Deflection
Deflection
(OP)
Hi There,
I hope there is someone out there that can help me.
I am producing a timber beam / joist design spreadsheet and have very nearly completed it but I need a bit of help.
I can't seem to find a deflection formula for partial UDL's for a simply supported beam.
I need it to work out three areas, namely
'A' - deflection at x from RA before UDL
'B' - deflection at x from RA during UDL
'C' - deflection at x from RA after UDL.
All structural/civil formula books, etc seem to neglect this information.
I don't really want to use equivalent UDL as this does not give a true depiction of the scenario.
Thanking anyone in advance.
Regards
Steve
I hope there is someone out there that can help me.
I am producing a timber beam / joist design spreadsheet and have very nearly completed it but I need a bit of help.
I can't seem to find a deflection formula for partial UDL's for a simply supported beam.
I need it to work out three areas, namely
'A' - deflection at x from RA before UDL
'B' - deflection at x from RA during UDL
'C' - deflection at x from RA after UDL.
All structural/civil formula books, etc seem to neglect this information.
I don't really want to use equivalent UDL as this does not give a true depiction of the scenario.
Thanking anyone in advance.
Regards
Steve






RE: Deflection
RE: Deflection
Steve, the information your lookinf ofr is readily available from any basic textbook or on the web. But you need to explain a bit more about the scenario.
RE: Deflection
http://www.awc.org/pdf/DA6-BeamFormulas.pdf
I have attached a link to a document I came across for formulas.
The deflection calculations I require are associated to Fig 2 from the pdf.
RE: Deflection
RE: Deflection
RE: Deflection
RE: Deflection
RE: Deflection
Beetlejuice, you can get there by superimposing the loads. You're loaded from a to b. Use the deflection from Figure 3 in your attachment to get the deflection with load from zero to b. Then use the same figure to get the deflection with load from zero to a. Subtract the second from the first, and you have deflection with load from a to b.
RE: Deflection
For an exact solution, you could use Moment-Area Theorems. First, write your moment as a function of x. That's given in NDS Figure 2. Then, integrate to find your end slope. By trial and error, find the point where your slope is zero; and intergrate to find the deflection at the zero slope point. For the solution (using Mathcad), see the attached file.
RE: Deflection
RE: Deflection
If you know the deflection as a function of x, then you can superimpose the deflections to get an exact answer*.
* Caveat: this only applies to an isotropic, linearly elastic material in the elastic loading range. NEITHER of which apply to wood.
RE: Deflection
Your're both right. That will work. I hadn't looked at figure 3 and assumed it only gave maximum deflections.
RE: Deflection
1. For a simple span the maximum deflection ALWAYS occurs within the middle 1/3 span and never moves more than 1/6 span away from midspan, no matter what kind of downward loading you have.
2. Within the middle third the deflected shape is so flat the delta "Y" from mid span to 1/3 span isn't going to be very much.
3. Calculated deflections, especially with wood, should always be suspect, due to variations in assumed loading, material quality, etc.
4. Wood creeps like green concrete. How do you plan to account for that. It also takes a long term "set" in part of the deflected shape.
There are other issues too. Can you account for cantilever moments too? Moisture content?
Just seems like you are expecting a bit too much accuracy given the material being used. Steel and concrete give better results, except for the uncertainty of the loadings.
Happy programming.
Old CA SE
RE: Deflection
Thanks again.
RE: Deflection
RE: Deflection
RE: Deflection
I own many text books for analysis and design but every book omits these formulas but gives deflection calculations for every other load case.
Does anyone have any thoughts why ?
In reply to mudflaps, I do appreciate that deflection results for timber should be "taken with a pinch of salt" but while programming excel I still needed the calculated deflected shape.