How many columns are needed to support the roof of an underground tunnel?

AI Thread Summary
The discussion focuses on calculating the total weight of ground material that square steel columns must support for an underground tunnel. The total weight was determined to be 1.54e9 N, based on the volume of the ground above the tunnel and its density. The next step involves calculating the compressive stress on each column to ensure it remains at half its ultimate strength. The user initially struggled with determining the load per column but eventually grasped the concept of dividing the total load by the number of columns. The conversation highlights key calculations needed for structural support in tunnel construction.
itachipower
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Homework Statement


A tunnel of length L = 151 m, height H = 7.7 m high, and width 6.2 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. 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.

hrw7_12-50.gif


(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?

Ultimate strength table:

http://imageshack.com/a/img841/9748/xup3.png

Homework Equations



F/A = (E * delta L)/L

The Attempt at a Solution



For a, I calculated the volume of the ground above the tunnel and multiplied it by the volume to ground material ratio given in the problem and multiplied it by 9.8 and got 1.54e9 N (which was correct)

For part b, I have no idea how to proceed with the problem. It says calculate the stress on each pillar which I calculated by doing:

F/A
1.54e9/.096 = 1.604e10

I have no idea where to go after this point.
Thanks for your help :)
 
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itachipower said:
It says calculate the stress on each pillar which I calculated by doing:

F/A
1.54e9/.096 = 1.604e10
Each pillar. If there are n pillars, what's the load on each?
 
haruspex said:
Each pillar. If there are n pillars, what's the load on each?

Oh okay. I got it! Thanks :)
 
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