Saint - Venant's Principle

Consider a slender bar with point loads at its ends as shown in above fig. The normal stress distribution across sections located at distances b/4 and b from one and of the bar is represented in the figure. It is found from figure 1.4 that the stress varies appreciably across the cross section in the immediate vicinity of the application of loads. The points very near the application of the loads experience a larger stress value whereas, the points far away from it on the same section has lower stress value. The variation of stress across the cross section is negligible when the section considered is far away, about equal to the width of the bar, from the application of point loads. Thus, except in the immediate vicinity of the points where the load is applied, the stress distribution may be assumed to be uniform and is independent of the mode of application of loads. This principle is called Saint-Venant's principle.