Axial force is typically zero for a beam under a uniformly distributed load, shear force is calculated by integrating the distributed load, and moment is found by integrating shear over the length of the beam, with specific expressions for maximum shear and moment.
To determine the axial force, shear, and moment as functions of position for a beam supporting a uniformly distributed load, one must apply the principles of structural analysis often taught in civil or mechanical engineering courses. The axial force is typically zero for a simply supported beam carrying a uniformly distributed load since there are no axial loads (the load is purely transverse). The shear force can be calculated by integrating the distributed load over the length of the beam. Moment is the integral of shear over the length of the beam. For a uniformly distributed load w on a beam of length L, the maximum shear occurs at the supports and is equal to wL/2, and the maximum moment occurs at the center of the beam and is given by wL^2/8. Remember to use the appropriate sign convention: positive shear forces cause clockwise rotation about a point to the left of the section, and positive moments cause compression at the top of the beam section.