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Beam Theory

Beam Theory

Beam Theory

(OP)
I have a question about what Beam Theory NASTRAN uses.  Here are 2 simple cases that are yielding different results:

Trial 1:  

 - 2 nodes connected with a beam element
 - Fixed at one end, free at the other
 - Apply body load

Trial 2:  

 - 2 nodes connected with a beam same beam element
 - Fixed at one end, free at the other
 - Apply distributed load along the element (matches body load magnitude and direction)

Both trials yeild the same bending moment but the second trial has a higher deflection.  Now the first trial matches the theoretical Bernoull-Euler beam theory, so I am assuming when you apply a body load NASTRAN is assuming a non-slender weightless beam so Timoshenko beam theory would apply.  Is this correct?  Is there a simply closed form solution to Timoshenko's beam theory (I have solved the 2 pde's but it's an ugly solution).  Thanks for any help.

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