1. 40. The flat roof (as seen from the air) has area A = 150 × 5.8 = 870 m2 . The volume of material directly
above the tunnel (which is at depth d = 60 m) is therefore V = A × d = 870 × 60 = 52200 m3 . Since the
density is ρ = 2.8 g/cm3 = 2800 kg/m3 , we find the mass of material supported by the steel columns to
be m = ρV = 1.46 × 108 m3 .
(a) The weight of the material supported by the columns is mg = 1.4 × 109 N.
(b) The number of columns needed is
1.43 × 109 N
n= −4 m2 )
= 75 .
2 (400 × 10 N/m ) (960 × 10
1 6 2
