Beam bending and moment of inertia

AI Thread Summary
To find the first moment of area and moment of inertia for two simply supported beams placed on top of each other under a vertical load, the parallel axis theorem is necessary for calculating the composite section's moment of inertia. If the beams act independently without transverse shear, the load can be evenly distributed between them. However, to determine the overall area moment of inertia, the individual moments of inertia must be combined using the parallel axis theorem, with the interface between the beams serving as the neutral axis. The discussion emphasizes that while the loads can be split equally, the calculation of the moment of inertia requires careful application of the theorem. Understanding these principles is crucial for accurate structural analysis in beam bending scenarios.
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If you have two beams, not attatched to each other, placed on top of each other in 3 point bending simply supported, what do you do to find the first moment of area and moment inertia of the two beams.
Thanks
 
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Hi Fred,
I think what ttlg is asking is if the two beams are simply sitting on top of each other such that there can be no transverse shear between the two (like a leaf spring on a car). The two beams, stacked one on top of the other, are then simply supported at the ends and loaded in the center with a verticle force. In that case, since there's no transverse shear between the two (ie: the beams act independantly) the parallel axis theorem doesn't apply to the beams as a set. In this case, the load acting on the beams can simply be split 50/50 between the two beams (each beam supports 1/2 the load).
 
Q,
The loads can be split the way you mention, but to find the area MOI of the assembly, i.e. the composite section, one needs to use the parallel axis theorem. I am using the interface between the two beams as the neutral axis (with no shear between the two as you mentioned). From there take the two individual beams' respective area MOIs and use the parallel axis theorem to calculate the overall area MOI.
 
ok, thanks for your help
 
FredGarvin said:
Q,
The loads can be split the way you mention, but to find the area MOI of the assembly, i.e. the composite section, one needs to use the parallel axis theorem. I am using the interface between the two beams as the neutral axis (with no shear between the two as you mentioned). From there take the two individual beams' respective area MOIs and use the parallel axis theorem to calculate the overall area MOI.

QGoest said:
since there's no transverse shear between the two (ie: the beams act independantly) the parallel axis theorem doesn't apply to the beams as a set.

Looking at Q's comments about the shear stress...he's right on that. The MOI is simply two times the individual MOIs.
 

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