Direct Analysis Method

[jscolostate]

I have been trying to replicate the results of a Direct Analysis Method example given in an article in "Structural Engineer". The analysis is of a fixed-free column subjected to an axial and lateral load at the free end. However, I have tried many different approaches and can not seem to match the values they get.

I know that many computer programs are now capable of doing second order analysis and even the Direct Analysis Method, but I would really like to understand how to obtain the answer by hand.

I have attached a file containing the article with the example, as well as my work. Does anyone know where I am going wrong?

 

[Lion06]

I just printed it out and ran through it quickly and I noticed that you used 0.47 for taub, but it should actually be 1.0.
If you look at page 16.1-198 of the 13th edition manual, you will see that for alphaPr/Py<=0.5 taub=1.
In your case alphaPr/Py = 0.43 so taub=1.
You used the equation when you shouldn't have.

 

[jscolostate]

Thank you StructuralEIT. I guess I was convinced that my error was in the procedure or theory, and overlooked my simple mistake. Sometimes it just takes another set of eyes.

 

[Lion06]

No problem. I just finished up the rest of it. One other thing I noticed is that the article uses an out-of-plumbness of 0.01 (I assume they actually mean 0.001 - which is 1/1000). I hope they don't actually mean 1/100.
Anyway, using 0.001 and taub=1.0, I get a Mu = 1772K-in. This is not exactly what they get in 1753K-in, but it's pretty close. Do you have the rest of the article? I would be interested in seeing it.
Check out the article I posted in this thread. You would probably be interested in reading it. It's directly from AISC

thread507-221470

 

[jscolostate]

So did you use a lateral load of 0.001Pu instead of 0.01Pu for your calculations, or did you just use the out-of-plumbness value of 0.001 for the calculation of Pe2?

And I actually found that article you posted yesterday, which was extremely helpful. I had been looking everywhere for an actual numerical example on the application of the Direct Analysis Method. It seems like DAM theory is everywhere, but what good is that if you don't know how to apply it?

I attached the full article that I was referencing. It is a little outdated, but still useful.

 

[Lion06]

I used a lateral load of 0.001Pu instead of 0.01Pu.
Thanks for the article.