Question

SOLUTION (a) Shaft \( A B \) : \[ \begin{aligned} P & =12 \mathrm{~kW} \\ f & =\frac{1260}{60}=21 \mathrm{~Hz} \\ T_{A B} & =\frac{P}{2 \pi f}=\frac{12 \cdot 10^{3}}{2 \pi(21)}=91 \mathrm{Nm} \\ c & =\frac{1}{2} d=12.5 \mathrm{~mm} \\ \tau & =\frac{T c}{J}=\frac{2 T}{\pi c^{3}} \\ & =\frac{(2)(91)}{\pi(0.0125)^{3}}=29.66 \mathrm{MPa} \quad \tau_{A B}=29.66 \mathrm{MPa} \end{aligned} \] (b) Shaft \( C D \) : \[ \begin{aligned} T_{C D} & =\frac{r_{C}}{r_{B}} T_{A B}=\frac{5}{3}(91)=151.7 \mathrm{Nm} \\ \tau & =\frac{2 T}{\pi c^{3}}=\frac{(2)(151.7)}{\pi(0.0125)^{3}}=49.44 \mathrm{MPa} \quad \tau_{C D}=49.44 \mathrm{MPa} \end{aligned} \]

          SOLUTION
(a) Shaft \( A B \) :
\[
\begin{aligned}
P & =12 \mathrm{~kW} \\
f & =\frac{1260}{60}=21 \mathrm{~Hz} \\
T_{A B} & =\frac{P}{2 \pi f}=\frac{12 \cdot 10^{3}}{2 \pi(21)}=91 \mathrm{Nm} \\
c & =\frac{1}{2} d=12.5 \mathrm{~mm} \\
\tau & =\frac{T c}{J}=\frac{2 T}{\pi c^{3}} \\
& =\frac{(2)(91)}{\pi(0.0125)^{3}}=29.66 \mathrm{MPa} \quad \tau_{A B}=29.66 \mathrm{MPa}
\end{aligned}
\]
(b) Shaft \( C D \) :
\[
\begin{aligned}
T_{C D} & =\frac{r_{C}}{r_{B}} T_{A B}=\frac{5}{3}(91)=151.7 \mathrm{Nm} \\
\tau & =\frac{2 T}{\pi c^{3}}=\frac{(2)(151.7)}{\pi(0.0125)^{3}}=49.44 \mathrm{MPa} \quad \tau_{C D}=49.44 \mathrm{MPa}
\end{aligned}
\]

SOLUTION
(a) Shaft A B :

P =12 kW

f =(1260)/(60)=21 Hz

TA B =(P)/(2 π f)=(12 · 10^3)/(2 π(21))=91 Nm

c =(1)/(2) d=12.5 mm
τ =(T c)/(J)=(2 T)/(π c^3)
=((2)(91))/(π(0.0125)^3)=29.66 MPa τA B=29.66 MPa

(b) Shaft C D :

TC D =(rC)/(rB) TA B=(5)/(3)(91)=151.7 Nm
τ =(2 T)/(π c^3)=((2)(151.7))/(π(0.0125)^3)=49.44 MPa τC D=49.44 MPa

Added by Ibrahim A.

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