Question

Two strips of metal are riveted together at their ends by four rivets, each of diameter $6.0mm.$ What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed $6.9\times {10}^{7}Pa?$ Assume that each rivet is to carry one quarter of the load.

Answer 1

Given,
Diameter of rivet $\left(d\right)=6mm=6\times {10}^{-3}m$

Each rivet is to carry one quarter of the load.

Step 1: Find Surface area
Surface area of a rivet
$A=\frac{\pi }{4}{d}^2$
$=\frac{\pi }{4}\times (6\times {10}^{-3}{)}^2$
$=9\pi \times {10}^{-6}{m}^2$

Now, Tension carried by each rivet is $\frac{T}{4}.$


Step 2: Find maximum tension

maximum shear stress$=\frac{\text{maximum shear−force}}{\text{surface area of rivet}}$
$6.9\times {10}^{7}Pa=\frac{\frac{T}{4}}{9\pi \times {10}^{-6}{m}^2}$

$T=(36\pi \times {10}^{-6})\times 6.9\times {10}^7$

$T=7799.76N$

This Tension is the total force which the strip can withstand.

Final Answer:$7799.76N$