What does the variables represent for STRESS= F/A involving concrete?

Question

A concrete column has a volume of 565 m cubed, and a height of 20 m. What is the max. weight (expressed in newtons) that the column can tolerate before fracturing?

i've researched that maybe

f=compression=horizontal pressure?

a=tension=vertical pressure?

and that i am looking to solve stress?

so where does the volumn come into play, and the height?

i am so lost! help please!

Answer 1

You're overthinking, this is a simple problem. You need the area to calc the stress:

Area = Volume / height

And, weight / area = max stress

because by definition, F/A = stress

So, weight = max stress * area

Note that you also need to do a column buckling calculation in real life, but I don't think this is expected... also can be complicated for brittle materials like concrete...

Edit:

Area = vol/H = 28.25m²

Concrete compressive strengths range is 5 - 50+ MPa. Your value of 20 MPa falls in nicely.

Your problem is that you need to take Physics I and II, where you study units and unit conversion. Pa is Pascals, or N/m². M is SI units ("metric") for mega or 10^6.

OK, so

weight = max stress * area

weight = 20 MPa * 28.25m² = 565 MN (mega Newtons, or 10^6 Newtons)

So, you got it!

Answer 2

wingsto is correct. If you are taking a mechanics of solids course however you may actually need to do the buckling calculation. Use wingso's formulas to get the variables you need then get the max pressure that can be exerted on the column from

Pressure = (pi^2*Modulus of elasticity of material*moment of inertia)/(length of column squared)

This is one of Euler's formulas. You can search the interned for the modulus of elasticity of your material and moment of inertial calculations should be in your book. Use Pressure=F/A to find the max weight (F=weight*gravity) on the column.