Theoretical and experimental study on strain distribution of curved beam in-plane force considering pre-bending
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(2020) 42:595
TECHNICAL PAPER
Theoretical and experimental study on strain distribution of curved beam in‑plane force considering pre‑bending Yanze Long1 · Ke Zhang1 · Huaitao Shi1 · Songhua Li1 Received: 22 June 2020 / Accepted: 9 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract Curved beam structures have been widely used in mechanical and architectural structures and other fields because of their high strength-to-weight ratio. This paper considers the strain distribution of a welded curved beam structure under the inplane force pre-bending. First, a constitutive relationship is obtained based on tensile test of wall of the curved beam structure. Second, the strain distribution of the pre-bending curved plate is theoretically analyzed and experimentally verified as the initial strain. Subsequently, the theoretical and experimental strain distribution under the action of plane load is applied to the plane curved beam by solid mechanics, finite element, higher-order plane element, and experimental verification analysis. Third, a mathematical expression of strain on the upper and lower plates of the curved beam structure and curved plates on both sides, considering the pre-bending action under in-plane load, is established. Fourth, we establish the residual stress model of curved beam structure under welding action and analyze the strain distribution under the welding action on the section. Finally, we obtain the strain distribution of the curved beam structure under the influence of the curvature change. This study provides a theoretical- and engineering-based approach for analyzing the mechanical properties of curved beam structures. Keywords Curved beam · Strain distribution · Constitutive relationship · Initial strain with pre-bending · Residual stress under welded
1 Introduction Owing to their high strength-to-weight ratio, curved beam members—especially the beam structure with rectangular section—are widely used in mechanical engineering and building structures. For this reason, prior studies have explored various theories that affect the performance of curved beams, including curvature, curved beam element Technical Editor: João Marciano Laredo dos Reis. * Yanze Long [email protected] Ke Zhang [email protected] Huaitao Shi [email protected] Songhua Li [email protected] 1
School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang 110168, China
analysis, warping, distortion, one-dimensional curved beam theory, and other curved beam structures during statics analysis. The earliest research on static analyses of thin-walled beams [1] was by Vlasov in 1960; Dabrowski expanded the thin-walled curved beam theory [2] in 1968. Focusing on different influencing factors, a large number of studies have been made to use the analytical solutions such as solutions considered beam elements [3–6], the effect of warping distortional analysis [7, 8], the higher-order one-dimensional analysis [9–12], and cross-sectional deformation modes and curvature effect [1
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