Continuous GLB analysis

[bruinboy]

Hi,
I'm having trouble figuring out how to develop the moment and shear diagrams for this beam configuration I am working on. I have a continuous GluLam beam over 3 unequal spans. The two outer spans are 9' long and the middle span is 24.5' long. There is a uniformly distributed dead and live load. I used EnerCalc to model the beam but I'm very curious as to what formulas are used to derive the equations for the moment and shear. ASD only has configurations for equal spans but they mention that the Theorem of Three Moments is used for continuous beams. Anyone have any idea how to model this situation?

 

[JStephen]

The numbers may get involved, but it shouldn't be that complicated. Look in AISC-ASD handbook, Formulas for Stress and Strain, or any Strength of Materials textbook. You've got a simply supported beam, supported at two ends, with uniform load. Calculate the deflection at the the two middle supports points assuming no support is there. Then find the forces required at those two points to make the total deflection zero at those points. Superimpose the results to get shear and bending moments.

If I remember right, either AISC-ASD or Formulas for Stress and Strain has a load case with two symmetrically placed loads- which will be quicker to use than applying single load case twice.

 

[chichuck]

bruinboy,

I don't know about Enercalc, are you just curious, or do you suspect something is wrong with the answers you get there?

You could analyze this using the Theorem of Three Moments; go to any basic structural analysis text for the details on that.
Or you could just do a moment distribution on it, it shouuld be easy and straightforward unless the supports settle. A basic structural analysis text should give you this as well. Either method gives you the moments at each support (the end supports may have zero moment depending on the details of the beam, model it according to what is really there.) Once you have the moments, you can use statics to get the reactions and the shear diagrams. (the reactions ought to be easy, your description is a symmetrical case.)

Good luck

chichuck

 

[JAE]

Whatever method you use, with two short outer spans you might get uplift on the outer columns as the center beam sags downward. This may make your numbers look a little goofy if you're not careful.