Two strips of metal are riveted together at their ends

cbse
properties-of-solids

#1

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 x ${{10}^{7}}$ Pa? Assume that each rivet is to carry one-quarter of the load.


#2

Diameter of each rivet, D = 6 mm

.’. Radius, r = D/2 = 3 mm = 3x${{10}^{-3}}$ m
Maximum shearing stress on each rivet = 6.9 X${{10}^{7}}$ Pa

Let w be the maximum load that can be subjected to the riveted strip. As each rivet carry one-quarter of the load.
Therefore, load on each rivet = w/4
Maximum shearing stress = Maximum shearing force / Area

6.9 x ${{10}^{7}}$ = w/4 /$\pi$ ${{r}^{2}}$

or w = 6.9 x ${{10}^{7}}$ x4$\pi$ ${{r}^{2}}$
or w = 6.9 x 4 x 3.14 x 9 x 10 = 7.8 x ${{10}^{3}}$ N