The GATE Grind

GATE 2026 ME – Question 19

Machine Design · Shafts and springs · 1 mark · Multiple choice

A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$. The maximum shear stress developed in the wire is

  1. $\frac{8FD}{\pi d^3} + \frac{4F}{\pi d^2}$
  2. $\frac{8FD}{\pi d^3} + \frac{2F}{\pi d^2}$
  3. $\frac{16FD}{\pi d^3} + \frac{4F}{\pi d^2}$
  4. $\frac{32FD}{\pi d^3} + \frac{4F}{\pi d^2}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $\frac{8FD}{\pi d^3} + \frac{4F}{\pi d^2}$

Explanation

The wire carries a twisting moment $T = \frac{FD}{2}$, which gives a torsional shear stress $\frac{16T}{\pi d^3} = \frac{8FD}{\pi d^3}$. It also carries the direct shear of $\frac{F}{\pi d^2/4} = \frac{4F}{\pi d^2}$. The maximum stress is the sum of the two.