Update exampleKcl.ts

[iterion]

@jgomez720 I recently went through onboarding again and noticed we duplicated some constants where we could just reuse the variable instead. I think my moment calculation is still correct, but wanted to get your thoughts and see if we can reuse any more.

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[github-actions]

src/lib/exampleKcl.ts has been updated in this PR, please review and update the src/routes/onboarding, if needed.

[iterion]

I stared at this more and now I'm realizing now that distance isn't related at all to shelfMountL or wallMountL. Just thinking through the problem, it would make sense to me the moment experienced at the end of the bracket would be related to those and not necessarily distance?
Also, why do we divide moment by 2? Is this just because we were originally assuming the distance of each arm of the bracket was 1/2 of the original distance of 12?

So, maybe it should be const M = shelfMountL * p?

[jgomez720]

Looking back at this, I don't like some of the variable names I chose.

We are dividing by two because there are two brackets holding up the shelf (assumed at equal distance apart from the load).
distance in this example is supposed to be the shelf length from the wall. I'm going to add this picture to the onboarding to make it more clear and update the code to follow. This is what it should be:

const sigmaAllow = 35000 // psi
const w = 6 // width of the bracket - in
const p = 300 // Force on shelf - lbs
const L = 12 // Length of the shelf from the wall - in
const M = L * p / 2 // Moment experienced at fixed end of bracket. Divided by 2 since there are 2 brackets holding up the shelf.
const FOS = 2 // Factor of safety
const shelfMountL = 8 // The length of the bracket holding up the shelf - in
const wallMountL = 6 // the length of the bracket mounted on the wall - in

// Calculate the thickness off the allowable bending stress and factor of safety
const t = sqrt(6 * M * FOS / (w * sigmaAllow))

Calculating the bending stress, we have
$$\sigma = \frac{M*c}{I} FOS$$

where

$$M = \frac{p L}{2}$$

$$c = \frac{t}{2}$$

$$I = \frac{1}{12} w t^3$$

plugging those in and simplifying:

$$\sigma = \frac{6 F L}{w t^2} FOS$$

so

$$ t = \sqrt{\frac{6 p L}{w \sigma} FOS} $$

I'm going to update the onboarding code and make it clearer. Thanks for bringing this up @iterion!

[jgomez720]

I updated the onboarding here
#2269

Let me know if this makes more sense

[iterion]

Thanks so much, for the improvements!