Torsion question

1. Dec 15, 2009

Dell

Each of the two aluminum bars shown is subjected to a torque of magnitude . Knowing that , determine for each bar the maximum shearing stress and the angle of twist at B.

b) 50.9Mpa 0.9510 degrees

my equations

τmax=$$\frac{T}{alpha*h*b^2}$$

$$\frac{dΦ}{dx}$$=$$\frac{T}{G*beta*hb^3}$$

so to find the angle of twist at B i can integrate $$\frac{T}{Gβhb^3}$$dx from 0 to 0.3, but since the moment is constant throughout, the integral comes to $$\frac{T}{Gβhb^3}$$*0.3

and i get

a) ΦB=$$\frac{1000}{26e9*0.14*0.06*0.06^3}$$*0.3=0.0211979 rad = 1.21455degrees

b) ΦB=$$\frac{1000}{26e9*0.245*0.095*0.038^3}$$*0.3=0.03011 rad = 1.725degrees

where the actual answers are much much smaller

for the shear strength used the equation

τmax=$$\frac{T}{alpha*h*b^2}$$

and i get

a)τmax=$$\frac{1000}{0.21*0.06*0.06^2}$$=22Mpa
b)τmax=$$\frac{1000}{0.26*0.095*0.038^2}$$=28Mpa

a seemingly simple question but i have managed to get 0/4 correct answers, can anyone see where im going wrong?