prob7.85 (team1)

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7.85: the 44-mm diamater shaft AB is made of a grade of steel for which the yield strength is stress yield= 250 MPA using the maximum-shearing -stress-criterion .determine the magnitude of the force P for yield occurs when T=1.5 KN.m.
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solution:
stress(y)=0
stress(x)=P/A

Txy=(Tc/J)
Txy=(1.5*1000*22*10^-3/0.5*3.14*(22*10^-3)^4)
=89.68 MPA
Tmax=0.5*stress yield=0.5*250 = 125 MPA

(Tmax)^2=(Txy)^2+(stressx-c)
(125)^2-(89.68)^2=0.5*stressx

stress x=174.155 MPA

P=stressx *A
P=174.155*10^6*(3.14/4)(.044)^2
P=264.8 KN