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name of support point (21.9% from end) with minimal deflection

name of support point (21.9% from end) with minimal deflection

name of support point (21.9% from end) with minimal deflection

(OP)
Hi,

I am looking for the name of the support points of a simply supported beam with a uniform loading, with two reaction points, with minimal deflection of the beam (midpoint and cantilever combined).
If memory serves me, this should be at around 21.9% from both ends.

These points have a name (probably named after the guy that first did this calc), and this method of supporting is widely used by metrology laboratory where, for example, they have to check (certify/validate/ ?) a straight edge.

Could somebody help me out here?
Thx!

http://www.fusionpoint.be
http://be.linkedin.com/in/fusionpoint

RE: name of support point (21.9% from end) with minimal deflection

point of inflexion ?

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

RE: name of support point (21.9% from end) with minimal deflection

(OP)
Thanks for your reply, I see what you mean but we're not talking about the same thing. The points I'm referring to should be more outwards than the inflection points (but please, let's not argue about that)...
It's really a guy's name (let's say for argument's sake, "Euclidian Points", it's not that, off course, but it's similar).

http://www.fusionpoint.be
http://be.linkedin.com/in/fusionpoint

RE: name of support point (21.9% from end) with minimal deflection

Gerber beam?

RE: name of support point (21.9% from end) with minimal deflection

I don't know the name of these points, but I'm curious where the 21.9% number comes from. I make it 22.3%, which sounds like a very small difference, but 21.9% gives 30% greater deflection at mid-span (under continuous uniform load).

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: name of support point (21.9% from end) with minimal deflection

kingnero:

They're called the Airy points after Sir George Airy. They are separated by a distance of approximately 57.7%. Here's a derivation of the points if your interested. Link

Regards,

DB

RE: name of support point (21.9% from end) with minimal deflection

Generally a simply supported beam with cantilever ends, supported at fifth points is what I've generally used.

Dik

RE: name of support point (21.9% from end) with minimal deflection

Interestingly, Airy's value of L/root3 for the central span gives a cantilever length of 21.13%, which is different to both the 21.9% in the thread header, and the 22.3% I get from iterating the deflection equations (or 22.3149101094592%, if you want to get exactly equal deflections).

The Airy value gives a cantilever deflection 91% higher.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: name of support point (21.9% from end) with minimal deflection

Reading the link on Airey's work, his intent was not to minimize deflections, it was to have the end faces of the bar with zero rotation, which makes sense for precision measurement.

See also: https://en.wikipedia.org/wiki/Talk:Airy_points

Quote (Wikipedia - talk)

The comment that the support at the Airy points limits bending or droop suggests that their function was to limit the deflection of the beam. Airy was concerned with the support of length standards as part of the 1844 revision of length standards in the UK. As such, he derived the condition for supporting a beam at two points in such a way that the ends of the beam remained parallel. It is this condition that gives rise to the location of the Airy points. Peter R Hastings 12:53, 11 February 2016 (UTC)

Airy wasn't addressing deflection of the beam, he looking at upper surface length expansion, and sought to find a solution with equal amounts of concave & convex. In his paper in "Memoirs of the Royal Astronomical Society" vol. 15 (1846) "On the Flexure of a Uniform Bar", his description is "and I undertook to investigate the position of the rollers which, supposing the pressure equal and the intervals equal, would so sustain the bar that its surface should not sensibly be lengthened.

The already referenced "Appendix C: Flexing of length bars" also supports this definition "The chosen solution is to support the bar on two points whose positions are chosen to make the ends of the bar vertical and parallel with each other. These are termed the 'Airy points' of the bar".

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

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