Continuous Beam - Two equal spans - uniform load on both spans

[Cristodul]

Hello all,

I have a situation where I have a continuous beam with two equal spans, uniform load on both spans, also I have a overhang load of 21.5 inches. (Please see attached picture)

I was searching in books and over the internet for formulas for this situation (for bow in Fig. 1 and deflection in Fig. 2) and I was having difficulties.
Anybody can direct me to the right source?

I really appreciate the help!

Thank's!

C

 

[40818]

I couldn' determine the support condition in your picture, but in any way, your situation is pretty common.
Have a look under things like:

Clapeyrons theorum
Moment area methods
beam on 3 supports


Most decent textbooks have sections devoted to statically indeterminate structures.

There are a variety of methods to solve your problem with a pencil and paper, or if you need to you could build a quick FEM.

 

[Cristodul]

Thank you for the prompt response.

I looked over and over but the only thing I found was the situation where I have a continuous beam, two equal spans, uniform load on one span, no overhanging.
Can you please give me more details?

Thank's

C

 

[JamesBarlow]

A copy of Roark's and some superposition should get you thru it.

I have not checked but's unlikely you will find something that will give the exact formula you need to for this problem.

Depending on how good you math is you good with the original beam Euler Bernoulli beam equation but Roark's is your best bet.

As a previous poster said since it's a simple beam there are a number of free programs online that could solve this but if you need to do it by hand so you can show your work then go with Roark's.

 

[dvd]

Since it is symmetric with uniform load, you could substiute a built-in connection at the middle support and solve half of the beam. I don't know if you would find a beam diagram for that one or not.

 

[rb1957]

this is a "simple" singly redundant beam. i would apply the unit load method ...

remove the middle support, solve the statically determinate beam, calculate the deflection where the removed support is.

apply a unit load at the removed support, opposite the deflection; solve this beam, calculating the deflection at the removed support.

calculate the removed support load = determinate deflection/unit deflection; factor the unit load solution by this factor, superimpose onto the original determinate beam.

 

[jte]

6#/ft? Over an unsupported span of 18 or so feet? Your beam will weigh more than that without any load applied to it!

jt

 

[desertfox]

Hi Cristul

Have a look at this paper:-

http://www.duke.edu/~hpgavin/ce130/three-mom.pdf

Regards

desertfox

 

[Qshake]

Desertfox - Not sure why that is in a recent paper as the three moment method has been around for decades...ever since the moment distribution method and slope deflection.

Anyway, I have not looked the diagram, but AISC has a table of beam formulas and so does Roarks which has been mentioned.

One way to attack such a problem with a known refernce for a two span continuous beam with uniform loading and one or two overhangs is to:

calculate the overhang moment and shear then look at the original problem without the overhangs solving and superimposing the results.

Regards,
Qshake

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