Edge-cracked beams under four-point bending: Approximate analytic solutions for stresses and displacements

Abstract An approximate analytic solution for the stress- and displacement-field developed in a notched prismatic beam under four-point bending test is presented. The solution is obtained adopting Muskhelishvili’s complex potentials technique. As a first step, the complex potentials are obtained and then the stresses and displacements are calculated all over central part of the beam. As an example, the solution is applied for a PMMA beam. Then, the analytical results for the strains are qualitatively compared against experimental data for a notched marble beam, obtained from literature. The comparison is quite satisfactory. The limitations of the analysis are discussed and means to overcome them are finally proposed.