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Problem 2 A metal composite shaft $AB$ with length $L$ consists of a steel rod with radius $r$, the outer surface of which is bonded to the inner surface of an aluminum tube, whose outer radius $r_o$ is equal to $1.5r$. The shaft has the geometry and cross section shown below. One end $(B)$ of the shaft is fixed onto a rigid wall while the other end $(A)$ is subjected to an external torque $T_A$. Take $G_{st} = 78$ GPa for the steel rod and $G_{Al} = 28$ GPa for the aluminum tube. (a) Find the angle of twist at $A$ ($\phi_A$) due to $T_A$. (b) Find the maximum shear stress in the steel rod. (c) Find the maximum shear stress in the aluminum tube. (d) If the allowable angle of twist is $(\phi_A)_{allow} = 2 \times 10^{-3}$ rad, determine the maximum length the shaft can have when subjected to the torque $T_A$ at the free end. Take $L = 1.2$ m, $r = 24$ mm, $T_A = 360$ N-m, $\phi_{A,allow} = 2 \times 10^{-3}$ rad.

          Problem 2
A metal composite shaft $AB$ with length $L$ consists of a steel rod with radius $r$, the outer surface of which is bonded to the inner surface of an aluminum tube, whose outer radius $r_o$ is equal to $1.5r$. The shaft has the geometry and cross section shown below. One end $(B)$ of the shaft is fixed onto a rigid wall while the other end $(A)$ is subjected to an external torque $T_A$.
Take $G_{st} = 78$ GPa for the steel rod and $G_{Al} = 28$ GPa for the aluminum tube.

(a) Find the angle of twist at $A$ ($\phi_A$) due to $T_A$.
(b) Find the maximum shear stress in the steel rod.
(c) Find the maximum shear stress in the aluminum tube.
(d) If the allowable angle of twist is $(\phi_A)_{allow} = 2 \times 10^{-3}$ rad, determine the maximum length the shaft can have when subjected to the torque $T_A$ at the free end.

Take $L = 1.2$ m, $r = 24$ mm, $T_A = 360$ N-m, $\phi_{A,allow} = 2 \times 10^{-3}$ rad.

problem 2 a metal composite shaft ab with length l consists of a steel rod with radius r the outer surface of which is bonded to the inner surface of an aluminum tube whose outer radius ro 55067

Added by Victor Manuel D.

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