Beam Deflection Question 1

[anthonyc007]

Here is a dumb question:
Item number 8 (Simple Beam - Concentrated Load at any Point) of the
ASD American Steel Association handbook (the "Green" one) gives a
formula for deflection at x (when x < a). What about if x is > a? How
does the formula change? I would appreciate a smart respose to a dumb
question.

Thanks.

anthonyc007

 

[Lutfi]

This is not a dumb question. It is better to ask than feel and look foolish.

Look at the free body diagram again, if x > a then flip the free body diagram (FBD) and (a) becomes (b) and (b) becomes (a) then compute deflection with proper substitutions as if x is still less than (a which is really your orginal b)!!!

Remember, no one said that (a) must be smaller than (b) and the said diagram did not say that either.

This is what I would do. If I am wrong, I stand to be corrected.

 

[chajakedude]

im not familiar with the book but if x>a would the load be off the beam? or is the starting point a and the ending point b, so that if x>b then the load is off the beam?

 

[anthonyc007]

That makes sense!

Here is another question: Situation No. 4 (Unifrom Load Partially Distributed) does not give a deflection formula. Does anyone know of a good one??

 

[PEinc]

The reference book is the Manual of Steel Construction, Allowable Stress Design, 9th Edition by the American Institute of Steel Construction (AISC).

Three methods to approximate the deflection for Diagram 4:
1. Convert the partial uniform load to a single concentrated load and use Diagram 8. The calculated deflection should be conservative.

2. Convert the partial uniform load to a series of concentrated loads spaced at about 1 or 2 feet on center. Then use Diagram 8 once for each concentrated load to find the deflections at the desired location. Sum the deflections for the desired location.

3. Assume the load is continuous across the entire beam. Find the deflection using Diagram 1. Then use Diagram 4 twice (once at each end of the beam to calculate the deduct deflections for the desired point. Sum the deflection and the deduct deflections to get the actual deflection.


Two recommendations:
1. Buy a beam design program.

2. Look for a free beam design program on the internet. Try the MathCad Library at the following web site:

http://www.mathcad.com/Library/DisplayCategory.asp?c=40&p=1&s=0

 

[Lutfi]

PEinc, I agree with you on the deflection for partial uniform load to obtain an approximate deflection. However, I am not a big fan of people buying and using beam programs if they lack the understanding of fundamentals. For crying out loud, we have engineers graduating who can not, without the help of computer program; do a moment distribution for a three span beam or frame. In my humble opinion, this can have tragic results.

I think all bona fide structural engineers should be able to perform moment distribution by hand and know it by heart. Because those programs may not function one of these days or someone has to verify their results. I am terrified at some of the results that I see.

I saw a report, signed and sealed by PE who is a Phd, for a sheet pile wall that was deflection 108 inches (yes, 9 feet) at the top. They said the results were fine!!!!!!!! I had a heart attack. I stopped the project to say the least. The section was way under designed for bending as well. I still have the original copy of the signed and sealed report.

This is why I am so much against blindly using computers.

Enough said and I shall get of my soap box.

 

[dlew]

Anthonyc007,

The book &quot;Formulas for Stress and Strain&quot; by Roark have formulas for partial uniform load on single span with different support conditions.

I do not include the formulas here because they need a sketch. If you want to see the pertinent book page, let me know your e-mail address and I will send a copy of the page to you.

Regards

AEF

 

[prex]

Anthonyc007,

you can view all the necessary formulae also in the site below, under Beams -> Simple bending -> [support condition] -> [load type] and clicking the button 'Formulas'

prex

http://www.xcalcs.com

Online tools for structural design

 

[corus]

Also try

http://www.engineerstoolbox.com

for general engineering formulae.

 

[reeves111]

I wholeheartedly agree with Lutfi. Furthermore, why not just analyze the beam without using a plug and chug equation? that would probably take less time than posting and waiting for a response as well...