The strength of a riveted joint would be _______. 

Concept: 

Riveted joint:

• The permanent joining of parts with the help of rivets is called a riveted joint.
• Rivets are the cylindrical-shaped metal body used to leakproof the joining of dissimilar metals.
• When two pieces of sheet joint with the help of riveted joint such that one sheet overlaps the other one then this type of joint is called lap joint.

The efficiency of the riveted joint is defined as the ratio of the strength of the plate in an unpunched condition.

\(\eta = \frac{{Strength\;of\;riveted\;joint}}{{Strength\;of\;unriveted\;solid\;plate}}\)

As the strength of the riveted joint depends on the tearing strength, shearing strength or crushing strength of the joint, the efficiency can be tearing efficiency, shearing efficiency and crushing efficiency.

Crushing efficiency: Crushing strength of the riveted joint/Strength of the unriveted solid plate

\( {\eta _c} = \frac{{Crushing\;strength}}{{Strength\;of\;solid\;plate}}\)

The resistance offered by a rivet to be crushed is known as crushing resistance or crushing strength of bearing value of the rivet.

Pc = ndtσc

where n is no. of rivets.

 \({\eta _c} = \frac{{Crushing\;strength}}{{Strength\;of\;solid\;plate}} = \frac{{n\times d\times t\times {\sigma _c}}}{{p\times t\times {\sigma _t}}}\)

Another two types of failure that occur in lap rivet joints:

Tearing of the plate: If the force is too large that stress in the plate exceeds the allowable tensile stress of plate material, then the plate may fail in tension along the row.

• Tearing efficiency: Tearing strength of the riveted joint/Strength of the unriveted solid plate

\(\begin{array}{l} {\eta _t} = \frac{{Tearing\;strength}}{{Strength\;of\;solid\;plate}}\\ {\eta _t} = \frac{{\left( {p - d} \right)t\;{\sigma _t}}}{{{p_t}\;{\sigma _t}}} = \frac{{p - d}}{p} \end{array}\)

Shearing of the rivet: When shear stress in the rivets exceeds the maximum allowable shearing stress then the shear failure of rivets takes place.

• Shearing efficiency: Shearing strength of the riveted joint/Strength of the unriveted solid plate

\({\eta _s} = \frac{\pi }{4}\left( {\frac{{{\sigma _s}}}{{{\sigma _t}}}} \right)\left( {\frac{{{d^2}}}{{pt}}} \right)kn\)

k is effective surface area (For double shear, k = 2), n is number of rivets in a pitch length

Explanation:

The strength of a riveted joint would be the least of the crushing resistance, tearing resistance and shearing resistance.

⇒ Privet = min {Pc, Pt, Ps}

So, the correct answer is option 2.