Deflection of Simple Beam With uniform load partially distributed 1

[racoxu]

Does anyone have a formula for Deflection of Simple Beam With uniform load partially distributed. All the references that I have ignores the deflection along th beam with this type of loading. . Help!

 

[XR250]

Find some cheap software. They have some free for an ipad.

 

[tony1851]

The equation is a PIA, but if you have a few hours to spare, it's here. If you just need the figure, use one of the free online calculators.

 

[AELLC]

If you have access to Excel, one way of figuring this fairly accurately is to divide the beam span into about 50 equal segments, and use a series of equivalent point loads at each applicable segment. It is fairly easy to set up by dragging and copying cell formulas.

 

[IDS]

The spreadsheet here:

http://newtonexcelbach.wordpress.com/2012/09/06/continuous-beam-spreadsheet-with-units/

will do what you want for simply supported spans or continuous beams with any number of segments with different properties, and any number of partial distributed loads (rectangular or trapezoidal), point loads or point moments.

By the way, we aren't supposed to post the same question in more than one forum.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rb1957]

the derivation from 1st principles isn't That hard ... deflection = double integral of M(x)/EI.

a short-cut might be to distribute the load over the entire span, it'll be very close if your load is distributed over more than 50% of the span

Quando Omni Flunkus Moritati

 

[structSU10]

to what rb is say, I did this a while back. It uses singularity functions, and 'a' is distance to start of load, 'b' is the length of the load, so 'c' is the remainder. The phi function is just mathcads singularity function.

 

[IRstuff]

The implementation of Roark's in Mathcad shows deflection over the length

TTFN
faq731-376

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[JoshPlumSE]

AISC 14th edition table 3-23. Item 4 is exactly the situation you describe. All formulas (other than deflection) are given.

If you want, you can get the deflection equations either by integrating the moment equations, or by using principal of super-position with item 6 (partial distributed load at one end) and item 1 (uniform load over entire beam).

 

[AELLC]

"If you want, you can get the deflection equations.... by using principal of super-position with item 6 (partial distributed load at one end) and item 1 (uniform load over entire beam)."

That is difficult unless you set it up on Mathcad or Excel because you don't know where the maximum deflection will occur

 

[Jerehmy]

Double integration?

Moment area?

Conjugate beam?

Stiffness?

Virtual Work?

This is literally a 10 minute calculation using double integration, arguably the longest way to calculate it.