for both stron eak axes. Figure 2(b) the column e is used for ck if the colu rry the load URAL DESIG N Instruc B) n at A. at C is the ng and A B C P y x . The deform buckles abo r column AB umn is adeq . CAE 30 N I: STEEL S tor: J. Shen, P E-mail mation when out y-axis. 1 BC. Service quate. If not, 3 – FALL 200 STRUCTURE Ph.D.,P.E., S.E l: Shen@iit.ed n 07 ES E. du
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2 Solution: P r = P u = 1.2P D + 1.6P L = (1.2 x 80% +1.6 x 20%) (650) = 832 kips (LRFD) P r = P a = P D + P L = 650 kips (ASD) Column: W 14 x 99 r x =6.17 in. r y = 3.71 in. K x 1.0, K y =1.0, L y = the larger of L y1 (= 18 ft) and L y2 (= 22 ft) = 22 ft, L x = 40 ft x KL r ⎛⎞ ⎜⎟ ⎝⎠ = 1.0 40 12 77.8 6.17 ×× = (controls) y KL r = 1.0 22 12 71.2 3.71 = KL r = the larger of y KL r and x KL r = x KL r = 77.8 The column will buckle about X-Axis, as shown in Figure 2. KL 77.8 r = <4.71 29000 E 4.71 134 Fy 36 == 2 e 2 E F 47.2 (KL/r) π ksi F cr = y e F F y 0.658 F = (0.727)(36) = 26.2 ksi P n = F cr A g = (26.2) (29.1) = 761.3 kips We need to have: P c P r LRFD: P c = cn r P (0.9)(761.3) 685.2 kips < P 832 kips φ= = = ASD: P c = n r c P 761.3 455.9 kips < P 650 kips 1.67 = Ω Inadequate for both LRFD and ASD Let’s increase the weight of the W14 shape from W 14 x 99 to W 14 x 120 with F y =36 ksi Check W 14 x 120: Column: W 14 x 120 r x =6.24 in. r y = 3.74in. A g = 35.3in 2 K x = K y =1.0, L y1 = 18 ft, L y2 = 22 ft (controls) L x = 40 ft x KL r = 1.0 40 12 76.9 6.24 = (controls) y KL r = 1.0 22 12 70.6 3.74 =
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3 KL r ⎛⎞ ⎜⎟ ⎝⎠ = the larger of y KL r and x KL r = x KL r = 76.9 The column will buckle about X-Axis, as shown in Figure 2(a). KL 76.9 r = <4.71 29000 E 4.71 134 Fy 36 == 2 e 2 E F 48.4 (KL/r) π ksi F cr = y e F F y 0.658 F = 26.4 ksi P n = F cr A g = (26.4) (35.3) = 932 kips We need to have P c P n LRFD: P c = cn r P (0.9)(932) 839 kips > P 832 kips ϕ= = = ASD: P c = n r c P 932 558 kips < P 650 kips 1.67 = Ω W 14 x 120 is adequate for LRFD, BUT inadequate for ASD.
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This homework help was uploaded on 04/07/2008 for the course CAE 303 taught by Professor Shen during the Fall '08 term at Illinois Tech.

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CAE303_Solution__5_F07 - CAE 303 FALL 2007 STRUCTURAL...

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