Continuous Beam - Two equal spans - uniform load on both spans
Continuous Beam - Two equal spans - uniform load on both spans
(OP)
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
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





RE: Continuous Beam - Two equal spans - uniform load on both spans
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.
RE: Continuous Beam - Two equal spans - uniform load on both spans
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
RE: Continuous Beam - Two equal spans - uniform load on both spans
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.
RE: Continuous Beam - Two equal spans - uniform load on both spans
RE: Continuous Beam - Two equal spans - uniform load on both spans
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.
RE: Continuous Beam - Two equal spans - uniform load on both spans
jt
RE: Continuous Beam - Two equal spans - uniform load on both spans
Have a look at this paper:-
http://www.duke.edu/~hpgavin/ce130/three-mom.pdf
Regards
desertfox
RE: Continuous Beam - Two equal spans - uniform load on both spans
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,
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