Question

For each of the following beams, state the expected flexural failure mode-plastic hinge, lateral torsional buckling (LTB), or local buckling The compression flange of each beam is traced at the locations marked with " "If the failure is by LTB. is it elastic or inelastic? Reference any charts or tables used and fully explain your answer. List any assumptions you have to make and be sure to consider in determining which limit state will control (a) The beam below is a W27x84 (Z = 244 in). A B 110 11 (b) The beam below is a W24x76 (Z = 200 in). A D B с 610 10 11 617 — (c) The beam below is a W21x55 (Z = 126 in). A B 12 it 12 ft

Answer 1

4 =1822 ft Ilft 11H Ignoring self weight of the beam from Part 3 of AISC Manual 6 = 1.32 For w 27 x 84 from AISC Manual) & 7.81ff L = 20.81 ft 46> Ly, so, there is elastic LT8. My = fer x SME GAME Er pt 0.078 Je 115/12s)* Sp ho ts

for w27 y su = 2.55 in J = 2.81 ho = 26.06 in Se = 213 in 22 x 12 2.55 Fer 1. 32 x 9 x 29000 22X12 2.55 2.818) If 0.078 x 213*26.06 42.05 ksi Mo - FerSx = 42.05 x 213 = 8956.65 kmin = 746.4 koff

Assuune fy = 50 KS Mp - Fyta = 50x244 = 12200 inok = 1616.6 fok Mr LMP ok, 6 P A B 6 ft 10ff 6 ff Ignoring self a weight of beam. from Parst 3 of Alse Manual G = 1.67 for AB and CD El for Be. C6 L = 10 ft. Assume ty = 50 ksi

5176 in Lr Loc 22tr for N248 76 S4= L = 6.78 lt = 19.52 ft Mo (Mp - 0.7 Fy Sox) ( LorLp is [Mp CMR Mp = ty ta = 50 x 200/12 = 883.33 kr ft

Ma =/10000 - 10.00 – 0. 7850 *176)( 10 -6.748 W الحداد B 7107 9029.45 inck (Mo Lp LLL Lr, there is in elastic LTB. 10 -6.78 19.52-6.78 4 = 12 ff 12 ff 12 ft Ignoring self weight of the beam from part 2 of AISC Manual G = 1.3 for N21 x 55 Lp = bill ft = 17.4ft Lo Sf = 110 in

SMP Ma = Go [Mo - (M. - 8. Ify Son) / Ly - Lp Lyrlp Mp = fy Zx = 50 x 126 = 6300 inost 13 6300 -(6800 -0.7850 x 110) = 6528 fork > Mp = 6 300 inak. = Mi 9 12-fill 17.4.Gill Mn = M = 6300 inak.