Foundations - Vibrating Machines 3

[Egnorant]

I have recently started reading “Design of structures and foundations for vibrating machines by Suresh Arya, Michael O’Niell and George Pincus. I wonder if somebody could help with the following queries:-

1. Table 1-4 on page 13 gives various expressions for Constant Force Excitation (CFE) and Rotating Mass Type Excitation (RMTE). In example 1 of Chapter 6, Fig 6-3 shows graph of unbalanced forces which I understand are time dependent viz. are not constant.. However solution in Table 6-2 uses expressions for CFE to calculate magnification factor and amplitude. Whereas in the same example expressions for RMTE are used to calculate resonance frequency. Why is this inconsistency? Why not just use expressions either for RMTE or CFE?

2. Similarly in example 2 of Chapter 6 forces are calculated using the formula mew2, for RMTE, but again solution in Table 6-3 uses expressions for CFE from Table 1-4. Could somebody explain, why?

3. A reduced value of Gs (soil Shear Modulus) is to be used for horizontal movement of pile supported foundation. What is the % reduction normally used in the industry, 10% 20 %...?.

4. In chapter 5 equations for yawning/twisting for pile supported foundations are missing. I was wondering whether somebody could provide literature/equation for these foundations

5. I intend to produce spreadsheets and was wondering if somebody could provide equations used to derive tables and graphs shown in the book.

 

[structSU10]

I took a quick look at the paper. With respect to question 5, if you are refering to the resonance charts, they are based off of solving the differential equations for a particular forcing function with assumed damping ratio's and such; these equations can be found in general dynamic texts, but are hard to apply broadly.

 

[Egnorant]

Hi structSU10 . Thanks for the reply. I am looking for equations to find out the following parameters:- f11.1; f11,2; f7,1; f7,2; f9,1; f9,2; S1; S2,  (alpha) and L (Alpha-L)

 

[WARose]

3. A reduced value of Gs (soil Shear Modulus) is to be used for horizontal movement of pile supported foundation. What is the % reduction normally used in the industry, 10% 20 %...?.

I’ve never reduced this value....instead, [since it is directly proportional to the spring constant for each mode] I have varied the spring constant by plus or minus 25-50% for a variety of runs to see if any variance in this value could hit a resonance “jackpot” [for a lack of a better way to put it]. Keep in mind: what the geotechnical engineer gives you will not be THE exact value. What it actually is will likely fall within a range of values that are +/- X% the value he gave you.

Given the above, that’s why it’s best to have a computer model/spreadsheet that figures this stuff fast because it could be a lot of runs.

4. In chapter 5 equations for yawning/twisting for pile supported foundations are missing. I was wondering whether somebody could provide literature/equation for these foundations

As good as that book was, I noticed that myself......an old text I have [that I think is referenced in the book you are talking about] has those equations (for amplitude of motion). The book is ‘Vibrations of Soils and Foundations’ by: Richart, et al.. The equations of interest [for rocking and torsion] are on p. 214 and 218 (equ. 7-41 & 7-47).

Of course, keep in mind: these are for the whole system modeled as a single degree of freedom [SDOF] system. If your machine is sitting on tall pedestals, they may contribute to displacement more than a model that considers soil stiffness (alone) anticipates.

 

[chichuck]

Egnorant,

I have recently been studying the same book. I too have been working on a spreadsheet(s) to do some of the analyses in the book. I'm almost done with one that does the analysis in Chapter 6 example 1. Maybe we can share experience and thogught.

I have a two-page errata sheet for the book, I've put a link to it at the bottom of this post. My the errata sheet has a correction for the very line in the very table you are speaking of. (My copy of the book is correct.) In the corrected version, the error you cite is still there.

In response to your questions:

1) My take on this is that it is just that, an error that has not been corrected. (In a book this old, I bet there will be no more corrections.) You are correct: for this problem, the input states clearly that the applied force is of the constant-force type. So that determines the formuoas to be used. This particular number, damped natural frequency, is one that is not used elsewhere in the analysis, so it could be left out. But, you would need to know the correct damped natural frequency, so that you can cofirm that the operating frequency is different. In this example, the book does use the correct formulas for magnification factor and transmissibility factor.
2) In example 2, he does use the expression for rotating mass type excitation to calculate the damped natural frequency. I used his values and got the same answers that are in the book. (My errata sheet shows no corrections for this example.)

3) I have not started working on the piled foundations yet.

4) I have not started working on the piled foundations yet.

5) I've used the graph in Figure 4-1 in my spreadsheet. My approach was to carefully read that graph, and make up a table for each curve. THen I used that table for calculation/interpolation to get a value. It's labor-intensive, tedious and it depends on my reading the graph accurately. It's crude, but I made it work for this case. I don't konw how it would work for other graphs. I too would like the formulas for the curves on the graphs, but I don't think they can be had.


May I make a comment on one of your points?

"...Fig 6-3 shows graph of unbalanced forces which I understand are time dependent viz. are not constant.. "

Constant Force Excitation as used in this book does not mean constant with time. It means constat at all frequencies. A reciprocating machine like a compressor applies the same forces to the foundation regardless of the fequency, so during start-up and shutdown, the applied forces do not change.

Not so with a centrifugal machine like a turbine. For those, the dynamic force does change with frequency. 1) the eccentricity varies by the equation shown in Example 6-2 (page 99, Subheading A. e = ebar/ (1-(f/fc)^2). ebar = static eccentricity, f = operating frequency fc = critical frequency for the rotar.

Further, dynamic force applied = Wr/g*e*omega^2. So then, the eccentricity varies with frequency and the applied force varies (further) weith the operating frequency. (see this in the samp location in Ecample 6-2.)

Good luck with your study and your spreadsheets.




Regards,


chichuck

 

[chichuck]

Sorry for the typos in my previous post.

chichuck