Question

Problem 6.121 The composto beam is made of steel ) bonded to brass and has the cross section shown 100 GPX E 200 GPa The web banding stress for the stoelis ( 180 MP and for the brass (. 0 MP gure 1) Part A Determine the main moment that can be tied to the beam Express your answer to three significant figures and include the appropriate units. Units Submit Restas 175 mm

Answer 1

solution:- mm * 175 I steel I T somm Ebe= 100 epa Est = 200-epa Brass 200 mm Est = 180 mpa 6bq = 60 Mpa Transforming Brass into Steel, equilamet width of brass is be = 175 x 100 = 87.5 mm goo x 175mm x x 50mm 108:33 2oo mm * Transformed section: T I AI = 87.5x200 = 17500 mm2 141067 II = 20% = 100mm ALI = 175x50 = 8750 mm 2t * * 87.5 YI = 200+5%=225 mm ģ= 17500xloo + 8750x225 - 1141067 mm 17500 +0750 Izz = 175x503 + 8750X (108:33-25² + 87.5x2000+ 12 17500X (141167 4002 1151.30 x 100mmy Est max = Estallow ² Mxy - 180 Mpe Izz » Mx 108.33 180 N/mm 2 7 M = 251.40 N-mm x too 151.30x1o6 > M = 251040 KN-m ] KN-m

6 max brass = fallow brass > Mxy x Egrass a to N/mm² Izz Esteel 7 Mx 141067 x 100 sto 151.3ox lot 200 7 M = /28.1578106 N-mm > M = 128.16 kN-m) maximam moment M = min of the two = 128.16 kNom