ASCE 7-16 15.4.4 - Approximating Seismic Period

[duckhawk]

Hello,

I have a question about section 15.4.4 in ASCE 7-16. I'm trying to use equation 15.4-6 to calculate the approximate period for a trussed tower. However, I don't understand the equation they give fully. It says fi represents any lateral force distribution, and then it says the elastic deflections need to be calculated using the applied lateral forces. My question is: do you apply all the lateral forces in 1 load case and use corresponding deflections, or do you apply 1 force at a time and use corresponding deflections?

I've tried both of these methods for the same force distribution and same trussed tower and I'm getting a different approximate period, so it looks like it does matter which one is chosen.

Appreciate it,
dh

 

[HS_PA_PE]

The 'i' represents the vertical level, or "story". For the force at each level, use the corresponding displacement at that level. This approximation uses the Rayleigh method, which you can look into if you are trying to get a better idea of how to apply it. I hope that helps a bit

 

[KootK]

I've tried both of these methods for the same force distribution and same trussed tower and I'm getting a different approximate period, so it looks like it does matter which one is chosen.

The method cannot be decoupled from the character of the forcing function, as you are finding. The method is based on energy and, therefore, the relative amount of work being done to excite the mass of each diaphragm matters as those diaphragms travel laterally.

You don't actually need the forces however. All you need is the shape of the force distribution. Similar to shape functions in general FEM.

So your process ends up being something like this:

1) Assume a base shear of any magnitude.

2) Distribute the base shear to the various diaphragms as you normally would.

3) Use the forces from [2] in the Rayleigh method to estimate the period.

 

[JoshPlumSE]

The 'i' represents the vertical level, or "story". For the force at each level, use the corresponding displacement at that level. This approximation uses the Rayleigh method, which you can look into if you are trying to get a better idea of how to apply it. I hope that helps a bit

Yup, simple Rayleigh method. When I've done this in the past, I've used whatever lateral force distribution I've already applied to the structure. Might be wind load, might be seismic.

I don't think apply a single load at a single floor would be a good idea though....

 

[JoshPlumSE]

I should also point out that I did an example problem (when I worked for RISA) that demonstrated how VERY accurate this method was when compared to a standard Eigensolution.

 

[duckhawk]

I should also point out that I did an example problem (when I worked for RISA) that demonstrated how VERY accurate this method was when compared to a standard Eigensolution.

This is one of the reasons why I'd like to understand equation 15.4-6 better. Using it, I'm calculating a period of about 0.6 seconds. Using the dynamic analysis in RISA, it is calculating a period of 1.2 seconds.

 

[HS_PA_PE]

That seems like a significant difference. Would you be able to post your calculation? One of the nice features of this method is that it can give very accurate results, as @JoshPlumSE pointed out, even when the shape function is not very exact.

 

[JStephen]

A while back, I was checking this on a tank. I tried distributing loads proportional to the deflections and iterating to a solution. Result: A lot of extra work and almost exactly the same frequency.
More clarity would definitely be helpful with the way it's presented there, though. For example, in the Vibrations textbook, it's given in terms of forces and masses, and you have to throw in a Gc constant here or there to make the units work out in that case. They don't show units on the variables here (so, for example, I think delta needs to be in feet, but it doesn't say that). Is P-delta deflection to be included? Is base rotation to be considered?

 

[duckhawk]

Here is an example problem with the Rayleigh method. In this example, it says all loads are considered in 1 load case, then the deflections at each level are determined. This seems to be the answer.

This is opposed to the original method of applying 1 load at a time.

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

 

[JoshPlumSE]

Here is an example problem with the Rayleigh method. In this example, it says all loads are considered in 1 load case, then the deflections at each level are determined. This seems to be the answer.

This is opposed to the original method of applying 1 load at a time.

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

Hey.... That's the one I put together for the RISA training manual on dynamics. I always liked putting together a classic hand calculation to demonstrate the validity of a feature in the program.

 

[duckhawk]

That seems like a significant difference. Would you be able to post your calculation? One of the nice features of this method is that it can give very accurate results, as @JoshPlumSE pointed out, even when the shape function is not very exact.

Turns out I was using wrong units for deflection.. when the right units are used, the Rayleigh method works and matches RISA, as JoshPlumSE stated above. Also, I can confirm that applying 1 lateral load at a time and getting corresponding deflections is incorrect. The correct way is to apply all lateral loads in 1 run and get deflections from it to use for the period equation.

Appreciate your help!

 

[Celt83]

Bondy has a good example with the Rayleigh Method in his Seismic Lecture series around the 9 minute mark in lecture 6: