Beam Bending of a Linearly Varying Beam with 2 point loads

[JasonL527]

I'm trying to design something and rather than solve it using FEA guess and check, I'm trying to mathematically solve it.

The part I'm getting stuck at is having 2 point loads on a linearly varying cantilever beam.

https://imgur.com/LtHCvCB

The closest example I could find to this that was close to a solution was this on page 4 & 5: https://engineering.purdue.edu/~ce474/Docs/Beam_Examples01.pdf But I'm not sure if I really even understand the solution.

I set up integrations to solve for in-between but I'm not sure if it's set up right...and also my calculus 2 is sorely lacking

*This is not for homework. This is what I'm designing and the above question relates to part of the design. Aka, how much force is required to cause enough displacement to move the snap fits in 1.35mm

https://imgur.com/xEnjcdw

Please help :)

 

[Chestermiller]

Is this a homework problem?

 

[JasonL527]

No, I'm designing something and I broke it up into individual parts that would resemble textbook examples so I could hopefully recognize and solve it.

I'm stuck at this part. I've already designed the snap fit and know how much force is required to snap the two parts together. But I haven't figured out how to translate the forces into something that would pull back the snap fit.