shaft is made of bronze at length AB and steel at length BC fixed at both ends. It is subjected  to a concentrated torsional moment at the junction, The steel segment is 1 meter long. Assume  that the Bronze has a diameter of 75mm, G = 35 GPa and τ = 60 MPa whilst the steel has a  diameter of 50mm, G = 80 GPa, and τ = 80 MPa. a) What is the ratio of the length of steel to the length of bronze such that the allowable  stress in each material is reached simultaneously.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A shaft is made of bronze at length AB and steel at length BC fixed at both ends. It is subjected 
to a concentrated torsional moment at the junction, The steel segment is 1 meter long. Assume 
that the Bronze has a diameter of 75mm, G = 35 GPa and τ = 60 MPa whilst the steel has a 
diameter of 50mm, G = 80 GPa, and τ = 80 MPa.
a) What is the ratio of the length of steel to the length of bronze such that the allowable 
stress in each material is reached simultaneously.
b) What is the reaction at the left end if the maximum torque is applied to the saft, in kN. 

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