Q $19.$ It is required to design a helical torsion spring for a mechanism. The spring wire diameter is $2\mathrm{.}5$ mm and the mean diameter is $25$ mm $.$ The ultimate tensile strength, su $=2550$MPa. The Yield strength $($sy$)$ of the material is $62\%$ of the ultimate tensile strength $($su$)$ and the factor of safety is $3\mathrm{.}0.$ The maximum bending moment acting on the spring is $510N-mm.$ Calculate the bending stress in the spring and compare it with design stress.

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$[6$ marks$]$