Question

Brass R Aluminum The composite beam shown is formed by bonding together a brass rod and an aluminum rod of semicircular cross sections. The radius of the beam is 0.85 in. The modulus of elasticity is 14.4 x 100 psi for the brass and 8.9 x 100 psi for the aluminum. Knowing that the composite beam is bent about a horizontal axis by couples of moment 6.9 kip.in, determine the maximum stress in the brass. Assumethe moment is applied to put the brass in compression and the answer should be in ksi with 1 digit of accuracy.

Answer 1

solution For Each semicirch: 12oobrien Az II se z 11349 w Yo= uu 37 UX0.85- 2 0-36075 in 3 T Raury # 10.8514 bare 8 7 = 0.20499 quy 8 R= Ebave Ayo = 0.20499-(1-1349) (0-3607512 I= 0.057293.pny we Aluminium haya reference matical Hal haluminily Eb z 14.4x100 8.926 1.6179 in boccass 2 n= EM Locate Neutral Anix - A (m2) nA (M²) go (en) nayo (ni) 1.1349 1.836242 0.3607 0.662424 1.1349 1.1349 -0.36075 0.40941 EhA22097114 20-25 oly

Yoz 0.253014 2.97114 = 0.08515799 the neutral anex lies 0.085157 in above the maternal entisfee di=0.36075-0.085157 = 0.27559 in d2z 0-36075+0.085157 = 0.445907 in 21 &i= niz trida = 1.6179*10.08729) +11-6179 )(1.1349)00-2755912 21= 0.232145 iny 22= n₂2+ n2 Ade 2 160.05749) + 161-1349) (0.44590712 2 22= 0.282945 9n4 22 DHRL= 0.232145+0.282945 I=0.575090 PnY

Manimum strees in brass :- M= 6.9 kip-su 14 28.5-0.085152)0-76484 in (Omen) b= incly) 2 (1•6179)(69) (0-764843) 2-16-5763 ks? (0.515090) Comen) brass= 16-5763 ks? (C)