If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the efficiency of the circumferential lap joint is:
Show Hint
To quickly find efficiency when given the $d/p$ ratio, simply subtract the ratio from 1. If the hole takes up 25% of the pitch space ($0.25$), then 75% of the solid metal remains to carry the load.
1. Efficiency Formula: The tearing efficiency ($\eta_t$) of a riveted joint is given by the formula:
$$\eta_t = \frac{p - d}{p}$$
Where:
• $p$ = Pitch of the rivets (the distance between the centers of adjacent rivets).
• $d$ = Diameter of the rivet hole.
2. Substituting Given Ratios: The question provides the ratio of the diameter of the rivet hole to the pitch as:
$$\frac{d}{p} = 0.25$$
We can rewrite the efficiency formula to incorporate this ratio:
$$\eta_t = \frac{p}{p} - \frac{d}{p}$$
$$\eta_t = 1 - \frac{d}{p}$$
3. Final Calculation: Substituting the given value:
$$\eta_t = 1 - 0.25$$
$$\eta_t = 0.75$$
To express this as a percentage:
$$\text{Efficiency} = 0.75 \times 100 = 75\%$$
Therefore, the tearing efficiency of the joint is 75%, which represents the percentage of the original plate's strength that remains after the holes have been drilled.