A tunnel of length L = 193 m, height H = 7.7 m, and width 10 m (with a flat roof

Question

A tunnel of length L = 193 m, height H = 7.7 m, and width 10 m (with a flat roof) is to be constructed at distance d = 78 m beneath the ground. (See the figure.) The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 1230 cm2. The mass of 1.0 cm3 of the ground material is 3.0 g. (a) What is the total weight of the ground material the columns must support? (b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?

Explanation / Answer

vol = 10*78*193 = 150540 m^3 = 150540000000cm^3 mass = 3*150540000000g = 451620000000g = 451620000kg force of this mass = 451620000*9.8 = 4425876000N area of col = 1230cm^2 = .123m^2 P = F/A

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