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A crane is set up for steel erection at the site of a 5 story office building where each story is 15 feet tall. The new building will be 50 feet wide and 75 feet long and the crane is located 5 feet off the southwesterly corner of the building. Assuming that you need a 10 foot boom clearance over the last piece of steel.

Required:
Compute the minimum boom length

Respuesta :

oladayoademosu

Answer:

127.58 ft

Explanation:

We need first to calculate the length from corner to corner of the story, L.

Since the length of each floor is 75 ft and its width 50 ft, and since each floor is a rectangle with diagonal, L, using Pythagoras' theorem, we have

L² = (75 ft)² + (50 ft)²

= 5625 ft² + 2500 ft²

L² = 8125 ft²

L = √(8125 ft²)

L = 90.14 ft

Since the crane is 5 ft off the southwesterly corner of the building, the working radius, R = L + 5 ft = 90.14 ft + 5 ft = 95.14 ft.(since the diagonal length of the floor plus the distance of the crane from the south westerly corner add to give the working radius)

The boom tip height, H = height of building h + clearance of boom, h'

h = height of each story, h" × number of stories, n

Since h" = 15 ft and n = 5

h = 15 ft × 5 = 75 ft

Also, h' = 10 ft

So, H = h + h'

H = 75 ft + 10 ft

H = 85 ft

So, the minimum boom length, L' = √(H² + R²)

substituting the values of the variables into the equation, we have

L' = √(H² + R²)

L' = √((85 ft)² + (95.14 ft)²)

L' = √(7225 ft² + 9051.6196 ft²)

L' = √(16276.6196 ft²)

L' = 127.58 ft

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