A tunnel of length L = 110 m, height H = 6.3 m, and width 6.9 m (with a flat roo
ID: 1375899 • Letter: A
Question
A tunnel of length L = 110 m, height H = 6.3 m, and width 6.9 m (with a flat roof) is to be constructed at distance d = 74 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 1240 cm2. The mass of 1.0 cm3 of the ground material is 2.5 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?
A tunnel of length L = 110 m, height H = 6.3 m, and width 6.9 m (with a flat roof) is to be constructed at distance d = 74 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 1240 cm2. The mass of 1.0 cm3 of the ground material is 2.5 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
The Volume of tunnel(V) = A x d
= (110 m x 6.9 m) x (74 m)
= 56166 m3
Density of tunnel roof (?) = 2.5 g/cm3
= 2500 kg/m3
Mass of tunnel roof (m) = ?V
= 2500 kg/m3 (56166 m3)
= 1.4041 x 10^8 kg
(a)
Total weight of the ground material the columns must support is
W = mg
= 1.4041 x 10^8 kg (9.8 m/s2)
= 1.376 x 10^9 N
(b)
The columns needed is
n = 1.376 x 10^9 N / [(1/2)(400 x 10^6 N/m2)(1240 x 10^-4 m2)]
= 55
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