Noe Ak You Teacher 01n points SAlgTng4 08101 As concrete dri

Noe Ak You Teacher 01-n points SAlgTng4 0.8.101 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 owing to shrinkage. (a) A beam 12.065 m long is cast in concrete that contains 750 kg/m3 water. What is the shrinkage factor S? (Round your answer to four decimal places.) How long will the beam be when it has dried? (Round your answer to three decimal places.) (b) A beam is 12.031 m long when wet. The manufacturer wants it to shrink to 12.027 m, so the shrinkage factor should be S - 0.00033. What water content will provide this amount of shrinkage? (Round your answer to the nearest whole number.) kg/m3 Noed Help? Watch Read it Notes Ask Your Teac 15. 0 1/1 points 1 Previous Answers SAlg Trig4 08.105 MI.

Solution

A.) Here, w = 750 kg/m^3.
Therefore, S = (0.032(750) - 2.5)/10000 = 0.00215

After drying, the beam will be (1 - 0.00215) x 12.065 = 12.039


b.) 0.00033 = (0.032w - 2.5)/10000
0.032w - 2.5 = 3.3
0.032w = 3.3 + 2.5 = 5.8
w = 5.8/0.032 = 181.25 kg/m^3
Therefore, the required water content is 181.25 kg/m^3