Question

Two strips of metal are riveted together at their ends by four rivets, each of diameter $6\,mm$.Assume that each rivet is to carry one quarter of the load. If the shearing stress on the rivet is not to exceed $6.9 \times {10^7}{P_a},$ the maximum tension that can be exerted by the riveted strip is then?
A. $2 \times {10^3}\,N$
B. $3.9 \times {10^3}\,N$
C. $7.8 \times {10^3}\,N$
D. $15.6 \times {10^3}\,N$

Answer 1

Let us get some idea about rivet. A rivet is a mechanical fastener that is permanent. A rivet consists of a smooth cylindrical shaft with a head on one end before it is attached. The tail is the opposite end of the head.

Complete step by step answer:
Let us talk about shearing stress. When an object is subjected to an external force, it deforms. If the force's path is parallel to the object's plane. Along that plane, the deformation will occur. Shear stress, also known as tangential stress, is the type of stress that the object is subjected to in this situation. It occurs when the force vector components are parallel to the material's cross-sectional area. The force vectors in normal/longitudinal stress are perpendicular to the cross-sectional area on which it works.

Given:
Metal strip diameter (d)$= 6.0\,mm = 6.0 \times {10^{ - 3}}\,m$
Radius, $r = \dfrac{d}{2} = 3 \times {10^{ - 3}}\,m$
$\text{Maximum shearing stress} = 6.9 \times {10^7}\,Pa$
$\Rightarrow\text{Maximum stress}=\dfrac{\text{maximum load or force}}{\text{Area}}$
$\Rightarrow\text{Maximum force} = \text{Maximum stress} \times \text{Area}$
$\Rightarrow\text{Maximum force} = 6.9 \times {10^7} \times \pi \times {r^2}$
$\Rightarrow \text{Maximum force} = 6.9 \times {10^7} \times \pi \times {(3 \times {10^{ - 3}})^2}$
$\therefore \text{Maximum force} = 1949.94\,N$
As given in the problem that each rivet carries one quarter of the load.
Maximum tension on each rivet $= 4 \times 1949.94 = 7799.76\,N= 7.8 \times {10^3}\,N$

Hence, the correct answer is option C.

Note: Shear stress occurs as a result of shear forces. They are a pair of forces of the same magnitude and opposite direction acting on opposite sides of a body. Shear stress is a quantity that is measured as a vector. This implies that, in addition to magnitude, direction is also essential.