To determine the critical load on a single-span two-storey frame
Abstract
To determine the critical load on a single-span two-storey frame
Incoming article date: 30.05.2022The cause of failures of building structures is design errors (18 - 51%). For metal structures the most frequent (22 - 44%) reason of failures is the loss of stability of its elements. At the conceptual design stage, it is important to have simple ways of determining design lengths of compressed structural members. A single-span two-storey hinge supported frame is considered. The magnitude of the critical load on the frame depends on the distribution of concentrated forces over the frame nodes. Doing a series of calculations, we find that: the minimum value of critical load is obtained when the force F of the left post of the second floor is loaded; maximum value is obtained by loading the first floor props with the same forces F/2. For practically important cases the parameters determining the critical load differ from one another by no more than 5% . The notion of ro-similar frames as frames with the same ratio of linear rigidity of a transom and a column is introduced. It is shown that the parameter, determining the critical load on the frame, is the same for ro-similar frames. For almost important cases, approximate formulas have been obtained, allowing to determine the critical load parameter and the calculated lengths of compressed rods with an error of not more than 5%.
Keywords: flat frame, loss of stability, critical force, design lengths, stability equation, ro-similar frames, approximation, least squares method.