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Beam on Elastic Foundation Theory

12/12/2008 1:45 AM

What is BEAM ON ELASTIC FOUNDATION theory? please guide me.

Beam on elastic foundation is used in nozzle reinforcement theory...but how ?

if any paper or site related to above........?

thanks

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Paresh B. Gujarati
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#1

Re: BEAM ON ELASTIC FOUNDATION

12/12/2008 2:37 AM

I am going to bed - it is late ............... I will answer your other questions this weekend, or maybe tomorrow.

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#2

Re: BEAM ON ELASTIC FOUNDATION

12/12/2008 5:04 AM

www.calculatoredge.com/structural/boef.htm

For solution to your 1st question a xls sheet.

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#3

Re: Beam on Elastic Foundation Theory

12/12/2008 2:10 PM

http://www.codeware.com/support/papers/bildy.pdf

(I am still developing a good answer to your other stress question - give me some more time)

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#4

Re: Beam on Elastic Foundation Theory

12/13/2008 8:22 AM

Get and study the books from Timoshenko on elasticity.

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#5

Re: Beam on Elastic Foundation Theory

12/14/2008 12:59 PM

Consider a beam with a concentrated load acting downward at midspan. If the beam is supported by a hinge at one end and roller at the other, the bending moments and shears can be readily calculated using elementary structural analysis.

If instead, the beam is supported by a hinge and three rollers, the bending moments and shears may be found by considering strain compatibility, knowing that the deflection must be zero at each support. Of course, if it so happens that one of the supports lies directly under the concentrated load, that support takes the whole load. The others take nothing and there is no bending or shear in the beam.

If instead, the hinge and rollers become spring supports, you can solve for the reaction at each spring by equating the beam deflection to the spring deformation at each support if you know the beam stiffness and the spring stiffnesses. It can be done by successive approximations...assume four reactions which add up to the applied load, check beam deflection at each point and compare with spring deformations.

The last example is a simple case of a beam on an elastic foundation. If the number of springs increases indefinitely, you have a beam resting on an elastic material. Each point in the elastic continuum deforms according to the pressure placed on it. This is the usual situation for a beam on an elastic foundation. Often, a beam resting on soil is deemed to be a beam on an elastic foundation even though the soil may not be truly elastic. As stated earlier, there are numerous references you may wish to read in order to solve a particular problem.

I do not know how a beam on elastic foundation is related to nozzle reinforcement theory. Perhaps someone else could enlarge on that aspect of your question.

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#6
In reply to #5

Re: Beam on Elastic Foundation Theory

12/14/2008 2:00 PM

Hello ba/ael,

If I had known how to say it I would have explained like that!

The nearest my thoughts got to it was, thinking it sounded like a wing of an aircraft. But, as I say, I am not qualified as you are and though I understand the theory, if a spanner is thrown in by way of a question, I am stuck, well, mostly.

'Engineering' has to be the most exciting and interesting and, often-time deep subject? It runs the full gamut of all the Laws of physics, nature etc. It is knowing how to use those 'kernels of knowledge' that makes a project a success or disaster?

Good explanation. GA to you.

Take care and happy holiday to you..................

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#7
In reply to #6

Re: Beam on Elastic Foundation Theory

12/14/2008 2:41 PM

Hello bearcub,

Thank you for your kind words and a very Merry Christmas and Happy New Year to you.

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#8
In reply to #7

Re: Beam on Elastic Foundation Theory

12/14/2008 3:05 PM

Hello ba/ael:,

I thank you indeed. Not on topic, but what is the whether like there in 'the winter?

At the moment I live in the south of the UK and it is not too cold, but we have lately had days where the ice lasts all day for several days. No problems with snow though.

Take care.........................

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#9
In reply to #8

Re: Beam on Elastic Foundation Theory

12/14/2008 3:50 PM

Until the last few days, we have experienced much milder weather than normal. Unfortunately, that has come to an end. It is -25oC now and sunny. The low for today is going to be -30oC. The low last night was -39oC. Brr!

So far this year, we have not seen much snow. I don't believe I have shoveled more than six inches from the driveway in total so far. A few days ago, we had freezing rain which triggered many accidents on the roads. It's like driving on an ice rink before the sanding crews get to work and spread salt laden sand at all the stop signs.

The snow tends to drift a bit in my back yard but it also tends to settle with time. On average, the yard has an average of about three inches of snow at the moment. I see fresh rabbit tracks in the snow in my back yard. They (the rabbits) are pure white at this time of year. In summer they are brown.

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#10
In reply to #9

Re: Beam on Elastic Foundation Theory

12/14/2008 5:31 PM

Hello ba/ael:

I can't really imagine how cold that is! The coldest we have had it is in 1969 (I think). We went to see a distant relative and everything in that part of the country stopped. No milk, bread, nothing. Cars were ordered off the roads because they were getting punctures cause by ice slivers.

It was just one white desert, as the small fields filled and the wind blew the snow into amazing shapes! The house we went to is an 'L' shaped Semi. And the two form a courtyard at the back and it completely filled in. Actual snow fall was about 4', but it was worse there because of drifting. But it was comparatively warm when I hear you have -25°. I assume that is Fahrenheit?

Take care and happy holiday........................

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#11
In reply to #10

Re: Beam on Elastic Foundation Theory

12/14/2008 7:04 PM

Hi bb,

The temperatures I gave were in Celsius (Centigrade), not Fahrenheit. When you get to forty below zero, it doesn't matter because the two scales converge at that point (-40oC. = -40oF.).

-25oC is equivalent to -13oF. It's not too bad if you dress for it, but if you happen to be walking into a stiff wind for any length of time, it can be a bit chilly.

If you want to make some quick conversions between these scales, try this site.

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#12
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Re: Beam on Elastic Foundation Theory

12/14/2008 7:56 PM

Hello ba/ael:

If you use Celsius as we do that would make your weather still very much colder than ours.

The 19 below we had was in general and where we stayed was a 'frost hollow' which was about 8 deg colder. As is usual in England, we are never ready for something like that. I suppose if you have 'proper' winters and know it is going to be -25 or so you can arrange your life around it? but when it is just once in a while it comes as a shock!

There was a time when I had nothing better to do, and though I could only just write, very shaky I was. I had a pad and pencil and worked out the temperatures in Fahrenheit, Celsius and Kelvin. So that is also the time I to realised -40F =

-40C. I work between the two automatically, though I have forgotten the Kelvin measurements.

Take care......................

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#13
In reply to #7

Re: Beam on Elastic Foundation Theory

12/15/2008 4:12 AM

same to you ... do u have any idea about combined loading calculations for vessel designed as per ASME VIII-2 ?

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#14

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