Elastic Stress Distribution in Rectangularly Notched Members by Finite Differences

The design of notched members by structural engineers has become a practice that is now being employed more frequently than in the past. This is particularly true in the aircraft, missile, automobile and shipbuilding industries where available space is necessarily a minimum. The determination of the elastic stress distribution in notched structural members is important because the introduction of a notch generally has the effect of subjecting the member to a situation of high combined stresses. The primary objective of this investigation is to obtain elastic stress distribution in rectangular notched structural members, employing the finite difference method and electronic computation. The structural members investigated are either plates or beams with rectangular notches. However, the methods of analysis developed in this work apply predominantly to thin plates. The stress distribution analysis consists of computing the normal stresses acting in the X and Y directions, the shearing stress acting on a plane normal to the X-axis and having its direction parallel to the Y-axis, the major and minor principal stresses and their orientations with respect to the x-axis. Many reports are available which discuss the elastic behavior of various structural sections containing cutouts or access holes of different shapes. Some investigation of stresses at web cutouts has also been accomplished by photo elastic methods. Several previous investigators employed the method of finite differences successfully when investigating stress distributions in deep beams. The result of the deep beam stress distribution analysis mentioned above indicated that the agreement between the finite difference method and a more accurate stress function solution in a closed form is good, even for a relatively coarse mesh