Abstract
Using the superposition and small deflection theories, thermal change perpendicular to a surface is considered. A CRTP (concrete rectangular thin plate) with two adjacent CEDs (clamped edges) and one SSED (simply supported edge) and one FED (free edge) under thermal change is seen as a RTP’s superposition with three SSEDs and one FED in the case of temperature change and a RTP with three SSEDs and one FED under the bending moment on two adjacent edges. Adopting the Levy method, by supposing the deflection function with undetermined parameter on the FED, the theoretical solution of a CRTP (concrete rectangular thin plate) with three SSEDs and one FED is obtained; the theoretical solution of a CRTP with three SSEDs and one FED is obtained under thermal change; taking the theoretical solution of a CRTP with four SSEDs under the bending moment on two adjacent edges, the theoretical solution of a CRTP with three SSEDs and one FED under the bending moment on two adjacent edges is obtained; the theoretical solution for the bending moment and deflection of a CRTP with two adjacent CEDs and one SSED and one FED under temperature change is obtained.
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Dobroskok, A.; Ghassemi, A.: Numerical simulation of crack propagation influence by thermal and porous liquid stresses. Int. J. Fract. 134(2), 29–34 (2005)
Bhothikhun, P.; Dechaumphai, P.: Development of DKT finite element formulation for thermal bending of thin plate. J. Therm. Stresses 38(7), 775–791 (2015)
Masoodi, A.R.; Arabi, E.: Geometrically nonlinear thermomechanical analysis of shell-like structures. J. Therm. Stresses 41(1), 37–53 (2018)
Misra, J.C.: On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation. Pure Appl. Geophys. 112(1), 83–89 (1974)
Pachinger, F.; Lrschik, H.: Fast convergent series solutions for thermal bending of thin rectangular plates. J. Therm. Stresses 21(7), 763–775 (1998)
Zhong, Y.; Zhang, Y.S.: Theoretic solution for rectangular thin plate with arbitrary boundary conditions by symplectic geometry method. Chin. J. Appl. Mech. 22(2), 293–297 (2005)
Hetnarski, R.B.; Eslami, M.R.: Thermal Stresses: Advanced Theory and Applications, vol. 158, pp. 105–130. Springer, Netherlands (2009)
Eslami, M.R.; Hetnarski, R.B.; Ignaczak, J.; et al.: Theory of Elasticity and Thermal Stresses, vol. 197, pp. 513–533. Springer, Netherlands (2013)
Zenkour, A.M.: Bending of orthotropic plates resting on Pasternak’s foundations using mixed shear deformation theory. Acta. Mech. Sin. 7(6), 956–962 (2011)
Shariyat, M.; Lavasani, S.M.H.; Khaghani, M.: Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders using a second-order point-collocation method. Appl. Math. Model. 34(4), 898–918 (2010)
Shariyat, M.: Nonlinear transient stress and wave propagation analyses of the FGM thick cylinders, employing a unified generalized thermoelasticity theory. Int. J. Mech. Sci. 65(1), 24–37 (2012)
Cheng, X.S.; Du, Y.F.; Li, H.: Analytic solution to rectangular thin plate with three clamped edges and one simply supported edge under temperature disparity. Adv. Struct. Eng. 8, 789–794 (2006)
Cheng, X.S.; Du, Y.F.; Li, H.: Discuss of analytic solution about rectangular thin plate with four clamped edges under temperature disparity. Special Struct. 23(4), 42–45 (2006). (in Chinese)
Cheng, X.S.; Du, Y.F.; Li, H.: A discussion on the analytical solution of rectangular thin slab under temperature load with four simply supported edges. Mech. Eng. 28(6), 28–32 (2006). (in Chinese)
Cheng, X.S.; Du, Y.F.: The discussion of the analytical solution about rectangular thin slab under temperature disparity with four simply supported edges. Low Temp. Archit. Technol. 4, 76–78 (2006). (in Chinese)
Cheng, X.S.; Du, Y.F.; Li, H.; et al.: Analytic solution about rectangular thin slab with three simply supported edges and one clamped edge under temperature load. Low Temp. Archit. Technol. 4, 59–61 (2007). (in Chinese)
Cheng, X.S.; Du, Y.F.; Li, H.; et al.: The analytical solution about rectangular thin slab with three clamped edges and one simply supported edges under temperature load. Struct. Environ. Eng. 34(4), 8–13 (2007). (in Chinese)
Cheng, X.S.; Du, Y.F.; Li, H.; et al.: The analytical solution about thin rectangular slab with two opposite clamped edges and two opposite simply supported edges under temperature loads. J. Gansu Sci. 19(2), 39–43 (2007). (in Chinese)
Cheng, X.S.; Du, Y.F.; Li, H.: An analytic solution for rectangular thin slab with two adjacent clamped edges and two adjacent simply supported edges under temperature loads. J. Gansu Sci. 20(1), 116–118 (2008). (in Chinese)
Cheng, X.S.; Du, Y.F.; Li, H.; Su, J.X.: The analytical solution about rectangular thin slab with two opposite edges clamped and two opposite edges simply supported under temperature load. Proc. Tenth Int. Symp. Struct. Eng. Young Expert 10, 213–217 (2008)
Cheng, X.S.; Su, J.X.; Shi, X.Y.: The thermal bend of concrete rectangular thin plate with four sides supported. Special Struct. 26(4), 56–60 (2009). (in Chinese)
Deshmukh, K.C.; Khandait, M.V.; Warbhe, S.D.; et al.: Thermal stresses in a simply supported plate with thermal bending moments. Appl. Math. Mech. 6(18), 1–12 (2010)
Liu, J.X.; Guo, X.H.; Su, J.C.: Water Supply and Drainage Engineering Structure, pp. 295–344. China Construction Industry Press (2006) (in Chinese)
Cheng, X.S.; Du, X.L.: The thermal bend of concrete rectangular thin plate with three clamped sides and one free side. Eng. Mech. 30(4), 97–106 (2013). (in Chinese)
Cheng, X.S.; Du, X.L.; Zhang, G.W.; et al.: The thermal bend of concrete rectangular thin plate with three simply supported sides and one free side. Chin. J. Appl. Mech. 30(1), 37–42 (2013). (in Chinese)
Cheng, X.S.; Nie, J.; Zhao, L.; et al.: The thermal bend of RTP with one edge clamped and two edges simply supported and one edge free. Arch. Appl. Mech. 85(2), 287–302 (2015)
Cheng, X.S.; Jin, F.: Thermal bending of rectangular thin plate with two opposite edges clamped and one edge simply supported and one edge free. KSCE J. Civil Eng. 20(1), 333–342 (2016)
Guo, Z.H.; Shi, X.D.: Behaviour of Reinforced Concrete at Elevated Temperature and its Calculation, pp. 106–108. Tsinghua University Press, Beijing (2003). (in Chinese)
Zi, W.: Study on Mechanical Properties and Durability of Concrete Structure After Exposure to High Temperature. Central South University, Changsha (2012). (in Chinese)
EN, 1992-1-2: Design of Concrete Structures. Part 1-2: General Rules—Structural Fire Design, Eurocode 2, European Committee for Standardization, Brussels, Belgium (2004)
GB 50010-2010: Code for design of concrete structures. National Standard of the People’s Republic of China (2015). (in Chinese)
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This paper is a part of the National Natural Science Foundation of China (Grant Number 51478212), and a part of science and technology project in the Zhejiang Traffic Quality Supervision Bureau (Grant Number ZJ201602), and a part of science and technology project in China Railway 12th Bureau Group (Grant Number 14B-3).
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Cheng, X., Gong, L. & Fu, X. Thermal Bend of Concrete Rectangular Thin Plate: Two Adjacent Clamped Edges, One Simply Supported Edge, One Free Edge. Arab J Sci Eng 43, 5689–5699 (2018). https://doi.org/10.1007/s13369-018-3416-7
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DOI: https://doi.org/10.1007/s13369-018-3416-7