2ndOrderAnalysisExample

[hoshang]

Hi all,
This link:

https://www.bgstructuralengineering.com/BGSCM14/BGSCM009/BGSCM00903.htm

has a 2nd Order Analysis Example:

https://www.bgstructuralengineering.com/BGSCM14/BGSCM009/2ndOrderAnalysisExample.pdf

MB=1040ft.lbf+500lbf*(.0403in)
They made this multiplication 500lbf*(.0403in) equal to 3.4ft*lbf.
Per my calculation this should be 1.677ft*lbf, am I missing something?

 

[Stress_Eng]

I’ve come across a number of ways to calculate the BM magnification effects of compression loads on beam columns, one being the tabular approach given in the example. The approach I usually apply are the solutions to the 2nd order differential equations for numerous loading cases. I suggest using a different source such as Roark and compare the results.

 

[SlideRuleEra]

hoshang - I agree with your math:

(500 lb) x (0.0403 in) / (12 in/ft) = 1.68 lb-ft

Not 3.4 lb-ft shown in the example.

 

[lexpatrie]

It looks like you're looking at the 14th edition of Bart's work. Make sure the fifteenth and sixteenth have this corrected and then email Bart with the question/correction (there's a report errors link to an email on the web site).

That way the error gets corrected everywhere. It's not your job to track down all the typos, but if there are typos or errors it'd help them out since they do that web site for tips, basically. I can't even find that design example through the web site.

The last copyright on the site is 2023 so it's fairly recent.

If you're confused or think there's a mistake then others are probably also staying quiet but having the same issue.

As a side note there's a closed form solution for this case, it's being used as an example of an iterative approach. I used it to debug a 2nd order elastic program quite a few years ago. It might be in Roark's.

I haven't read this in enough detail, but if you thing it's a calculation error (500 * .0403 / 12 in/ft) = 1.679 k-ft, that is also in the 13th edition PDF on the web site as well, that one I can find.

https://www.bgstructuralengineering.com/BGSCM13/BGSCM009/2ndOrderAnalysisExample.pdf

https://www.bgstructuralengineering.com/BGSCM15/BGSCM009/2ndOrderAnalysisExample.pdf

(same potential error)

https://www.bgstructuralengineering.com/BGSCM16/BGSCM009/2ndOrderAnalysisExample.pdf

(same potential error)

It's a conservative error, if it's an error, the design still works.

 

[Stress_Eng]

Your case is in Roark’s, 7th edition, table 8.8, case 3a (cantilever under compression and BM at the free end).

Both my template and Roark give the same max BM. If I’ve used the example inputs correctly, you get 1042.4 lbf-in.

 

[lexpatrie]

I'm not convinced this is in the public domain, but the Internet Archive has it.

https://www.eng-tips.com/faqs.cfm?fid=2789

 

[lexpatrie]

Bart has confirmed a typo and intends to revise.