This thesis has two theoretical parts and one part for results. The first part is a strict one. In the first part exact parametric differential equations of plane section rotations for beams are derived. Those differential equations show that using parametric sine and cosine functions for deflections, parameters and functions of the curvature angle for beams under bending can be defined via experiments. The second part gives one suggestion for functions of curvature angle. In the third part some comparisons are presented between results with parametric function derived in the part two, current theory, called Linear Elastic Theory for Small Deformations, and models that are presented in Appendix B (My Ideas for Future Development).