# Elasticity problem

1. Jul 15, 2006

### mikejones2000

A tunnel of length L = 154 m, height H = 7.4 m high, and width 6.1 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. (See Figure 12-50.) The tunnel roof is to be supported entirely by square steel columns, 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?
N
(b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?
columns

I know that for the first question the total weight must be equal to the volume x density x gravity but for some reason I keep screwing up finding the density and the number is much too low. Am I approaching this question badly?

2. Jul 15, 2006

### 3trQN

I got something near 157 Tonne of rock.

But my maths is weak.

Make sure your using the right units, wright the units out for each step and ensure that your density is correct ( g per square meter or centimeter ).

$$1m^{2} = 1m\times1m = 10cm\times10cm = 100cm^{2}$$
therefor the density is:
$$2.8g cm^{-2} = 2.8(100)g m^{-2}$$

Last edited: Jul 15, 2006