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I'm studying this text about buckling.

There a factor called $\lambda_1$ is defined:

$$\lambda_1=\pi \sqrt{\frac{E}{f_y}}=93.9\sqrt{\frac{235}{f_y}}$$

But how was that last step made? Where did that factor of 93.9 come from? Usually we take the elastic modulus of structural steel as around 200GPa, so how is there 235 under the square root? I feel like there is some step missing.

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  • $\begingroup$ What assumptions are stated in the text? I'm not chasing the text to do the reading though. $\endgroup$
    – Solar Mike
    Dec 15 '20 at 12:58
  • $\begingroup$ 93.9 was declared as the legal value of pi in the state of Indiana :) $\endgroup$ Dec 15 '20 at 21:36
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Edit

I have changed the units to MPa, basically cranking their numbers back to see what unit they have used for E.

Without looking at your source, it makes sense if they are using the unit of MPa.

$E=210.000MPa$

then:

$$\lambda_1=\pi\sqrt\frac{210,000}{F_y}=\sqrt\frac{893.617*235}{F_y}$$

$\lambda_1=93.91\sqrt\frac{235}{F_y}$

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  • $\begingroup$ For steel E = 210GPa, not 210kPa. 210kPa is 1000 times more "floppy" than polystyrene foam. $\endgroup$
    – alephzero
    Dec 15 '20 at 16:36
  • $\begingroup$ @alephzero, Thanks it was a typo, I fixed it. I used the correct value in my calcs tho. and the answer is correct. $\endgroup$
    – kamran
    Dec 15 '20 at 17:06
  • $\begingroup$ The unit is still wrong. There is also an error in the calculations. But the principle is correct. $\endgroup$
    – ingenørd
    Dec 15 '20 at 19:52
  • $\begingroup$ sorry, I am babysitting my grand daughter. I fix the arithmetic later. $\endgroup$
    – kamran
    Dec 15 '20 at 20:15
  • $\begingroup$ I'm sorry but I think your math is still wrong. How do you get 93.91 as the square root of 893617? I get approximately 945.31.. $\endgroup$
    – S. Rotos
    Dec 17 '20 at 12:40

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