Natural Frequency Equation NBCC 2010 2

[EngDM]

Hey guys,

Does anyone know the units in this equation, or have any examples to see? The code doesn't define what units are to be used for the deflection or for the weight.

 

[JoshPlumSE]

This looks like the Rayleigh method to me. Instead of using M_i in the denominator, I prefer to use W_i/g. That way, the force units and weight units are the same.... You just need to remember to divide the weight by the acceleration of gravity.

Obviously, the distance units used for deflections have to be consistent with each other as well.

There are plenty of examples using the Rayleigh method. Here is one I put together some years ago for RISA.
[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1639177951/tips/Rayleigh_Method_m3ghfj.pdf[/url]

 

[EngDM]

Yes I've made the units for force and mass consistent, but the deflection's don't all cancel out with eachother in the denominator unit wise, and it doesn't specify what to take. For now I just took the SI for everything (newtons, meters, etc) as that is my best guess to keep it consistent.

Further, it's not clear with what deflections to take. Either take the total storey drift at a floor i, or take the amount of deflection each floor has WRT to floor i-1. It says that the deflection is caused by force Fi which is force per floor, so that leads me to believe that it should be the latter.

 

[TLHS]

If you're using Newtons in the top, you should use meters for your deflection. Adjust depending on your overall units. Expand out your force unit to kg*m/s^2 for Newtons or an equivalent for whatever else you're using, and then things will make sense. Your units cancel out to 1/sec^2 inside the root symbol, then you take the root and have 1/sec for frequency and it all lines up.

 

[EngDM]

That actually clarifies it a lot, I didn't understand how it gave Hz before without a time term.

 

[JoshPlumSE]

That actually clarifies it a lot, I didn't understand how it gave Hz before without a time term.

This is one of the reasons why I prefer to use weight instead of mass. Because, then I have to convert to mass by using the acceleration of gravity which is given in units of "distance per seconds squared".

 

[EngDM]

This looks like the Rayleigh method to me. Instead of using M_i in the denominator, I prefer to use W_i/g. That way, the force units and weight units are the same.... You just need to remember to divide the weight by the acceleration of gravity.

Obviously, the distance units used for deflections have to be consistent with each other as well.

There are plenty of examples using the Rayleigh method. Here is one I put together some years ago for RISA.

https://res.cloudinary.com/engineering-com/image/upload/v1639177951/tips/Rayleigh_Method_m3ghfj.pdf

Is the deflection the total deflection at that floor, or the difference from the last floor. In the third bullet point it says the deflection caused by force Fi. This reads as if it is the difference in deflection from the previous floor i-1 (i.e. what would be from the floor i).

 

[JStephen]

As I understand it, you apply all the forces simultaneously, calculate total deflections at each point, then run it through that equation.
There's a similar equation in ASCE 7, in the non-building structures (15.4-6 in ASCE 7-16). I don't know that it's any clearer, though. They include a g factor, but then also they are using weights rather than masses.
One thing that's not clear to me is that they say to apply the wind force. For calculating natural frequency, I would think you'd assume force proportional to the mass of each floor, rather than wind force on each floor. Natural frequency should be independent of the wind distribution but dependent on the mass distribution. As long as both are somewhat uniformly distributed over the height, I suppose it doesn't much matter.