Structural engineering is a sub-field of civil engineering in which structures like bridges, buildings and even things like concert stages are designed and analyzed. Structural engineers must consider environmental factors, what a structure will be used for and what type of weight will be put on it, and how this all might change from day to day before even beginning a design. Their work keeps us safe in and around all types of man-made structures.

When designing a bridge, there are two main structural pieces: beams and columns. The size of the columns and beams is determined by the loads (or types and amount of weight) that the bridge will support, as well as natural forces that may be applied. For example, a bridge that will support trains and cars will require much larger beams and columns than a bridge that supports pedestrians and bicycles. A bridge in a location that experiences tornadoes will have different specifications than a bridge in a location that experiences heavy snow or earthquakes.

2.1 The figure shows the cross-section of a bridge column. As the dashed lines show, this cross-section is composed of 5 congruent squares of side length 8 inches and 4 congruent quarter circles. What is the cross-sectional area of this bridge column? Express your answer to the nearest whole number.

2.2 The formula shown is used to determine the maximum load, in pounds, that a column can support. The area refers to the cross-sectional area of the column, and material strength is a constant value that is assigned to each type of building material. An engineer is designing a concrete bridge across a river in Michigan, where they must account for weather conditions. For this particular bridge, the dead load (weight of fixed elements, like the concrete roadway and signs) is 1,161,080 pounds; the live load (weight of temporary elements, like vehicles and people) is 632,500 pounds; the snow load (temporary weight from snow) is 98,000 pounds; and the wind load (temporary weight from wind) is 8500 pounds. If it were to be snowing and windy at the busiest time of day on the bridge, all of these loads would be acting on the bridge at the same time. Given that the material strength of concrete is 4200 lb/in2, what would the cross-sectional area of the column need to be to support this load? Express your answer as a decimal to the nearest tenth.

2.3 This bridge will have 8 identical right circular cylinder columns, each with diameter 3 feet and height 14 feet. Based on this, what is the total volume, in cubic inches, of the concrete needed to make these columns? Express your answer to the nearest whole number.

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CCSS (Common Core State Standard)