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Question 16.10: Repeat Example 16.9 if the smaller coil is placed inside the...

Repeat Example 16.9 if the smaller coil is placed inside the larger coil.

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Stiffness of smaller spring,

\frac{P_1}{\delta } =\frac{80000\times3^3}{640\times7.5^3} =24  N/mm

Stiffness of larger spring,
\frac{P_2}{\delta } =\frac{80000\times3^3}{640\times12.5^3} =5.184  N/mm

Since, stiffness is more for smaller coil, it will take more load for same deflection and it will reach permissible shear earlier.

P_1=\frac{\tau \pi d^3}{16R\left\lgroup1+\frac{d}{4R} \right\rgroup } =\frac{160\times \pi \times3^3}{16\times7.5\times\left\lgroup1+\frac{3}{30} \right\rgroup } =102.8  N

 

\delta =\frac{102.8}{24} =4.283  mm

 

P_2=\delta \times k_2=4.283\times5.184=22.2  N

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