The discussion focuses on calculating 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 essential for determining the overall area moment of inertia of the composite section, especially when considering the interface between the beams as the neutral axis. Each beam independently supports half the load, and the total moment of inertia can be calculated by summing the individual moments of inertia and applying the parallel axis theorem. The absence of transverse shear between the beams allows for this independent analysis.
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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.