**Introduction**:

A Rivet is a permanent mechanical fastener (see Figure 1) with head-on at one end and a cylindrical stem called a tail at the other end that has the appearance of a metal pin. Parts of a rivet includes head, shank/body and tail. Rivets are non-threaded fasteners typically made of mild steel, or brass, copper and aluminum. Types of rivet may include: blind rivet, solid rivet, split rivet, friction-lock rivet, self-piercing rivet, drive rivet, span head or cup head rivet, pan head rivet, countersunk head rivet, hollow head rivet etc. They are used in structures, sheet metal operations, ships and many industries often by fastening them to plates (see Figure 2).

**Failure patterns of a rivet**

1. Single shear failure of a rivet

2. Double shear failure of a rivet (usually found in butted rivet)

3. The plate may tear off along the line of the rivet

4. The material may fail to resist the bearing pressure between the rivet and the plates

5. The plate may shear between the rivet hole and the edge of the plate

6. The plate may split between the rivet hole and the edge of the plate in a line perpendicular to the edge.

**Parameters of the Rivet**

The following parameters apply to the rivet;

p = pitch of the rivet

d = gross diameter of the rivet

t = thickness of the plate

σ_{t} = self-tensile stress in the plates

P_{t }= tearing strength per pitch length

σ_{ut} = ultimate tensile stress of the plate

P_{ut} = pull applied per pitch length for tensional forces

τ = self-shearing stress of the rivet

P_{s }= shearing strength per pitch length of the rivet

τ_{u} = ultimate shearing stress of the rivet

P_{us} = pull required per pitch length for shear failure

σ_{c} = allowable crushing/bearing stress of the rivet or plate whichever is greater

P_{c} = crushing strength per pitch length of the rivet or plate

σ_{uc} = ultimate crushing stress of the rivet

P_{uc} = pull per pitch length for crushing/ bearing failure

**Formulas Applicable to Rivet**

**Tearing efficiency, n _{t}**

_{ }= P

_{t}/ (P . t. σ

_{t}) = [(p – d) . t . σ

_{t}]/ (p . t. σ

_{t}) = (p – d)/ P

**Shearing efficiency, n _{s}** = P

_{s}/ (P . t. σ

_{t}) = [n . (πd

^{2}/4) . τ]/ (p . t. σ

_{t}) – for single shear or [n . (πd

^{2}/4) . τ . 2]/ (p . t. σ

_{t}) – for double shear

**Crushing efficiency, n _{c}** = P

_{c}/ (P . t. σ

_{t}) = [n . d .t . σc]/ (p . t. σ

_{t})

**Resistance to tearing per pitch length, R _{t}** = P

_{t}= (p – d) . t . σt

**Resistance to shearing of rivet per pitch length, R _{s}** = P

_{s}= n . A . τ – for single shear or n . A . τ . 2 – for double shear; where n is the number of rivet per pitch length

**Resistance to bearing or crushing pressure per pitch length, R _{c}** = P

_{c}= n . d . t . σ

_{c}

**Efficiency of riveted joints, n** = (Least of P_{t}, P_{s} or P_{c})/ (p . t. σ_{t})

Where, (p . t. σ_{t})is the strength of the solid plate per pitch, denoted by P

**Note:** Unwin’s theory relates the diameter of rivet and thickness of plate as follows; d = 1.91√t

**Example**

Two plates, 15 mm thick are joined by a double riveted lap joint. The pitch in each row of rivet is 60 mm. rivet gross diameter is 20 mm. Values of permissible stresses are: σ_{t} = 150 N/mm^{2}, τ = 94.5 N/mm^{2} and σ_{c} = 212.5 N/mm^{2}. Determine the maximum tensile force permissible on the joint per pitch length and also determine the efficiency of the joints.

**Solution**

t = 15 mm = 0.015 m; P = 60 mm = 0.06 m; and d = 20 mm = 0.02 m

Maximum tensile force, R_{t} = P_{t} = (p – d) . t . σ_{t} = (0.06 – 0.02) . 0.015 . 150 x 10^{6 }= 90,000 N = 90 kN

Maximum resistance force, R_{s} = n . A . τ = 2 . (π . 0.02^{2}/4) . 94.5 x 10^{6} = 59376.10115 N 59.3 kN

Maximum resistance to crushing pressure, R_{c} = P_{c} = n . d . t . σ_{c} = 2 . 0.02 . 0.015 . 212.5 x 106 = 127,500 N = 127.5 kN

Efficiency = P_{s}/ (p . t. σ_{t}) = 59.3/ (0.06 . 0.015 . 150 x 10^{6}) = 43.95%