Question

As concrete dries, it shrinks—the higher the water content, the greater the shrinkage. If a concrete beam has a water content of w kg/m3, then it will shrink by a factor
S =
0.032w − 2.5
10,000
where S is the fraction of the original beam length that disappears due to shrinkage.

(a) A beam 12.027 m long is cast in concrete that contains 550 kg/m3 water. What is the shrinkage factor S?

How long will the beam be when it has dried? (Round your answer to three decimal places.)

(b) A beam is 12.047 m long when wet. We want it to shrink to 12.033 m, so the shrinkage factor should be
S = 0.0012.
What water content will provide this amount of shrinkage? (Round your answer to the nearest whole number.)

Answer 1

A.) Here, w = 550kg/m^3.
Therefore, S = (0.032(550) - 2.5)/10000 = 0.00151

After drying, the beam will be (1 - 0.00151) x 12.027 = 12.009


b.) 0.0012 = (0.032w - 2.5)/10000
0.032w - 2.5 = 12
0.032w = 12 + 2.5 = 14.5
w = 14.5/0.032 = 453 kg/m^3
Therefore, the required water content is 453 kg/m^3