# Modal Analysis



## dakota_79 (Feb 19, 2012)

In Williams' "Structural Engineering PE License Review Problems &amp; Solutions (6th ed.)", problem 1.14, part 2 (dynamic method), he does not scale down the story forces (Fi) by the I/R factor. My reading of ASCE 7-05 12.9.2 is that those forces can be scaled down by I/R (assuming the spectral accelerations and velocities given in the problem statement are based on one of the response spectrum methods referenced in ASCE). What am I missing there?

I'm from the midwest and have rarely done seismic design, and never done an ASCE-based modal analysis in my life, so forgive me if I'm missing something stupid.


----------



## McEngr (Feb 20, 2012)

dakota: I'm originally from the midwest and now working in the northwest for the past 6 years. That being said, I can relate with your frustration. The truth is, the modal (or dynamic) analysis methods are rare in this day and age because they are usually on substantial projects where it is warranted.

I once owned SK Ghosh's dynamic analysis book, but I decided to sell it so I could purchase more testing material related to the new codes of the SE exam. I say this also because I doubt that you will see substantial coverage of dynamic analysis on the exams. I will merely skim it because it's not in my daily practice and I think I can afford to miss just one problem in a morning session (&lt;1% chance of it being covered in the afternoon in my opinion).

Now, on to your question:

I assume that you noticed that the Vt&gt;0.85V is noted at the bottom of page 66. The ASCE 7 disallows the seismic base shear to be less than 85% of the prescriptive ELF procedure. This means that you would have to perform both a modal and ELF procedure to ensure that the modal analysis procedure is still within code prescribed limits (very time consuming). Nonetheless, the 164 kips x 0.85 = 139.4 kips. Because the modal analysis procedure is 146 kips, you would only be allowed to reduce to 139.4 kips because 139.4 is the lower limit. If anything, it shows that for most structures, it may not be cost-effective to pay an engineer the kind of calculations it would take to go with the dynamic method. On page 67, it appears that Williams doesn't exhaust his analysis procedure by setting Vt=0.85V.

I hope this is helpful. Otherwise, I will digress...


----------



## wmmw (Feb 20, 2012)

dakota,

I do not have this book however you are totally right..Before comparing between Vt (dynamic base shear) &amp; 0.85*V (ELE) you have to scale down the story forces (Fi) from the model (dynamic method) by the I/R factor


----------



## dakota_79 (Feb 20, 2012)

Thanks for the feedback, guys.

McEngr: yeah, unless it shows up on an afternoon problem, (and even then) I'm guessing they can't go too in depth with a dynamic problem. But since I'm pretty comfortable with the ELF stuff and distributing base shears up the building, figured I'd heed the advice of the couple CA SE's from my office and at least have a fundamental understanding of the dynamic methods, calc-ing a basic frame's actual (as opposed to prescribed) period, etc. Not going to waste much more time on it aside from running through a couple problems. Better to be over-prepared, and good for building the knowledge base if nothing else.


----------



## kevo_55 (Feb 21, 2012)

dakota_79 said:


> Thanks for the feedback, guys.
> 
> McEngr: yeah, unless it shows up on an afternoon problem, (and even then) I'm guessing they can't go too in depth with a dynamic problem. But since I'm pretty comfortable with the ELF stuff and distributing base shears up the building, figured I'd heed the advice of the couple CA SE's from my office and at least have a fundamental understanding of the dynamic methods, calc-ing a basic frame's actual (as opposed to prescribed) period, etc. Not going to waste much more time on it aside from running through a couple problems. Better to be over-prepared, and good for building the knowledge base if nothing else.


dakota,

The advice from the couple of CA SE's at your office is pretty good. A general understanding of dynamic methods is all that is required. This isn't rocket science, it is structural engineering.

And this is comming from another CA SE.


----------



## dakota_79 (Feb 22, 2012)

Thanks for the 2c, kevo. I really respect your opinion based on what I've read on this forum.


----------

