Calculating the value of Deflection

[Eagle9]

And one more question-in your last post you wrote 2 180 000 in Load (W), why? The whole mass of the rod is equal to 314 000 kg (volume 3140 m^3, material’s density as said 0.1 g/cm^3), how this transformed into 2,180,000? I remember in post 6 where you wrote this:
Then take line load in N/m to be density*area*g =~3080N/m which you then factor by cos(45) =~2180N/m
But this was regarding Line pressure load on beam, p: and not total load/mass of the rod. Actually as I understand 2180N/m was for 1 meter while my rod’s length is 1000 meters, 1000 times more, that’s why you wrote 2,180,000 (N-s, here load is indicated in Newtons:

)

 

[Pinwheel]

Actually as I understand 2180N/m was for 1 meter while my rod’s length is 1000 meters, 1000 times more, that’s why you wrote 2,180,000 (N-s, here load is indicated in Newtons:

Yes, you answered your own question. It was 2180 Newtons PER Metre. Total load is 2180 Newtons/Metre x Length = 2,180,000 for a 1km beam.

 

[Pinwheel]

What should be written in Distance to neutral axis/plane (Z)? You wrote 1000

No I didnt, if you look closely i wrote 1.000 not 1,000.

You wrote 500 in Distance (x), may I know why? This is half of rod's length. I tested there various values but the result in Maximum Deflection at Center (y) stayed the same again....

This distance is used to calculate the displacement of ANY point along the beam, where as the the maximum delfection is the point where the displacement is largest, and there is only one point that occurs: the centre of the beam. If that really confuses you just ignore that parameter and concentrate of the maximum deflection.

 

[Eagle9]

Pinwheel

No I didnt, if you look closely i wrote 1.000 not 1,000.

Oh, I confused comma with dot, actually 1.000 and 1,000 means different numbers in USA and in Europe

This distance is used to calculate the displacement of ANY point along the beam, where as the maximum deflection is the point where the displacement is largest, and there is only one point that occurs: the centre of the beam. If that really confuses you just ignore that parameter and concentrate of the maximum deflection.

Well, actually I need only maximum deflection

So, now I know how to calculate the deflection, but if it is too high the rod probably breaks into two pieces, how this can be estimated? In case of my 1000 m length rod the deflection was 36 meters, I think that it is not high, but if it was 500 m? The rod would be broken or what?

 

[Pinwheel]

Oh, I confused comma with dot, actually 1.000 and 1,000 means different numbers in USA and in Europe

Ha! Well I'm not in the USA I'm in the UK and we dont use dots we use commas.

So, now I know how to calculate the deflection, but if it is too high the rod probably breaks into two pieces, how this can be estimated? In case of my 1000 m length rod the deflection was 36 meters, I think that it is not high, but if it was 500 m? The rod would be broken or what?

The deflection doesnt mean anything unless you know what the properties of the material, such as Yield Stress and Ultimate Tensile Strength are. In this case you will need to know the stress in the beam, not the deflection.

 

[Eagle9]

Pinwheel

The deflection doesnt mean anything unless you know what the properties of the material, such as Yield Stress and Ultimate Tensile Strength are. In this case you will need to know the stress in the beam, not the deflection.

Ok, and where can I find/calculate the value of stress in the beam?


As for Deflection, in our case it was equal to 36 meters for 1 000 long rod- about 3 % and I think that it is acceptable, could you please tell me where is limit for Deflection? 10 % (from rod’s length of course)? 20%

 

[Pinwheel]

As for Deflection, in our case it was equal to 36 meters for 1 000 long rod- about 3 % and I think that it is acceptable, could you please tell me where is limit for Deflection? 10 % (from rod’s length of course)? 20%

The limit would be based on stress, not deflection, and WHAT MATERIAL. Think about it, if you had two identical sized beams: one made of rubber and one made from steel, what sense would there be in both having a deflection "limit". Rubber can bend much more without breaking. So click on stress on the calculator, the button is right there. And compare it against yield or ultimate tensile stress.

 

[Eagle9]

Pinwheel

The limit would be based on stress, not deflection, and WHAT MATERIAL. Think about it, if you had two identical sized beams: one made of rubber and one made from steel, what sense would there be in both having a deflection "limit". Rubber can bend much more without breaking. So click on stress on the calculator, the button is right there. And compare it against yield or ultimate tensile stress.

Ok, I put in that calculator the same data:

I need to compare this 0.347 GPa (or maybe -2.73 × 10^8 N-m?) to yield or ultimate strengths, these value are available here: http://en.wikipedia.org/wiki/Yield_stress but not for Carbon nanotubes but let’s assume that Carbon Fiber (CF, CFK) and Carbon nanotubes are the same (still both of them are Carbon), the Ultimate strength for this material is 5650 MPa, or 5.65 GPa and this is more than 0.347 GPa, so the rod will not be broken, right?

 

[Dywyddyr]

It's the same problem as in your earlier thread: compare the total stress to the actual strength (e.g. the ultimate strength multiplied by the cross-sectional area).