00:01
Welcome to this new murray tutorial.
00:04
So here we have a cylindrical hollow vertical tank made from steel, which has a yield stress specification for the given material of 200 mega pascels, which is measured in, in this case, during pressurization, the tank wants to stretch apart.
00:31
So 200 million newton, of stretching force per cross -sectional area of the material, in this case steel.
00:45
So if the tank was a solid rod, one meter in diameter, of course, that would be 0 .785 square meters, 0 .785 of 200 million neutens of stretching force is where the tank, or in this case a rod, one meter in diameter would start to deform and then reach its yield to ultimate stress and then fail.
01:16
But we are dealing with a hollow tank, obviously, shaped in a cylinder, pressurized to seven megapascals of, let's say, compressed air, which is about 1 ,015 psi gauge pressure.
01:41
And as this happens, the longitudinal force will increase and cause the tank to elongate somewhat.
01:54
So this is an application of young's modulus, the stress over strain, sigma stress divided into epsilon strain.
02:04
So sigma is the stretching force in this case divided by the cross -sectional area of the material, not the free space of the tank, but only the, if we cut out the free space, if this was a one meter diameter rod instead of a cylinder, a hollow cylinder, the cross -sectional area of the material, which is part of the diameter.
02:29
So during the pressurization, there will be longitudinal stress as the tank tries to stretch apart on its vertical plane.
02:43
That is what is meant by the longitudinal stress.
02:48
So the first step is to comply with the specifications in the problem and the approved longitudinal stress limit is specified at less than 20 % of the yield stress.
03:15
So we will select 19 % or 0 .19.
03:21
9, this is 19%.
03:30
We then multiply 19 % or 0 .19 times 20 megapascals yield stress of the given steel material and this equals 38 megapascals approved longitudinal stress limit.
04:01
Then we can take the ratio of 38 mega pascal and then divide that into the yield stress limit of the steel material, 200 megapascals, and then multiply this times the cross -section area of the steel material, not the free space of one square meter cross -sectional area.
04:35
So if this was a circular beam solid steel, the cross -sectional area of that beam would be.
04:44
Be the cross -sectional area.
04:45
So now we cut out a majority of that beam and turn it into a hollow cylinder and then we're left with the wall thickness, the steel material wall thickness.
04:58
So that's the conceptualization.
05:00
So in this case, there is a cross -sectional area of the steel wall thickness equal to 0 .19 squared meters...