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Mechanical Properties of Solids

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Question : 20 of 21
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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 6.9×1076.9 \times 10^{7} 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 W4\frac{}{4}.
Maximum shearing stress on each rivet =6.9×107= 6.9 \times 10^{7}Pa.
Let A = area of each rivet on which the shearing force acts.
∴\therefore Shearing stress on each rivet =Shearing forcearea= \frac{\text{Shearing force}}{\text{area}}
=W4A=W4A= \frac{\frac{W}{4}}{A} = \frac{W}{4A}
If WmaxW_{\text{max}} be the maximum permissible tension or load (i.e. force) exerted by the riveted strip, then Wmax4A=6.9×107\frac{W_{\text{max}}}{4A}=6.9 \times 10^{7}
or Wmax=4A×6.9×107…(i)W_{\text{max}} = 4A \times 6.9 \times 10^{7} \dots (i)
Here, diameter of each rivet, D=6D = 6 mm =6×10−3m= 6 \times 10^{-3} \text{m}
∴A=πD24\therefore A = \frac{\pi D^{2}}{4}
=3.142×(6×10−3)24…(ii)= \frac{3.142 \times (6 \times 10^{-3})^{2}}{4} \dots (ii)
From (i) and (ii), we get
Wmax=4×3.142×36×10−64×6.9×107W_{\text{max}} = 4 \times \frac{3.142 \times 36 \times 10^{-6}}{4} \times 6.9 \times 10^{7}
=7804.73N=7804.73N= 7804.73 \text{N} = 7804.73 \text{N}
=7.8×103N= 7.8 \times 10^{3} \text{N}
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