A stepped shaft ACB having solid ciruclar cross section withtwo different diamet

Question

A stepped shaft ACB having solid ciruclar cross section withtwo different diameters is held against rotation at the ends (seefigure). If tha allowable shear stress in the shaft is 6000psi, what isthe maximum torque (T0)max that may be applied at thesection C? The answer in the back of the book is T0max=3680 lb- in For some reason I keep on getting T0max =3485.07 I got that by TA+TB=To Somax=16TA/(.75)3=6000psi TA=497.01 max=16TB/(1.5)3=6000psi TB=3976.08 3976.08-497.01=3485.07
Somax=16TA/(.75)3=6000psi TA=497.01 max=16TB/(1.5)3=6000psi TB=3976.08 3976.08-497.01=3485.07

Explanation / Answer

Anyone can copy in answer out of the S/M but to turely understandwhat you are trying to acomplish is the true goal. If you arelooking for max torque, we intuitively know that the smallest crosssection will govern. You have the first part already figuredout: Ta= 497 lb-in. Use the compatibility equation we end upwith: [(Ta x Lac) / Ipac] + [(Ta x Lcb) / Ipcb] = [(To x Lcb) / Ipcb] We get: [(Ta x 223.335) / in3 ] = [(To x0.135)] Now sub in the value you found for Ta I get 3677 lb-in I know the book says 3680 lb-in but I figure the difference is inrounding.

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