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

In summary, the problem involves constructing a tunnel with specific dimensions and determining the total weight of ground material the columns must support, as well as how many columns are needed to keep the stress on each column at one-half its ultimate strength. The solution involves calculating the volume of ground above the tunnel, determining the stress on each pillar, and using this information to find the number of columns needed.
  • #1
itachipower
10
0

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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  • #2
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?
 
  • #3
haruspex said:
Each pillar. If there are n pillars, what's the load on each?

Oh okay. I got it! Thanks :)
 

What is the difference between stress and strain?

Stress is the force applied to an object, while strain is the resulting deformation or change in shape of the object. In simpler terms, stress is the cause of the change and strain is the effect.

How is stress and strain measured?

Stress is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2). Strain, on the other hand, is measured as the ratio of the change in length or shape of an object to its original length or shape.

What are the different types of stress and strain?

There are three main types of stress: tensile (pulling) stress, compressive (pushing) stress, and shear (twisting or sliding) stress. Similarly, there are three main types of strain: tensile strain, compressive strain, and shear strain. Each type of stress and strain has a different effect on an object.

How does stress and strain affect the behavior of materials?

The behavior of materials under stress and strain is determined by the material's properties, such as its elasticity, strength, and ductility. Some materials, like rubber, are highly elastic and can return to their original shape after being stretched, while others, like glass, are more brittle and will break when subjected to stress.

What are some real-world applications of stress and strain?

Understanding the concepts of stress and strain is crucial in fields such as engineering, construction, and materials science. These concepts are used to design and test structures, predict the behavior of materials under different conditions, and ensure the safety and reliability of various products and systems.

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