Question

1. For the beam loaded as shown in the figure, find the following: The beam is rectangular and made of steel, it has a width of 20mm and a height of 40mm. Find: a. The reactions on the beam. b. The maximum bending stress at the base. c. The maximum deflection. F=850N 0.2 m 1 W=80N/m 0.7 m

Answer 1

1 TAI 20x 40° 40mm 20mm * I= 106666.667 mm 4 F = 80N W=80 N/m Bi ------ 0.5 m. 0.2 m 0.5m. » - LRA 6.7 m . TEMA =0 MA - 850 X0.7 - 80 x 0.5 x (0.2+ 2) = 0 IMA = 613. nom. I Efy=0 RA-850 - 8080.s=0 RA =890 N. I © 6 Mials - MA + RAX - 80xx (Z-0.27 a Mix = -613 + 890% – 40 (X-0.272 0 +8902 <x M (oc) =-613 <0.2 M(O): -613 Nom ~ m (0.2) = -435 Nomi 0,2<*$0.7 Mix) = -613 + 890X-4012-0.21? =-613 + 890% - 40152-0.4% +0,04) ☆ My = -614.6 +906X - 40 x2 dmca co + 906 – 2X400 20 2= 11325 da lounde limit) M (0.7) = -014.6 +906x0.7 - 40X0.72 Honce map bending moment. Mb, maro = -613 N.m

( ET de 12 = mix) З ЕТ :3 - 613 + 890X. - 40 <-0.272 + Ej dy = -6138 + 445*? – 4,9 <2-0.27% +C @xzo dy 203 0=.ca GEO EI dy = -613x +445? - 40 (x-0.2)3 * EIY = - 306.5x2 + 445.x - 40 (1-0,274 +62 @xzo, y=o o = C & Cao * EIY = - 306.57L? +148.333X° -10 <X-0.279 Rit x=0.7 ms 700 mm. EI YOU - 306.5 X0.7 +148.333 x0,93 – 19 x 0.54. N.m3 ESYO -99.515 Niyons N.mm? * EILE -99.515 8 10 09 7 ya 1 x 1-99.515) x109 mm. EI (Et Nummel ye-' -* 99.575 X10% mm Ex106666.667 You Ex106666.667 * Tone - 3234194 mm 932954.194 ma (Ein Mommy