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Question 3.60:  A 20-mm-diameter steel bar is to be used as a torsion sprin...

A 20-mm-diameter steel bar is to be used as a torsion spring. If the torsional stress in the bar is

not to exceed 110 MPa when one end is twisted through an angle of 15°, what must be the length

of the bar?

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\begin{aligned}&\tau=\frac{16 T}{\pi d^{3}} \Rightarrow T=\frac{\pi}{16} \tau d^{3}=\frac{\pi}{16}(110)\left(10^{6}\right)\left(0.020^{3}\right)=173 \mathrm{~N} \cdot \mathrm{m} \\&\theta=\frac{T l}{J G} \Rightarrow l=\frac{\pi d^{4} G \theta}{32 T}=\frac{\pi\left(0.020^{4}\right)(79.3)\left(10^{9}\right)\left(15 \frac{\pi}{180}\right)}{32(173)} \\&l=1.89 \mathrm{~m} \quad \text {  . }\end{aligned}

 

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