(i) Show that the efficiency of a self locking screw is less than 50%

(i) efficiency of screw η = tan α / tan(α +φ) And for self locking screws, φ ≥α or α≤ φ Efficiency ≤ tan(φ) /tan(φ +φ) ≤ tan φ/tan 2 φ ≤tan φ/ (2 tan φ/(1-tan2 φ)) ≤tan φ X (1-tan2 φ)/ (2 tan φ) ≤ ½-tan2 φ/2 From this expression efficiency of self locking screw is less than 50%