Question

Problem 2. A steel beam has the dimensions shown, and yield stress Fy = 36 ksi. 12" 1.5" a. Find the elastic properties A, yes (from the top), Ixx, lwy, Stop, Shot. b. Find the moment, M., (in inch-kips) needed to just cause first yield in the section. Where does that yielding 21.5" happen? c. Find the plastic properties Ycg and Z. d. What is the full plastic moment capacity, M? e. How would the first yield moment, M, and the fully plastic moment, Mp, change if the bottom flange were made from steel with Fy = 48 ksi, but the remainder was made from the F, = 36 ksi steel? f. Without doing any calculations, state whether you think that M, and M, would change if the top flange were made of the stronger steel, while the web and bottom flange were made from the original steel with F, = 36 ksi. Explain your reasons.

Answer 1

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Fy-36 Ksi 8.983 a 1.5" tossa - A 24' 0.5'' .517 Ⓡ yt = " (2x1.5x1.5+ (21.540.5)4 (15+24x) + (axı) x (23.5) (12x1.5), + (21.540.5) + (10x1) > Je = 10.483 in yoz 24 – 10.483 = | yb = 13.517 in Area = 12x1.5 + 215x0.5 +1261 3 A = 40.75 (cine}} + Sax = 0,5 48:33 + 05 *(2.5ing+ box 15 + 10 p + (2x1.5)x (9.733)* + (2x1) (13.0173" Đ Inn = 4190.509 Ant Stop = Ina = 4190.509_unt Stop = 399.743 in 1 (A) tst - Sbottom= Itop Inn bottom 10.483 in = 4190.50g 1.517 Sbottom=310.017 in > Jogg = 15kqpP+ 31540g Tyg = 360.223 int ( o 53= 36 Ksi hne E For My = SxFg] La my = SbX Fy For just to cause first yeld Scanned with Scanner My = 11160.612 ench-kips |

11.5" At Plastic State Neutial Axis divide the Ť Area into two equal parts. yeg 4.75 | 1.5" N (24-red tiskos (12x1.5+ (99–1,5) 0.5 = [tax! + a (93-4g) ons ] 8 5.25 +0.5yeg = 11.5 -0.5 yeg Yeg = 6x25" § 34 Haxhusty : 25TSJKABI 20 = (ax 1.5)446-25-135) + (4.75X0.5)44.2 + (16.75X0.5)*16.75 + (lax 1) (16.75+0.5) = 17p = 381.7812 in? (d) Mp = Fyx Zp4 Mp= 36% 381.7812 Mp=13744. 1232 (anch-kips) =e) for My - (Myle = (Fu) top (y) = (Fabolton (8t) top Inn To Mye 36x399.743 = 14390.748 inch kipa) | My2 = 488 310.017 = 14880.816 inch-kips As My , <My so I My in this case = My =14390.748 In Tunch-kips! Scanned with CamScanner.

change the width of bottom section by (48) times 12" - 161 11.5" 8.75" the " 91.5" . all I" F 16" 12x1.5 + 0.5 x (91–1.5) = (16 x 1) + (23-Yu)x0.5 1-25 + 0.5 yi = 11.5 -0.5y, = y1= 10.25) zps (12x1,5) (9.5) + (6.75X0.5) 8,25) + (12.75805) X12:35 + (16* 1) (13-25) Fzp=524.0625 in? Mp= Fyx Zp = 36x 524.0625 Mp= 18866.25 (anch-kips) (f) vory would not change but Mp would change Ims