Thread: Concrete slab reinforced - density

There is only one question I am slightly stuck on. Here it is:

A concrete lintel of 2.6 x 0.15 x 0.10m and density 2215 kg/m3, is reinforced by two 15mm diameter steel bars. Assuming the density for mild steel to be 8000kg/m3, calculate the mass of concrete in the lintel.

Someone please help! It would be much appreciated!

You have two cylinder of steel, presumably 2.6 m long and 15 mm diameter. Volume of a cylinder of length l and diameter d is pi.l.(d/2)^2 The cuboid is 2.6 x 0.15 x 0.10 cubic m and you have to subtract the volume of the 2 cylinders to find the volume of concrete. Now volume of concrete x density of concrete = mass of concrete. (You're not asking for mass of steel, so density of steel is irrelvant at this point.)

I assume this lintel is a reinforced concrete lintel beam whose:
>>>average density is 2215 kg/(m^3)
>>>length = 2.6 meters
>>>length per steel bar = 2.6 m also
(In reality, the rebars are not exactly as long as the concrete beam. They are either longer,if their ends are hooked, or shorter because of the required concrete covering.)

density is mass per unit volume.
Or, density = (mass)/(volume)

If the material is composite, or made up of various types of materials, then its density is its average density.
The reinforced concrete lintel beam is composite.
Its average density is (total mass)/(total volume).

ave. density = (mass of concrete + mass of steel bars) / (volume of concrete + volume of steel bars)

For lintel beam:
Total volume = (2.6)(0.15)(0.10) = 0.039 m^3
So,
2215 = (total mass)/(0.039)
total mass = (2215)(0.039) = 86.385 kg ----***
That is, (mass of concrete +mass of steel bars) = 86.385 kg.

For the steel bars,
total volume = 2[(pi/4)(15/1000)^2 *2.6] = 0.0009189 m^3
So,
8000 = (mass)/(0.0009189)
mass = (8000)(0.0009189) = 7.351kg ---***

Therefore, mass of concrete = 86.385 -7.351 = 79.034 kg
Or, mass of conrete = 79 kg -----answer.

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I assume also that you know:
>>>1 mm = 1/1000 m
>>>Volume of rod = [pi*(radius)^2](length) = [(pi/4)(diameter)^2](length).