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Four identical hollow cylindrical colum...

Four identical hollow cylindrical columns, support a ig structure of mass M. The inner and outer radii of a column are `R_(1)`, and `R_(2)`, respectively. Assuming the load distribution to be uniform, the compressional strain of each column is
(where Y is Young's modulus of the column).

Text Solution

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Here , `Y = 2.0 xx 10^11 Pa` , Mass (M) = 51,000 kg.
inner radius, `r_1`= 30cm = 0.3 m
Outer radius, `r_2` = 60 cm = 0.6 m
Force acting on each columns,
`F = (Mg)/(4) = (50,000 xx 9.8)/(4) = 122500N`
Area of cross-section of each column, i.e.,
`A = pi r_2^2 -pi r_1^2`
` =pi (r_2^2 - r_1^2) = 3.14 (0.36 - 0.09) = 0.85 m^2`
Compressional stress on each column,
`F/A = (122500)/(0.85) = 1.44 xx 10^5 Pa ` As Y = stress/strain
stress (compressional) = Strain (compressional)/Y
strain = `(1.44 xx 10^5)/(2.0 xx 10^11) = 7.2 xx 10^(-7)`
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