Question 16.9: Two springs of mean diameters 15 mm and 25 mm are connected ...
Two springs of mean diameters 15 mm and 25 mm are connected in series. Each spring has 10 coils and the diameter of spring wire is 3 mm. Determine the deflection of the spring under maximum load if the permissible shear stress is 160 MPa and the shear modulus is 80 GPa
Using Eq. (16.1), maximum load is given by
\tau =\frac{16PR}{\pi d^3} \left\lgroup1+\frac{d}{4R} \right\rgroup (16.1)
P=\frac{\tau \pi d^3}{16R\left\lgroup1+\frac{d}{4R} \right\rgroup }where R = 7.5 mm,
P=\frac{160\times \pi \times3^3}{16\times7.5\times\left\lgroup1+\frac{3}{30} \right\rgroup } =102.8 Nwhere R=12.5 mm
P=\frac{160\times \pi \times3^3}{16\times12.5\times\left\lgroup1+\frac{3}{50} \right\rgroup } =64 NSince both springs carry equal load, it should not exceed 64 N. The deflection corresponding to 64 N is given by Eq. (16.2) as follows
\delta =\frac{64nP(R^3_1+R^3_2)}{Gd^4} =\frac{64\times10\times64\times(7.5^2+12.5^2)}{80000\times34} =15 mm
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