Beam deflection problem 1

[Integrator62]

Double Integration method and Area moment method is used to determine beam deflection assuming that the elastic curve is very flat with the result of ds=dx.

How much deflection can be measured using this process without serious error?

In the picture below (Cantilever beam),
After using double integration method is it valid to use Arc length equation to determine the actual displacement along x axis?

 

[JoshPlumSE]

Just Google "small deflection theory".

When I do that, I get an article addressing the exact situation you're referring to. It seems to me (based on the figures at the end of the report) that you'd be talking about an end rotation of about 25 degrees before the solution based on small deflection theory starts to diverge from the exact solution.

file:///C:/Users/JOSHP/Downloads/EJP_v23_n3_p371_2002pre.pdf

 

[JoshPlumSE]

I would have thought that for a simply supported beam something more along the lines of deflection < 10 to 20% of the depth of the beam. But, that paper seems to imply a good bit more than that.

 

[rb1957]

Josh, i don't think you uploaded your doc ...

another day in paradise, or is paradise one day closer ?

 

[JoshPlumSE]

It's not my document, so I didn't feel comfortable posting it. I just copied and pasted the URL. Looks like I mucked that up though not paying attention to what I pasted. Let's try that again:

Link:

 

[rb1957]

the assumption of a massless beam brings to mind the BBT physist's joke "only works for spherical chickens in a vaccuum". this assumption probably has impact on the solution than "small displacements" but ...

another day in paradise, or is paradise one day closer ?

 

[Integrator62]

Thanks everyone. I like to go through the link.