A tunnel of length L = 150 m, height H = 7.2 m, and width 5.8 m

Question:

A tunnel of length L = 150 m, height H = 7.2 m, and width 5.8 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. (See Figure) The tunnel roof is to be supported entirely by square steel column; each with a cross-sectional area of 960 cm2. The mass of 1.0 cm3 of the ground material is 2.8 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?