Mechanical Properties of Solids

Question : 20

Total: 21

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivets is not to exceed 6.9×107 Pa? Assume that each rivet is to carry one quarter of the load.

Solution:

When the riveted strip is subjected to a stretching load W, the tensile force (i.e. tension) in each strip (equal to W) provides the shearing force on the four rivets. Since the load is sheared uniformly, i.e. each rivet is under a shearing force equal to W/4.
Maximum shearing stress on each rivet =6.9×107Pa.
Let A = area of each rivet on which the shearing force acts.
∴ Shearing stress on each rivet =

Shearing‌force

area

W∕4

If Wmax be the maximum permissible tension or load (i.e. force) exerted by the riveted strip, then

Wmax

=6.9×107

or Wmax=4A×6.9×107...(i)

Here, diameter of each rivet, D=6 mm =6×10–3m
∴A=

πD2

3.142×(6×10−3 )2

...(ii)
From (i) and (ii), we get

Wmax=4×

3.142×36×10−6

×6.9×107

=7804.73N=7804.73N
=7.8×103N

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