Question

Problem 4. 6–165. The beam is made of elastic-perfectly plastic material. Determine the maximum elastic moment and the plastic moment that can be applied to the cross section. Take Ty = 36 ksi. 6 in. 1.5 in. 3 in. 1.5 in.

Answer 1

. Given that Ty=36ksi zin to las in 3 in Tos Referring to hig@, the location of centroid of the cross section is, 16in. g= SJA EA ū 5.25 in. - 7.5x3x6 + 3x683 386 +683 9 = 5.25 in -

The moment of inertia of the cross section about neutral aneis is, I -. *3x6 + 386X(5.25–33 + tax 6x3+ 683x(7.5-5025) I = 249.75 int Here, Iman=oy= 36ks, and c=y=masin 36 = My.(5.25) . 249.75 My = 1712.57 kip.in My = 143. kip. ft. o ne moremme! Referring to fig@ stress block shown. Soda = o's . T-C-G=0. 0x3836-62)x3836–386434 = 0. d=6in. since id=6in, :.950..

Here, T=6= 3x6x36 = 648 kip Thus, mp = TX 4.5 Mp = 648x4.5 kip.in Mp = 2916 kipin. Imp = 243 kip.ft manimum plastic moment.