| Practice Problem 4-1 |
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Given: A cylindrical concrete column with a diameter of 3.5 ft. has an initial height of 250 ft. Assume the density of concrete is 145 lbf/ft3 and Elastic modulus of concrete in compression is 2.5 Msi. Req'd: How much does the top of the column deflect, D, under its own weight [in.]? |
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Solution: Since the load is discontinuous throughout the height of the column the integration approach is used. The best approach is to convert all lenghts and units to inches:
A(x) = constant = p(42 in)2/4 = 1385 in2 E(x) = constant = 2.5 Msi P(x) on an element dx which is at a distance of x from the top of the column is P(x) = Vol x Density = A(x)·x·r Integrating gives:
D = (0.0839 lb/in3)(3000 in)2 / (2)(2.5x106 psi) = 0.151 in |
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