First slide

Stress and strain

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 river is not to exceed $6.9 \times 10^{7} P a$ , the maximum tension that can be exerted by the riveted strip is

Easy

A

$2 \times 10^{3} N$
B

${3.9 × 10}^{3} N$
C

$7.8 \times 10^{3} N$
D

$15.6 \times 10^{3} N$

Solution

Radius of a rivet
r = $\frac{6}{2} mm = 3 mm = 3 \times 10^{- 3} m$
Maximum stress = $6.9 \times 10^{7} Pa$
Maximum load on a rivet
= Maximum stress $\times$ Area of cross-section
= $6.9 \times 10^{7} \times π {(3 \times 10^{- 3})}^{2}$
= 1950 N
Maximum tension that can be exerted by rivet strip
= $4 \times 1950 N = 7800 N = 7.8 \times 10^{3} N$

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