CENTROID DETERMINATION CALCULAS 3

[Structural Engineer 2222]

Can anyone tell me how the red-marked result came? I did not understand this "dL" part. I know Pythagorean formula is used here but how the final result came?

 

[3DDave]

It's how dy is removed from below the radical. Multiply the radical by dy and divide what is under the radical by dy^2 to compensate.

root(a^2 + b^2) = root(b^2(a^2/b^2 + b^2/b^2)) = b*root(a^2/b^2 + b^2/b^2) = b*root(a^2/b^2 + 1)

 

[rb1957]

the "dy" is outside the square root sign (poorly written, brackets would have helped)

so they've divided both terms in the square root by "dy^2" ...

clear as mud ?

another day in paradise, or is paradise one day closer ?

 

[BridgeSmith]

Divide both terms under the square root by dy^2, and multiply by the square root of dy^2 = dy.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[dik]

= sqrt(3^2+4^2)

=sqrt((3/4)^2+4) ???


maybe for small numbers?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[ProgrammingPE]

= sqrt(3^2+4^2)

=sqrt((3/4)^2+4) ???

√(3²+4²) = 5
√(4²*(3²/4² + 4²/4²) = 5
4*√(3²/4² + 1) = 5

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[Structural Engineer 2222]

Thank You guys for responding. I really appreciate your eagerness to solve the problem

 

[rb1957]

how does the graph (and equation) work when you add dimensions to it ?

x = y^2

when y = .5m
x = 0.25m^2 ??

what if you switch units, to say mm ...
y = 500mm
x = 250000mm^2 (which = 250mm ?)
do you have to say that the curve passes through (1m, 1m) so ...
y = 1000mm
x = 1000000mm/1000mm = 1000mm
(and in the previous case x = 0.25m^2/1m = 0.25m)

another day in paradise, or is paradise one day closer ?

 

[Structural Engineer 2222]

Can anyone please tell me how can I reply to each comment and thank them separately with their name mentioned?

 

[dik]

Thanks prog, but that's not quite what the formula shows, the arithmetic is what the correct expansion is, but not quite the formula... No need to thank people individually... just a 'thanks all' is more than enough...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[rb1957]

give "purple stars" to the responses

another day in paradise, or is paradise one day closer ?

 

[ProgrammingPE]

how does the graph (and equation) work when you add dimensions to it ?

The formula is unit specific. If you want to use different units then you need to incorporate the unit conversions into the formula, so if you want to use mm for x and y,

x = (y*1m/1000mm)²*(1000mm/1m) = y² / 1000​

(First conversion is to change the y value to meters then second conversion is to change the result from meters back to mm.)

Thanks prog, but that's not quite what the formula shows, the arithmetic is what the correct expansion is, but not quite the formula...

It matches the formula. The square root does not include dy (parentheses would have made this much clearer), so it is √[(dx/dy)² + 1]*dy

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[rb1957]

sorry but no, the formula is not "unit specific" ... x is in meters, not meters squared.

correct would be x = y^2/1m (or /1000mm).

another day in paradise, or is paradise one day closer ?

 

[ProgrammingPE]

It's unit specific meaning that the equation is only correct when the x and y values are in meters. There's lots of equation that do this. Concrete's shear capacity in imperial units is 2*√(f'c)*b*d which would resolve its units to be √(psi)*in*in = √(lb)*in^1.5, but the result is actually in pounds. If you want to use SI units, then the formula is 0.17*√(f'c)*b*d.

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[rb1957]

but that's the point ... x = y^2 isn't dimensionally correct (as written) ... x = y^2/1m is, and identifies the units of x and y.

another day in paradise, or is paradise one day closer ?

 

[3DDave]

The x = y^2 description of the curve means the scalar component of the x-coordinate is equal to the square of the scalar component of the y-coordinate.

 

[IDS]

There's lots of equation that do this. Concrete's shear capacity in imperial units is 2*√(f'c)*b*d which would resolve its units to be √(psi)*in*in = √(lb)*in^1.5, but the result is actually in pounds. If you want to use SI units, then the formula is 0.17*√(f'c)*b*d.

In that case the constant has implied units. In the case being discussed x, y and dL are all in length units, so the units can be anything as long as x and y have the same units.

Edit:
I should have looked at the diagram before posting. The formula only works for the curve x=y^2 which obviously is unit dependent. To make it unit independent it would have to be:
x = y^2/ymax

Doug Jenkins
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[IRstuff]

Those constants are either aggregated fundamental constants with units or empirical constants with units

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[3DDave]

How is x = y^2 unit dependent? It works for feet, inches, mm, parsecs as does the integration. No correction factor is required to change units.

 

[IDS]

3DDave - using mm units y = 0 to 1000 so x = 0 to 1,000,000.

Doug Jenkins
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