I have a model of a tall, slender structure that I am investigating using both shell and $3D$ frame elements.
The shell elements are type MITC4, $4$-node membrane elements. The frame elements are the basic line ($1D$) elements found in any introductory structural analysis / stiffness method book - they include axial, bending, and torsion, but no shear deformation.
Both analysis are linear-elastic (no geometric or material non-linearties), small-deformations using the direct-stiffness formulation.
As a test case, I loaded the structure with a unit load at the top node (or nodes, for the shell element model), once in a direction perpendicular to the long axis of the structure ($X$-axis), and once down the axis of the structure for pure axial loading ($Z$-axis). I neglected all self-weight for this test case.
[I also compared $X$ and $Y$ direction bending, which matched exactly as expected, since the structure is symmetric.]
I compared these results with those found by simple hand computations for a linear-elastic beam:
Axial deformation ($Z$-axis) = $PL/(AE)$ Bending deformation ($X$-axis) = $PL^3 / (3EI)$
For the frame element model, these results matched exactly.
For the shell element model, the axial value was nearly identical (which I take as a good sign that the area is correct).
The bending deformation for the shell element model were somewhat smaller (~8%).
What I would like to know is, is this expected behavior? Should I expect the shell element model to be "stiffer" than the frame element in general?
I understand that the choice of Poisson's ratio in the shell element has an effect here as well. I'm using $0.30$ for steel.