This project involved many assumptions as well as a lot of actual measurement. Things that we assumed are that the concrete in the South Stadium was all of the same density and that the pillars underneath were spaced so they each carry the same load. These assumptions are practical because in reality they are mostly true. Also we had to pick values for certain calculations, such as an average weight for a Nebraska fan, which we choose to be 170 lb . We also had to pick a value for the density of concrete, which we choose to be 142 lb/ft3. The actual values, which we determined, are also somewhat theoretical because we used a previously determined step size for two different people and paced of areas of the stadium and averaged the values. Using these values we were able to determine a square footage for the stadium and then using an average thickness of the stadium we can find a volume.
Now, using the fact that the capacity of the South Stadium is 26,400 people and our estimate of the average weight is 170 pounds per person, the weight of the people on gameday is 4,488,000 pounds or 2,244 tons. This is a significant amount in that this is almost as much as all of the concrete weighs itself. This means that when the Huskers play, the South Stadium weighs roughly twice what it does when it's empty.
One other interesting calculation we can do with this information is the weight carried by each pillar. The South Stadium of Memorial Stadium is held up by 83 pillars of concrete with a 1.75 ft radius. Thus when the stadium is empty each pillar is holding up 32.7 tons and when filled to capacity each pillar holds up 59.7 tons. Upon finding that the cross sectional area of each pillar is 114,984 in2 , we can also express the weight in terms of pounds per square inch (psi). Specifically when the stadium is empty each pillar is under a pressure of 47 psi and when filled the pillars are under a pressure of 86 psi.
If we assume that the concrete is capable of supporting 3,000 psi, we find there is a comfortable safety margin. The stadium is capable of supporting 26,400 fans weighing 542 tons each.
Also, since we are assuming a uniform density, we can easily determine where the centroid is located.
(Assuming our x and y -axes are placed at the bottom center of the middle segment)
Therefore, the center of mass of the South Stadium lies 113.4 ft from the base. Since 98 rows constitute this portion of the Memorial Stadium, the actual seat in which the centroid lies is in the middle of the 50th row.