Indeterminate Structures and Stress

[G-reg]

Homework Statement

A tunnel of length L = 141 m, height H = 6.9 m high, and width 6.0 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


What is the total weight of the ground material the columns must support?

I have attached the picture that goes with this problem; hopefully it works!

Homework Equations

Volume = L(w)(d) = (141m)(6m)(60m) = 50760m^3

1.0cm^3 = .01m^3

2.8g = .0028kg

Total weight = Volume * .0028kg * 9.8m/s^2

The Attempt at a Solution

Total weight = Volume * .0028kg * 9.8m/s^2

I know that this is wrong but I can't come up with anything else that makes sense and could use some help! Thank you in advance!

 

[anathema]

Thank you for your question. I would approach this problem by first calculating the total volume of the columns that need to be supported by the ground material. This can be done by multiplying the cross-sectional area of each column (960 cm2) by the number of columns (unknown at this point).

Next, I would calculate the mass of each column by multiplying the volume of each column by the density of the steel material (unknown at this point). This will give us the total mass of the columns that need to be supported.

Finally, we can calculate the total weight of the ground material by multiplying the total mass of the columns by the acceleration due to gravity (9.8m/s^2). This will give us the final answer for the total weight of the ground material that the columns must support.

I hope this helps in solving the problem. If you have any further questions or concerns, please do not hesitate to ask.



Scientist at [Your Institution]

 

[kerimek]

I would approach this problem by first identifying the key factors and assumptions. The tunnel is being constructed underground, which means it will be subject to a certain amount of stress from the surrounding ground material. The tunnel will also have a specific length, height, and width, and will be supported by square steel columns. The ground material has a known mass per unit volume.

To calculate the total weight of the ground material that the columns must support, we need to consider the stress on the columns and the force of gravity on the ground material. The stress on the columns will depend on the dimensions of the tunnel and the weight of the ground material above it. The force of gravity on the ground material will depend on its volume and density.

Using the given information, we can calculate the volume of the ground material above the tunnel to be 50760 m^3. Converting this to cubic centimeters, we get 50760000000 cm^3. Multiplying this by the density of the ground material (2.8 g/cm^3), we get a total weight of 141888000000 g or 141888000 kg.

However, this is only the weight of the ground material above the tunnel. We also need to consider the stress on the columns. To do this, we can use the formula for stress: stress = force/area. In this case, the force is the weight of the ground material (141888000 kg) and the area is the total cross-sectional area of the columns (960 cm^2). This gives us a stress of 147800 kg/cm^2.

In conclusion, the total weight of the ground material the columns must support is 141888000 kg, but the stress on the columns will be 147800 kg/cm^2. This means that the columns will need to be strong enough to withstand this stress in order to support the weight of the ground material and the tunnel itself.