Refined shear correction of polygonal plates with static loads

Abstract

This paper establishes the shear correction factors of simply supported thick plates of pentagonal, hexagonal and other regular polygonal shapes that are uniformly loaded. By converting the Kirchhoff theory of the generic polygonal thin plates to the Reddy and Mindlin shear deformation models for thick plates, the shear correction factors of the thick polygonal Mindlin plates were obtained by benchmarking against the thick polygonal Reddy plates. Results show that the shear correction factor is a function of the dimensionless plate thickness, the Poisson's ratio of the plate material and the number of plate sides, and that simplification of the shear correction factors leads to the customary – and the lower bound – shear correction factor of 5/6. Comparison of the shear correction factors across the various polygonal plates shows that the shear correction factor increases with the number of plate edges, but the rate of increase then tapers off, asymptotically approaching the factor for a circular plate. The established semi-empirical model allows the shear correction factors of other regular thick polygonal plates to be estimated.