Consider the style of shear isolation mount shown. A cross-section through it wo
ID: 1717757 • Letter: C
Question
Consider the style of shear isolation mount shown. A cross-section through it would appear as the figure on the right. Let h = 6 cm, ro = 2.5 cm, and ri = 0.5 cm. Soft grades of rubber are measured on the shore hardness D scale. The slope of the dotted line showing the shear deformation is approximately
a) Find the deflection y as a function of radius.
b) If a 0.5 cm deflection ? is permissible when the mount supports 500 kg, find the minimum required hardness of the rubber.
Shore-D to Young’s Modulus (in MPa): E = e ((Shore-D durometer + 50)*0.0235-0.6403)
Explanation / Answer
slope dy /dx = tan (P/2 Pie h G )
deflection wrt to y by integrating the slope equation
y = - log P/2 pie hG
b) if y = 0.5 cm and P = 500 kg
0.5 = log 500 /2 x 3.14 x 6 x G
e*0.5 = 250 /3.14 x 6 x G
G = 250 /3.14 x 6 e^0.5
G = 9.76