Hoover Dam - What is the area of this approximation = 490...

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Analysis of Hoover Dam
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The dam was built in the years 1931 to 1936. Its height is 726 feet. The length of its crest is 1,244 feet. A straight line across the arc at the top is 860 feet. In determining the net force of the water against the dam in the forward direction, the straight-line length is the dimension needed. My estimate that the straight line length across the base of the dam is 490 feet. To calculate the force on the dam in the direction of the canyon we project the image of the dam onto a vertical plane perpendicular to the direction of the canyon. We assume that this is a trapezoid to make the calculation simple.
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Unformatted text preview: What is the area of this approximation? ! = 490 ⋅ 726 + ! ! ⋅ 860 − 490 ⋅ 726 = 490 , 050 !" ! What is the height of the centroid of this approximation? ℎ = !"# ! ⋅ !"# ⋅ !"# ! ! ! ⋅ !"# ! ! ⋅ ( !"# ! !"# ) ⋅ !"# !"# , !"# / !"! ≈ 396 !" The total outward force on the dam at full capacity is 505,245 tons. This is arrived at by the following calculation using the appropriate conversion factors to convert to tons. ! = ! ⋅ ! ⋅ 726 − 396 !" ⋅ 490 , 050 ! ! ! The operating depth of the dam is much less than the maximum capacity. So, the dam is rarely subjected to this force. 860 ft 490 ft 726 ft...
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