Beam Bending of a Linearly Varying Beam with 2 point loads

AI Thread Summary
The discussion focuses on the mathematical solution for beam bending in a linearly varying cantilever beam subjected to two point loads. The user is attempting to avoid finite element analysis (FEA) and is instead seeking a more analytical approach, but is struggling with the integration setup due to a lack of confidence in their calculus skills. They reference a specific example from a Purdue engineering document that is somewhat related to their problem but express uncertainty in understanding the solution. The goal is to determine the force required to achieve a specific displacement of 1.35mm to facilitate a snap fit design. The user clarifies that this is not a homework problem but rather a part of their design process.
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.

LtHCvCB
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

xEnjcdw
https://imgur.com/xEnjcdw

Please help :)
 

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Is this a homework problem?
 
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.
 

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