Answer to Question #208642 in Mechanical Engineering for Mkhuseli Dlamini

Question #208642

A thin rim is made by joining two halves with rivets as shown in figure 3.8. Determine the required diameter of the twelve rivets if the rim must rotate at 600 r/min and the allowable shear stress in the rivets is 63 MPa. Ignore the effect of the cover plates. The density of the material used 7800 kg/m3 


1
Expert's answer
2021-06-21T05:52:35-0400

Rim rotation "= 600 r\/min"

Allowable shear stress "= 63 MPa"

Density of Materials "=7800 \\frac{kg}{m^3}"

velocity "= \\frac {\\pi DN}{60}= \\frac {\\pi \\times 1\\times 600}{60} = 31.41 \\frac{m}{sec}"

Hoop Stress "\\sigma_h = \\rho \\times v^2 =7800 \\times 31.41^2 = 7.69 Mpa"

Now Force due to above stress

"F_s = \\sigma_h \\times (2\\times t \\times l)= 7.69 \\times 10^6\\times 0.012 \\times 0.1)" "=18475.985 N"

According to shear stress theory,

"F_s = 12 \\times \\frac{\\pi}{4}\\times d^2\\times \\tau_s"

"d^2 = \\frac{F_s}{12\\frac{\\pi}{4}\\times \\tau} = \\frac{18475.985\\times 4}{12\\times \\pi\\times 63\\times 10^6}"

"d = 5.6 mm"


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