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 in-plane 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.
Similar content being viewed by others
References
Vlasov VZ (1961) Thin-walled elastic beams, 2nd edn. National Science Foundation, Washington
Dabrowski R (1973) Curved thin-walled girders, theory and analysis. Cement and Concrete Association, London
Lin KC, Lin CW (2011) Finite deformation of 2-D laminated curved beams with variable curvatures. Int J Non-Linear Mech 46:1293–1304
Lin KC, Hsieh CM (2007) The closed form general solutions of 2-D curved laminated beams of variable curvatures. Compos Struct 79:606–618
Shahba A, Attarnejad R, Jandaghi Semnani S, Honarvar Gheitanbaf H (2013) New shape functions for non-uniform curved Timoshenko beams with arbitrarily varying curvature using basic displacement functions. Meccanica 48:159–174
Ashkan Afnani, Emre Erkmen R, Vida Niki (2017) An efficient formulation for thin-walled beams curved in plan. Int J Steel Struct 17:1087–1102
Sapountzakis EJ, Tsiptsis IN (2015) Generalized warping analysis of curved beams by BEM. Eng Struct 100:535–549
Tsiptsis Ioannis N, Sapountzakis Evangelos J (2017) Generalized warping and distortional analysis of curved beams with isogeometric methods. Comput Struct 191:33–50
Kim JH, Kim YY (2000) One-dimensional analysis of thin-walled closed beams having general cross sections. Int J Numer Meth Eng 49:653–668
Kim YY, Kim Y (2002) A one-dimensional theory of thin-walled curved rectangular box beams under torsion and out-of-plane bending. Int J Numer Meth Eng 53:1675–1693
Kim Y, Kim YY (2003) Analysis of thin-walled curved box beam under in-plane flexure. Int J Solids Struct 40:6111–6123
Kim NI, Jeon CK (2013) Improved thin-walled finite curved beam elements. Adv Mech Eng 2013:1–16
Zhang L, Zhu Z, Shen G, Cao GA (2015) Finite element for spatial static analyses of curved thin-walled rectangular beams considering eight cross-sectional deformation modes. Arab J Sci Eng 40:3731–3743
Zhang L, Zhu Z, Shen G, Cao G (2015) Finite difference modeling of sinking stage curved beam based on revised Vlasov equations. J Cent South Univ 22:4219–4227
Ban Huiyong, Shi Gang, Shi Yongjiu, Wang Yuanqing (2013) Residual stress of 460 mpa high strength steel welded box section: experimental investigation and modeling. Thin-Walled Struct 64:73–82
Gardner L, Bu Y, Theofanous M (2016) Laser-welded stainless steel i-sections: residual stress measurements and column buckling tests. Eng Struct 127:536–548
Xiong G, Kang SB, Yang B, Wang S, Bai J, Nie S et al (2016) Experimental and numerical studies on lateral torsional buckling of welded q460gj structural steel beams. Eng Struct 126:1–14
Oliveira PI, Antunes FV, Loureiro A, Costa JM (2019) Effect of the angular misalignment of laser welded T-joints on fatigue curves. Int J Fatigue 128:105180
Rezaiee-Pajand M, Ramezani M, Gharaei-Moghaddam N (2020) Using higher-order strain interpolation function to improve the accuracy of structural responses. Int J Appl Mech 4:2050026
Rezaiee-Pajand M, Gharaei-Moghaddam N, Ramezani M (2020) Higher-order assumed strain plane element immune to mesh distortion. Eng Comput ahead-of-print.ahead-of-print(2020)
Rezaiee-Pajand M, Gharaei-Moghaddam N, Ramezani M (2020) Strain-based plane element for fracture mechanics’ problems. Theor Appl Fract Mech 108:102569
Rezaiee-Pajand M, Gharaei-Moghaddam N, Ramezani M (2019) A new higher-order strain-based plane element. Sci Iranica 26(4):2258–2275
Rezaiee-Pajand M, Gharaei-Moghaddam N, Ramezani M (2019) Two triangular membrane elements based on strain. Int J Appl Mech 11(1):1950010
Li S, Wei C, Long Y (2020) Deformation analysis of engineering reinforcement straightening based on bauschinger effect. Int J Steel Struct 20:1–12
Tu S, Ren X, He J, Zhang Z (2018) A method for determining material’s equivalent stress-strain curve with any axisymmetric notched tensile specimens without bridgman correction. Int J Mech Sci 135:656–667
Moaveni BS (1999) Finite element analysis theory and application with ANSYS, 3rd edn. Prentice Hall, Upper Saddle River
Rasmussen KJR, Hancock GJ (1988) Deformations and residual stresses induced in channel section columns by presetting and welding. J Constr Steel Res 11:175–204
Salerno G, Bennett C, Wei S (2018) On the interaction between welding residual stresses: a numerical and experimental investigation. Int J Mech Sci 144:654–667
Pandit D, Srinivasan SM (2016) Numerical analysis of large elasto-plastic deflection of constant curvature beam under follower load. Int J Non-Linear Mech 84:46–55
Choo YS, Choi N, Lee BC (2006) Quadrilateral and triangular plane elements with rotational degrees of freedom based on the hybrid Trefftz method. Finite Elem Anal Des 42(11):1002–1008
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 51375317), the National Key Technology R&D Program of China (Grant No. 2011BAJ02B07), and the National Key Research and Development Program of China (Grant No. 2017YFC0704003/2017YFC0703903).
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: João Marciano Laredo dos Reis.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Long, Y., Zhang, K., Shi, H. et al. Theoretical and experimental study on strain distribution of curved beam in-plane force considering pre-bending. J Braz. Soc. Mech. Sci. Eng. 42, 595 (2020). https://doi.org/10.1007/s40430-020-02678-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-020-02678-8