Beam bending refresher 2

[rcfraz37]

So its been a while since I did beam bending back in school and now I'm having some trouble.

The regular equations, I believe, assume fixed ends, at least the ones I can find. Trouble is I am looking for the length by which a beam gets shorter as it bends, and my end points rotate.

See pic
A is rigidly affixed translationally but allows the beam to rotate freely. B prevents Translation in the Y direction but no other Direction.

I'm trying to make my design driven because we keep changing materials so I'm going with F= force (assuming a uniform load across the length) L= length I=moment of inertia and E= modulus of elasticity.

I tried finding the deformation with (5*F*L^4)/(384*E*I)=d. and then the slope with w*L^3/(24*E*I). and using those to back out the geometry of the arc but the math isn't right.

Am I heading in the right direction?

Any help would be a life saver

 

[GregLocock]

Stress_Eng - yes, that is the question and when I get my script working, I'll be able to answer it. The problem with looking at SAE style leaf springs is that they are either multileaf or non constant thickness, rather than simple cantilevered uniform beams like this one, and in reality they have a weird end constraint called a shackle which allows for the longitudinal motion, but has dire effects on the linearity of the rate curve. For so called lab tests we either use a true roller, or a very long (of the order of the spring length) shackle.

This is the sort of nonsense I dealt with for literally years of my life. Taken from the bible SAE HS788

Cheers

Greg Locock


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