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.(adsbygoogle = window.adsbygoogle || []).push({});

Answers: a) 40.1Mpa 0.6630 degrees

b) 50.9Mpa 0.9510 degrees

my equations

τ_{max}=[tex]\frac{T}{alpha*h*b^2}[/tex]

[tex]\frac{dΦ}{dx}[/tex]=[tex]\frac{T}{G*beta*hb^3}[/tex]

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

and i get

a) Φ_{B}=[tex]\frac{1000}{26e9*0.14*0.06*0.06^3}[/tex]*0.3=0.0211979 rad =1.21455degrees

b) Φ_{B}=[tex]\frac{1000}{26e9*0.245*0.095*0.038^3}[/tex]*0.3=0.03011 rad =1.725degrees

where the actual answers are much much smaller

for the shear strength used the equation

τ_{max}=[tex]\frac{T}{alpha*h*b^2}[/tex]

and i get

a)τ_{max}=[tex]\frac{1000}{0.21*0.06*0.06^2}[/tex]=22Mpa

b)τ_{max}=[tex]\frac{1000}{0.26*0.095*0.038^2}[/tex]=28Mpa

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

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