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

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SUMMARY

The discussion focuses on calculating the number of steel columns required to support the roof of an underground tunnel measuring 151 m in length, 7.7 m in height, and 6.2 m in width, located 60 m below ground. The total weight of the ground material above the tunnel is calculated to be 1.54e9 N. To determine the number of columns needed while maintaining the compressive stress at half the ultimate strength, the user initially calculated the stress on each column using the formula F/A, resulting in a stress of 1.604e10 N/m². Further clarification was sought on how to distribute the load across the columns.

PREREQUISITES
  • Understanding of basic physics principles, particularly force and stress calculations.
  • Familiarity with structural engineering concepts, including compressive strength and load distribution.
  • Knowledge of material properties, specifically the ultimate strength of steel.
  • Proficiency in using formulas related to force, area, and stress (F/A).
NEXT STEPS
  • Research the ultimate strength of various steel grades to determine appropriate materials for column construction.
  • Learn about load distribution techniques in structural engineering to optimize column placement.
  • Study the principles of tunnel design and the effects of ground pressure on underground structures.
  • Explore advanced calculations involving safety factors in structural engineering to ensure stability.
USEFUL FOR

Civil engineers, structural engineers, and students studying tunnel construction or underground structural support systems will benefit from this discussion.

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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