Subtopic: Overload safety devices used in farm machinery
Question Statement:
A shear bolt of diameter $8\text{ mm}$ is located at a radial distance of $60\text{ mm}$ from the axis of a flanged PTO coupling. If the ultimate shear strength of the bolt steel is $320\text{ MPa}$, the torque (in N.m) at which the coupling disengages in single shear is:
Answer Key:
965.1
Step-by-Step Solution & Explanation
Cross-sectional area of $8\text{ mm}$ bolt:
$A_s = \frac{\pi}{4} d^2 = \frac{\pi}{4} (0.008)^2 = 5.0265 \times 10^{-5}\text{ m}^2$
Shear force required to sever bolt:
$F_s = \tau_u A_s = (320 \times 10^6) \times (5.0265 \times 10^{-5}) = 16084.95\text{ N}$
Disengagement torque at radius $r = 0.06\text{ m}$:
$T = F_s \times r = 16084.95 \times 0.06 = 965.10\text{ N}\cdot\text{m}$