The figure shows two bodies connected through a riveted joint with one rivet. The diameter of the rivet is d (in m). The joint transmits a load of F (in N) whose line of action is perpendicular to and intersects the vertical axis of the rivet. Neglect any effect of bending of the rivet. If the allowable shear stress for the material of the rivet is τ N/m^{2}, the diameter of the rivet required to prevent failure in shear is

This question was previously asked in

GATE PI 2020 Official Paper

Option 2 : \(\sqrt{\dfrac{2F}{\pi\tau}}\)

__Explanation:__

**L**ap joint:

- When two pieces of sheet joint with the help of riveted joint such that one sheet overlaps the other one.
- In this problem, there is a
**double shearing area.**

**For safe design**:

Induced stress ≤ Allowable stress

\(\frac{F}{2\;\times\;\frac{{\pi}d^2}{4}}=\tau\)

\(d^2=\frac{2F}{{\pi}{\tau}}\)

\(d=\sqrt{\frac{2F}{{\pi}{\tau}}}\)

__Additional Information__

Riveted joint:

- The permanent joining of parts with the help of rivets is called a riveted joint.
- Rivets are cylindrical-shaped metal bodies used to leakproof the joining of dissimilar metals.

Butt joint:

- In this type of riveting, the plates to be joined are kept in alignment butting/ touching, without forming an overlap.
- Another plate known as the cover plate is placed over either one side or on both sides of the main plates, then it is riveted with main plates.

Failure | Force of Failure | Failure area | Diagram |

Shearing | Due to shearing | \({{\rm{A}}_{\rm{s}}} = {\rm{n}} \times \frac{{\rm{\pi }}}{4}{\rm{d}}_{\rm{r}}^2\) | |

Bearing / Crushing | Due to compressive force | Ac = n(dr× t) | |

Tearing of plate | Due to tensile force | At = (P - dh)t |