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Thin (slender) steel plates possess shear strength beyond the elastic buckling load which is commonly referred to as the post-buckling capacity. Semi-empirical equations based on experimental tests of plate girders have been used for decades to predict the ultimate post-buckling strength of slender webs. However, several recent studies have shown that the current models for predicting the ultimate shear post-buckling capacity of thin plates are based on some incorrect assumptions regarding their mechanical behavior. As a result, the current design equations provide an approximate estimate of capacity for the range of parameters in the test data upon which they are founded. This paper explores the fundamental behavior of thin plates under pure shear. Such a fundamental examination of shear post-buckling behavior in thin plates is needed to enable design procedures that can optimize a plate’s shear strength and load-deformation performance for a wider range of loading and design parameters. Using finite element analyses, which are validated against available results of previous experimental tests, outputs such as plastic strains, von Mises stresses, principal stresses, and principal stress directions are examined on a buckled plate acting in pure shear. The internal bending, shear, and membrane stresses in the plate’s finite elements are also evaluated. In this study, these evaluations are performed for a simply-supported plate with an aspect ratio equal to 1.0 and slenderness ratio equal to 134. Results show that localized bending in the plates due to the out-of-plane post-buckling deformations appear to be a significant factor in the ultimate shear post-buckling capacity of the plate. Also, the compressive stresses continue to increase beyond the onset of elastic buckling in some regions of the plate, contrary to current design assumptions. Overall, this study provides new insights into the mechanics of shear post-buckling behavior of thin plates that can be exploited for design procedures that are consistent with mechanical behavior.
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ESTIMATION OF PLATE PARAMETERS FROM VERTICAL DISPLACEMENT DATA USING A FAMILY OF PLATE MODELS
We develop a method for estimation of parameters of an elastic plate resting on a Winkler-type elastic foundation solely from data on the vertical displacements of the plate. The method allows one to estimate components of the external body force density field, plate thickness, elastic foundation stiffness parameters, horizontal displacements of the plate, and stresses. The key idea of the method is that multiple plate models are used simultaneously, namely the proposed reduced three-dimensional (R3D) plate model, the Mindlin plate model, and the thin plate model. The three plate models form a hierarchy of elastic plate models based on assumptions imposed on stresses, with the R3D plate model being the most generalized model and the thin plate model being the most constrained one. The hierarchical relationship among the plate models allows one to incorporate prior information into the estimation technique. The applicability of the proposed estimation method is illustrated by a numerical example.
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- Award ID(s):
- 1848554
- PAR ID:
- 10423993
- Date Published:
- Journal Name:
- Electronic journal of differential equations
- Volume:
- 15
- ISSN:
- 1072-6691
- Page Range / eLocation ID:
- 1-24
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.58997/ejde.2023.15
