Riveted joints – Unwin’s empirical formula for rivet diameter According to Unwin’s rule, the recommended rivet diameter d (mm) for a plate of thickness t (mm) is approximately:

Introduction / Context:
Sizing rivets for structural and boiler plate work often uses empirical relations that balance plate tearing and rivet shear. Unwin’s formula provides a quick estimate of rivet diameter from plate thickness.

Given Data / Assumptions:

• Plate thickness t is in millimetres.
• Rivet diameter d is desired in millimetres.
• General-purpose structural riveting (lap/butt joints) without special constraints.

Concept / Approach:
Unwin’s rule of thumb states that the rivet diameter should scale with the square root of plate thickness: d ≈ k * √t with k close to 6 (many texts quote 6 or 6.05). This ensures practical proportions and adequate capacity without oversizing.

Step-by-Step Solution:
Select the baseline Unwin coefficient: k ≈ 6.Write the relation: d = 6 √t (mm, mm).Alternative close variant: d = 6.05 √t (option b) is essentially the same in practice; option (a) is the classic rounded form.

Verification / Alternative check:
Checking typical plates (e.g., t = 16 mm): d = 6 √16 = 24 mm, which aligns with common practice.

Why Other Options Are Wrong:

• d = 5 √t underestimates diameter for many standards.
• d = 1.5 t + 4 grows linearly with t and becomes excessive for thick plates.
• d = 0.5 t ignores the square-root dependence and oversizes thin plates while undersizing thick ones.

Common Pitfalls:
Forgetting unit consistency (t in mm), and using the formula outside its empirical range without checking code requirements.

Final Answer:
d = 6 √t