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Stress and strain physics

  1. Nov 17, 2013 #1
    1. The problem statement, all variables and given/known data
    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 [Broken]

    2. Relevant equations

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

    3. 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 :)
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 17, 2013 #2

    haruspex

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    Each pillar. If there are n pillars, what's the load on each?
     
  4. Nov 18, 2013 #3
    Oh okay. I got it! Thanks :)
     
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