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Strength of Beams

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duncan webster10/09/2020 23:37:41
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As others have said this gets fairly complicated fairly quickly. Basically you want to get the section as tall and thin as possible but if you overdo it you get buckling. A very good book for starters is Structures or Why Things Don't Fall Down by a chap called Gordon. He has a companion volume called The New Science of Strong Materials.

Torsion of non circular sections, especially things that don't resemble bars or tubes gets even more complicated

ega10/09/2020 23:47:40
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Posted by duncan webster on 10/09/2020 23:37:41:

As others have said this gets fairly complicated fairly quickly. Basically you want to get the section as tall and thin as possible but if you overdo it you get buckling. A very good book for starters is Structures or Why Things Don't Fall Down by a chap called Gordon. He has a companion volume called The New Science of Strong Materials.

Torsion of non circular sections, especially things that don't resemble bars or tubes gets even more complicated

The latter of these good books is sub-titled "Why You Don't Fall Through the Floor".

Michael Gilligan10/09/2020 23:51:33
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Posted by duncan webster on 10/09/2020 23:37:41:

Torsion of non circular sections, especially things that don't resemble bars or tubes gets even more complicated

.

Imagine doing the calculations for a monocoque car body-shell surprise

... and so to bed.

MichaelG.

duncan webster11/09/2020 00:02:28
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I'm told that back in the 1930's they used to do FE anaysis of aircraft structures using rooms full of (mainly) women, who each did one particular bit of the sum then passed it on to the next. Sounds mind boggling to me. These ladies were known as 'computers'

John MC11/09/2020 07:25:30
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For a book that would help with the calculation side of this topic I would heartily recommend "Strength of Materials" by Geoffrey H Ryder. I've had a copy most of my working life. Still using it now.

I've also used Roark's and Shipley's books on the subject.

John

Sam Longley 111/09/2020 07:54:51
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Posted by Martin Kyte on 10/09/2020 11:39:03:

Re castellated beam

Interesting way they make those. The webs are cnc cut (Water jet or Plasma) so that the two half profiles stack inside each other to fit onto a blank less than the final width of the finished web. The 'points are then butt welded to form a web with a series of circular hole down the middle. Add top and Bottom and you have your castellated beam.

regards Martin

Just one point-- They are not normally circular holes but hexagonal. That gives flat surfaces for the weld at the new meeting point.

Going back to the OP's post & comment about the ruler. It is certainly stronger on edge.

Just an itemt that may solve a problem for someone. If they want a beam for a construction in a house etc, then a piece of flat plate the depth of the joists (or slightly less), bolted betweem 2 timber joists makes an excellent beam. It is cheap, & can be inserted into construction easily. Plasterboard etc can be easily nailed to it without awkward noggins etc. Herringbone noggins can be added in the space as normal if required to avoid rotation

 

Edited By Sam Longley 1 on 11/09/2020 08:06:32

DC31k11/09/2020 08:05:50
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Posted by duncan webster on 11/09/2020 00:02:28:

These ladies were known as 'computers'

I thoroughly endorse your recommendation of Gordon's books.

Not only do they deal with traditional engineering materials of concrete and steel, but also give very good accounts of building in stone, as well as interesting discussion of nature's own building materials, wood, bone and sinew.

On the 'computers' issue, applied to the US space program, the book 'Hidden Figures' is very good.

JA11/09/2020 08:16:52
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Posted by John MC on 11/09/2020 07:25:30:

For a book that would help with the calculation side of this topic I would heartily recommend "Strength of Materials" by Geoffrey H Ryder. I've had a copy most of my working life. Still using it now.

I've also used Roark's and Shipley's books on the subject.

John

Ryder took me through college and then I sold it. It is one of the few text books I wish I had kept.

JA

DC31k11/09/2020 08:17:46
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Posted by Sam Longley 1 on 11/09/2020 07:54:51:
Just one point-- They are not normally circular holes but hexagonal. That gives flat surfaces for the weld at the new meeting point.

It is horses for courses.

The traditional ones give long spans for efficient material use, good for single-storey warehouses and industrial buildings.

However, when it comes to multi-floor construction (office space), the circular ones are much more popular. They allow the myriad of building services to pass through the holes in the web rather than under the bottom flange. This means the overall structural depth can be reduced, allowing more than one extra floor (with its per square foot rent).

Where rectangular holes are needed, they can be incorporated, usually with stiffener ribs above and below the opening.

The march of technology has also had an influence. Traditional castellated beams were cut out of pre-existing rolled sections. Most modern cellular beams are cut from three plates and welded together. This gives you a lot more choice on both flange thicknesses and widths and also web height. CNC profiling and automatic welders facilitate this.

Michael Gilligan11/09/2020 08:25:52
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Posted by Sam Longley 1 on 11/09/2020 07:54:51:

Just one point-- They are not normally circular holes but hexagonal. That gives flat surfaces for the weld at the new meeting point.

.

I suppose that would depend upon one’s definitions of ‘they’ and ‘normally’

As I mentioned yesterday:

_____

Here’s an interesting page:

**LINK**

Edited By Michael Gilligan on 10/09/2020 21:34:21

_____

MichaelG.

Michael Gilligan11/09/2020 08:37:46
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Posted by Sam Longley 1 on 11/09/2020 07:54:51:

Going back to the OP's post & comment about the ruler. It is certainly stronger on edge.

.

Sorry to be a bore, Sam ... but :

whilst certainly stiffer, I think stronger remains interestingly debatable.

MichaelG.

DC31k11/09/2020 08:40:04
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I am glad that people are slowly coming to the conclusion that the question is unanswerable as posed.

For a given area of material, anything other than a regular shape (circle, equilateral triangle, square, etc.) can be made to have an almost infinite second moment of area.

Take the I-beam, for example. I read that gold can be hammered to 4 millionths of an inch thick. So use 1% of the material to make a web of this thickness and divide the rest of the material between the two flanges.

Totally impractical as a real-world object but fits the question very well.

A little thought on the first example given in the original post would show the form of the question presents difficulties.

You do not need to be Superman to deflect a rectangle on edge. Take a ruler and try it. Press not too hard and it will buckle out of the plane of the applied load. And that is the problem every real-world engineer has to face. Pushing on things in one way induces forces and effects in another.

A more simple example is compression. Intuitively, why would we expect a structure to behave much differently when we squash it as opposed to when we pull it apart? But it does. And this has been known since Euler's time.

So when we bend something, we have both tension and compression (and anyone who has ever cut a branch of a tree will know this) and the member subject to bending will inherit some of its behaviour from both of these.

Nicholas Farr11/09/2020 11:00:34
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Posted by Sam Longley 1 on 11/09/2020 07:54:51:
Posted by Martin Kyte on 10/09/2020 11:39:03:

Re castellated beam

Interesting way they make those. The webs are cnc cut (Water jet or Plasma) so that the two half profiles stack inside each other to fit onto a blank less than the final width of the finished web. The 'points are then butt welded to form a web with a series of circular hole down the middle. Add top and Bottom and you have your castellated beam.

regards Martin

Just one point-- They are not normally circular holes but hexagonal. That gives flat surfaces for the weld at the new meeting point.

Going back to the OP's post & comment about the ruler. It is certainly stronger on edge.

Just an itemt that may solve a problem for someone. If they want a beam for a construction in a house etc, then a piece of flat plate the depth of the joists (or slightly less), bolted betweem 2 timber joists makes an excellent beam. It is cheap, & can be inserted into construction easily. Plasterboard etc can be easily nailed to it without awkward noggins etc. Herringbone noggins can be added in the space as normal if required to avoid rotation

 

Edited By Sam Longley 1 on 11/09/2020 08:06:32

Hi Sam, well not always hexagon, in fact most lorry trailers that I've seen with castellated beams had what you might call a clipped diamond shape. But whatever shape they are, it's the term that is used for this type of beam.

Of course back before water jet, plasma cutting and CNC were around, they were flame cut and in many cases by skilled people.

Regards Nick.

Edited By Nicholas Farr on 11/09/2020 11:01:49

Zan11/09/2020 11:45:39
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The “strength” of the beam we are talking about is bending I.e stiffness

If I remember back correctly to my engineering classes, any beam in bending, the strength is simply width * depth ^3. (Cubed) so double the with and double the stiffness,  but double the depth It goes up from 1to 8 As the beam is in both tension and compression then there is zero force at its centre(neutral axis) resulting that  most of the material in the beam should be placed as far from the neutral axis as possible, hence the economy of the I beam in both terms of material used and it’s weight .

The problem is in resisting flexing ((sideways deflection and twisting). The ruler being very thin for its depth will Easily flex sideways . Applying this to the boring bar is interesting as the resultant forces are neither vertical or horizontal so directly but as the cutting point extends outside its geometric form then there is an additional rotational component The bar is cantilevered at the tool post, but the bit is cantilevered at right angles to that.  Very complex! So round or square would be best  and as big as possible!

in his articles about boring bars, G Thomas talked about the bar with the bit clamped by a push rod along its axis and commented on how little difference the hole for the rod made to the stiffness of the bar

Edited By Zan on 11/09/2020 11:49:31

Edited By Zan on 11/09/2020 11:56:34

Nicholas Farr11/09/2020 12:17:53
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Posted by Zan on 11/09/2020 11:45:39:

The “strength” of the beam we are talking about is bending I.e stiffness


The problem is in resisting flexing ((sideways deflection and twisting).

Edited By Zan on 11/09/2020 11:49:31

Edited By Zan on 11/09/2020 11:56:34

Hi putting this with SOD's hanging a load on the end is fine, but lifting the same load that is not sideways perpendicular with the beam maybe a different matter altogether and the further away from sideways perpendicular the load is, the worse the situation becomes and can lead to permanent distortion or even failure of the beam.

Regards Nick.

Sam Longley 111/09/2020 13:00:24
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Posted by Michael Gilligan on 11/09/2020 08:25:52:
Posted by Sam Longley 1 on 11/09/2020 07:54:51:

Just one point-- They are not normally circular holes but hexagonal. That gives flat surfaces for the weld at the new meeting point.

.

I suppose that would depend upon one’s definitions of ‘they’ and ‘normally’

As I mentioned yesterday:

_____

Here’s an interesting page:

**LINK**

Edited By Michael Gilligan on 10/09/2020 21:34:21

_____

MichaelG.

The example you refer to with circular holes is not what I was referring to. If one wants to put a cut along the web of a beam then separate the 2 halves & offset & then re weld to form a deeper castellated beam one needs an edge to weld to. If the line was a wavey one the meeting points would not meet in a way which could be suitably welded & the holes would NOT be circular. Standard castellated beams cut from a simple I beam would be cut such that the line has flat edges for the weld. The hexagonal hole thus remaining would still leave room for services & I do not recall having difficulty installing them. I did fit quite a few tonnes of the stuff in a number of new schools halls etc But I do confess, that was 40 years ago & things move on, so If I am wrong then I stand corrected

The example in the one in the link would , presumably, be cut from an I beam with considerable waste.

John MC11/09/2020 13:16:12
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Posted by JA on 11/09/2020 08:16:52:
Posted by John MC on 11/09/2020 07:25:30:

For a book that would help with the calculation side of this topic I would heartily recommend "Strength of Materials" by Geoffrey H Ryder. I've had a copy most of my working life. Still using it now.

I've also used Roark's and Shipley's books on the subject.

John

Ryder took me through college and then I sold it. It is one of the few text books I wish I had kept.

JA

Have a look at the secondhand copies for sale on Amazon, postage costs more than the book.

I worked with Geoff Ryder, the author, for a few years. With out a doubt an extremely intelligent man who could right a very good book, but ask him to explain something verbally, oh dear......

John

Michael Gilligan11/09/2020 13:49:33
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Posted by Sam Longley 1 on 11/09/2020 13:00:24:
.
The example you refer to with circular holes is not what I was referring to.

.

Sorry, Sam ... My misunderstanding blush

I did try to cover that possibility with my opening line:

[quote] I suppose that would depend upon one’s definitions of ‘they’ and ‘normally’ [/quote]

MichaelG.

Michael Gilligan11/09/2020 13:57:04
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Posted by Sam Longley 1 on 11/09/2020 13:00:24:

.

The example in the one in the link would , presumably, be cut from an I beam with considerable waste.

.

Here’s a direct quote from the linked page:

The top and bottom tees are frequently cut from different rolled sections, with the resulting asymmetric Westok beam formed with each tee/flange designed to suit the load it resists and the restraint conditions which apply locally.

.

From which it seems clear that there are many ways to skin these cats

MichaelG.

Howard Lewis12/09/2020 11:25:17
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As Zan says, stiffness is B x D^3 / 12, which is fairly easy to calculate for a square or rectangular beam.

But a circular, hexagonal, octagonal, or any irregular section surely will require an integration based on depth and width starting at Zero and increasing to the maximum depth, based on a formula taking into account the actual section, circular or otherwise.

Don't ask me to derive the formulae!

Howard

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