Assumptions for the One-Dimensional Beam Element

There are always assumptions associated with every finite element formulation. The one-dimensional beam element assumes the following:

Nodal Forces and Moments
Constant Load
Weightless Member
Prismatic Member
Slender Member
The Beam Bends without Twisting
Cross Section Remains Plane
Axially Rigid
Displacements and Rotations are Small
Homogeneous Material
Isotropic Material
The Proportional Limit is not exceeded

If all the assumptions above are valid for a given situation, then the one-dimensional beam element will yield an exact solution.