Abstract:Semi-infinite beam is extended from free end to infinitely long beam. Based on solutions for infinitely long beam on Winkler foundation, the shear force and bending moment at the free end of semi-infinite beam under the concentrated couples are derived. The external load applied at the free end is obtained by using the condition of the free end to meet zero moment and zero shear. The deflections at the action points are calculated separately under external loads and concentrated couples and the deflection at the action points are calculated under superposition of concentrated couples and external loads, and the calculation formula for cantilever influence coefficient with the action of concentrated couple is presented. According to the conditions of static equilibrium and deformation compatibility, general formulas for distribute load on joints of cantilever crossed foundation beams under vertical load and moments are given.