Calculating the Specific strength for the rod

Imagine the skyscraper and the very long rod placed on its top that rotates from horizontal position to upwards.

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I would like to know how is it possible to calculate/ascertain the maximal length and minimal width of the rod made of some certain material, let’s say steel. For example, is it possible to hold the rod with the length of 5 km horizontally (not by hands of course

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)? The rod will be broken? What, if I need to hold much longer rod (let’s say 50 km)? Which material should I use? How can I calculate its maximal possible length? As far as I know I need to use the values of Specific strength, right? In Wikipedia I found the article: http://en.wikipedia.org/wiki/Specific_strength and the values for various materials, then what? Let’s assume I am using the carbon nanotubes and I created the rod (not the elastic ribbon like Space Elevator’s cable), how can I calculate its possible maximal length? Is there any formula for this purpose?

 

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What you're looking for is simply supported beams. More specifically the subset known as cantilevers.
There's a quick calculator here (imperial values

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) for uniformly distributed loads (i.e. nothing but its own weight) and Gieck's would be the standard reference work.

Specific strength is not the figure you need but rather the E value (Young's Modulus)

5 km is highly unlikely since it would bend under its own weight, simply making it thicker to prevent bending will only increase the weight and make it bend more.

 

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Dywyddyr
I looked at this calculator but these values are unknown for me:
1. Line pressure load on beam, p:
2. Distance from neutral axis
to extreme fibers, c:
3. Moment of Inertia, I:
Where can I find these values? Imagine, that we are using carbon nanotubes and we know their density and E value (145,000,000 according to Wikipedia), what about others?

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And main question: If I should put the Length of beam, L: there then what this calculator calculate at all? I thought that it would calculate the possible maximal length of the rod........

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As shown by the drop-down menu this is the loading of the beam (in your case it will simply be the weight per metre length).

Since you're using a cylinder then this will be the radius of the rod.

This the Second Moment of Area (called I because it's also referred to as Moment of Inertia in some text books). This is calculated by:
pi.r[sup]4[/sup]/4

There's a longer (i.e. it has the equations) version here and a calculator here.

The calculation will give the maximum deflection (how much it bends) of the rod (among other things).
If you want to know a maximal length for a given rod size/ mass then you'll have to use the equation, transpose the values to get L as the solution and decide beforehand (and then enter those values) the allowable deflection and stress.

 

Dywyddyr

So, I just need to calculate the weight of the cylinder’s part with the length of 1 meter, right? I will calculate its volume (according to diameter and height-1 meter) and multiply it to its density, is it right?

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Since you're using a cylinder then this will be the radius of the rod.
More precisely radius of the rod’s cross-section, right?

Here this r is radius of the rod’s cross-section?

These online calculators give the same results of course as the one that you gave me in the previous post? These two seem to be more complex and in the beginning I will try the first calculator

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Deflection in which unit, degrees?

Yes, I am seeking exactly this

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so, which equation should I use? Which values should use and transpose and how exactly?

 

Yes: that figure will be the mass per metre.

More precisely? There is only one radius.

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Yes. If you can find any other radius you're welcome to use it.

They should give the same result.

No, in millimetres/ feet/ whatever units of length you use. This will be the maximum deflection at the free end of the rod.

Ideally you should use them all (although the one for Deflection at specified point is largely irrelevant, since you want to know deflection at the free end which is given in the third equation). You'll need not only the deflection but the stress (to check that the rod won't break).
Which values should you use?
What maximum allowable deflection you consider safe/ acceptable is up to you.
You mean you're attempting this project and you don't know how to transpose equations? How much engineering/ mathematics have you done? Transpositions was secondary school (age 13+) mathematics for me.

 

Dywyddyr

So, where is here the value of deflection? If I understood correctly this is distance between rods’ free ends in unbent and bent positions, right? In the image below you can see rod on the land (red) and ascended rod (green) in two possible positions-without deflection (light green) and with deflection (dark green). Where is value of deflection?

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Well, I finished school many years ago and actually I never liked Mathematics

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So, please tell me what should do I now. I:

So, tell me what to do step-by-step, otherwise the much information that you wrote here confuses me

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I will write again what I need to know:

And how can I know the value of stress? In that web-site is equation Stress at specific point, is that what I need?

 

Your sketch is correct.

You need to work out how much deflection you can allow.
You need to know what stress the material will withstand (and how much stress the mounting can withstand) and the equation will give stress at a specific point and at a selected point.
This will also depend on your selected factor of safety.
Unfortunately for you much of engineering is mathematics.

Until you assign an allowable deflection and an allowable maximum stress (again depending on factor of safety) there is no such thing as "maximal length".
It depends entirely upon the application and the allowable parameters given above: for example if the deflection allowed is (say) 1 meter the length could be 1 km (I doubt those are valid figures but you get the idea) then the "maximal length" may be 2 km for someone who will accept a 2 metre deflection. Likewise with the FoS: if the factor of safety for one operator is half that of another then their "maximal lengths" will also differ.

 

Dywyddyr

This is much more complex than I thought

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Ok, then let’s go step-by-step slowly, tell me what first should I calculate? Should I begin with this calculator?

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http://www.efunda.com/formulae/soli...study_display.cfm?case=cantilever_uniformload

 

Yes.
Why do you think engineers have to study?

In truth the calculation is a small part of it.
Ideally you should begin by knowing exactly what you're doing and why. A calculation only confirms (or invalidates) that what is intended is valid.
In other words you can't start with "Hey I think we should do so-and-so" unless you have extensive knowledge and experience.

 

Dywyddyr

Of course I understand this, but I am not engineer or architect

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I simply would like to know answer to this question……

Just imagine that somebody ordered to build very long rod for some Sci-Fi purpose

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and we need to know which materials should be used (apparently carbon nanotubes would be the most suitable) for this purpose. I understand that the rod may be bent, but I just need to calculate the maximal possible length of the rod for some certain material…..

 

Then that equation is the one you'd use: but first you have to decide the rod's diameter.

 

Dywyddyr

Which one? At this web-site given by you http://www.engineersedge.com/beam_bending/beam_bending8.htm
there are several equations

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Let’s assume that the rod has got circular cross-section and its diameter is equal to one meter

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As stated earlier: all of them.
You need to know the deflection you also need to know the maximum stress.

 

Dywyddyr
Ok, let’s begin with this calculator http://www.engineersedge.com/beam_bending/calculators_protected/beam_deflection_8.htm
Until I calculate I need to set some values, there and I want to clarify this problem

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There are given the following values:
Modulus of Elasticity (E) -where can I find the values for this parameter?
Moment of Inertia (I) -you already told me: pi.r[sup]4[/sup]/4
Load (W) -what do they mean? The mass of the rod?
Distance (l) -do they mean rod’s length?
Distance (x) - do they mean rod’s half length?
Distance to nuetral axis/plane -what do they mean?

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Er, you gave it in post 3.

Yes.

Yes.

No, they mean the distance desired for any particular point under consideration. E.g you can discern the deflection 25% of the way along the beam or 99%, or...

I already made this easy for you: for a cylindrical rod it's the radius. (Post 4).

 

Dywyddyr
Well, there is significant progress

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but this is still a bit vague:

So, which number should I set as “Distance (x)”? Where should this point be on the rod? What would you advise me?

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As per post 6.
You're only interested in the maximum deflection, which is, of necessity, at the extreme end.
Oh, one hint: make sure you are absolutely using compatible units. One calculation I did at work took three of us three days to sort out - and then I discovered that the reference material gave I in cm[sup]4[/sup] where every other value was in mm. No wonder we had a deflection of ~1.5 metres on a 750mm length.

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Dywyddyr

Well, I do not need to calculate the deflection with this formula:

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because deflection is possible to calculate according this calculator:

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and for accomplishing this calculation I need to know what number to put at “Distance (x)”, however your post:

does not tell me the exact answer

No, I need to know the maximal possible length of the rod eventually

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Of course!

Of course, I will use only one units-metric standard and only one unit from them-presumably meters.

 

You're making an error.
You are not interested at all in deflection at a specific point (point x) since all you want is the maximum deflection - at the end of the rod.
Therefore you can ignore the calculation for "deflection at x".
And, again, unless you have transposed the equation (as referred to above), you're going to have to numerous iterations with differing lengths until you decide what is acceptable and what isn't.