Patterns in the Distribution Capacity of Thin Plates Under Different Condition for Their Resting on Supports

Abstract

This paper reports a study into the distribution capacity of a flexible plate in different cross-sections exposed to the external vertical concentrated forces applied in any place of its area. A plate with one pinched side and a series of racks arranged at any distance from the pinching has been considered. In terms of the theory of elasticity and mathematics, solving this problem poses significant difficulties. This has study found that a lateral distribution coefficient could be used to simplify calculations aimed at determining the stressed-strained state of the system. In determining the stressed-strained state of the plate, the calculation method described in work [1] was applied. The plate is cut into a series of longitudinal strips that represent, from the standpoint of construction mechanics, a console strip with one pinched end and resting on a stationary support located at any distance from the pinching. It has been revealed that the distribution capacity of the examined plate in the same cross-section depends insignificantly on the point of application of the concentrated load along the length of the longitudinal strip (between 2.6 and 6.7 %). The distribution capacity in different cross-sections does differ greatly (in the range of 10 to 30 %). The result of this study is the proposed unified and easy-to-implement method of calculating plates under any conditions for their resting on supports and when exposed to any external loads. There is also no difficulty in calculating the plates backed by edges in both directions. Other estimation methods in these cases require a different mathematical approach, and, for the case of a series of external loads, or under difficult plate rest conditions, the issue relating to the stressed-strained state of the system remains open