Weak-Form Quadrature-Element Method for Creep and Shrinkage Analysis of Steel–Concrete Composite Beams
Publication: Journal of Engineering Mechanics
Volume 146, Issue 4
Abstract
In this paper, a displacement-based weak-form quadrature element (WQE) is formulated and implemented for long-term response analysis of steel–concrete composite beams. The effects of creep and shrinkage taking place in reinforced concrete slabs are considered by using an integral type viscoelastic model. Timoshenko and Kant higher-order beam theories are applied to depict the reinforced concrete slab and steel beam, respectively, so as to achieve accuracy close to that of the 3D shell model, but at a much lower computational cost. The proposed model and program are verified through comparisons with the 3D shell and classical beam models. To investigate the improvement of convergence performance contributed by the differential quadrature technique, detailed comparisons are made between the WQE and conventional finite element. Numerical results show that the composite beams modeled with the Timoshenko-Kant kinematical assumption can achieve accuracy close to that of the 3D shell model; due to the ability to conveniently adjust interpolation order, the proposed WQE acquires much higher computational efficiency than the conventional finite element; the severe numerical smoothness problem common in the displacement-based finite element model (FEM) is significantly alleviated by the higher-order WQE method.
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Data Availability Statement
All data and models used in the study appear in the submitted article. All codes generated or used during the study are available in a repository online in accordance with funder data retention policies. The conventional finite element program can be downloaded through https://gitee.com/guanghuihe/FEM-for-SCCB. The WQE program can be downloaded through https://gitee.com/guanghuihe/WQEM-for-SCCB.
Acknowledgments
The authors acknowledge support from Research Fund of Shanghai Construction Group (Grant No. 18YJKF-10).
References
ACI (American Concrete Institute). 1992. Prediction of creep, shrinkage, and temperature effects in concrete structures. ACI 209R. Farmington Hills, MI: ACI.
Amadio, C., and M. Fragiacomo. 1997. “Simplified approach to evaluate creep and shrinkage effects in steel-concrete composite beams.” J. Struct. Eng. 123 (9): 1153–1162. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:9(1153).
Bažant, Z. P. 1995. “Creep and shrinkage prediction model for analysis and design of concrete structures—Model B3.” Mater. Constr. 28 (180): 357–365.
Bažant, Z. P., M. H. Hubler, and Q. Yu. 2011. “Pervasiveness of excessive segmental bridge deflections: Wake-up call for creep.” ACI Struct. J. 108 (6): 766–774.
Bažant, Z. P., and Y. Xi. 1995. “Continuous retardation spectrum for solidification theory of concrete creep.” J. Struct. Eng. 121 (2): 281–288. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:2(281).
Bellman, R., and J. Casti. 1971. “Differential quadrature and long-term integration.” J. Math. Anal. Appl. 34 (2): 235–238. https://doi.org/10.1016/0022-247X(71)90110-7.
Bellman, R., B. G. Kashef, and J. Casti. 1972. “Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations.” J. Comput. Phys. 10 (1): 40–52. https://doi.org/10.1016/0021-9991(72)90089-7.
Bertagnoli, G., D. Gino, and E. Martinelli. 2017. “A simplified method for predicting early-age stresses in slabs of steel-concrete composite beams in partial interaction.” Eng. Struct. 140 (1): 286–297. https://doi.org/10.1016/j.engstruct.2017.02.058.
Berthet, J. F., I. Yurtdas, Y. Delmas, and A. Li. 2011. “Evaluation of the adhesion resistance between steel and concrete by push out test.” Int. J. Adhes. Adhes. 31 (2): 75–83. https://doi.org/10.1016/j.ijadhadh.2010.11.004.
CEB (Comit Euro-International Du Beton). 1998. CEB-FIP Model code 1990: Design code. London: Thomas Telford.
Costabel, M., M. Dauge, and C. Schwab. 2005. “Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains.” Math. Models Methods Appl. Sci. 15 (4): 575–622. https://doi.org/10.1142/S0218202505000480.
Dezi, L., C. Ianni, and A. M. Tarantino. 1993. “Simplified creep analysis of composite beams with flexible connections.” J. Struct. Eng. 119 (5): 1484–1497. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:5(1484).
Dezi, L., G. Leoni, and A. M. Tarantino. 1996. “Algebraic method for creep analysis of continuous composite beams.” J. Struct. Eng. 122 (4): 423–430. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:4(423).
Dezi, L., and A. M. Tarantino. 1993a. “Creep in composite continuous beams. I: Theoretical treatment.” J. Struct. Eng. 119 (7): 2095–2111. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(2095).
Dezi, L., and A. M. Tarantino. 1993b. “Creep in composite continuous beams. II: Parametric study.” J. Struct. Eng. 119 (7): 2112–2133. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(2112).
Erkmen, R. E., and M. A. Bradford. 2011. “Time-dependent creep and shrinkage analysis of composite beams curved in-plan.” Comput. Struct. 89 (1–2): 67–77. https://doi.org/10.1016/j.compstruc.2010.08.004.
fib (International Federation for Structural Concrete). 2013. fib model code for concrete structures 2010. Lausanne, Switzerland: Wilhelm Ernst & Sohn.
Fragiacomo, M., and A. Ceccotti. 2006. “Long-term behavior of timber–concrete composite beams. I: Finite element modeling and validation.” J. Struct. Eng. 132 (1): 13–22. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:1(13).
Fu, C., and X. Yang. 2018. “Dynamic analysis of partial-interaction Kant composite beams by weak-form quadrature element method.” Arch. Appl. Mech. 88 (12): 2179–2198. https://doi.org/10.1007/s00419-018-1443-1.
Han, S. M., H. Benaroya, and T. Wei. 1999. “Dynamics of transversely vibrating beams using four engineering theories.” J. Sound Vib. 225 (5): 935–988. https://doi.org/10.1006/jsvi.1999.2257.
Hedegaard, B. D., C. K. Shield, and C. E. W. French. 2015. “Smeared-bar model for viscoelastic analysis of uncracked reinforced concrete structures.” J. Struct. Eng. 141 (7): 04014167. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001124.
Hou, H., and G. He. 2018. “Static and dynamic analysis of two-layer Timoshenko composite beams by weak-form quadrature element method.” Appl. Math. Model. 55 (Mar): 466–483. https://doi.org/10.1016/j.apm.2017.11.007.
Kant, T., and A. Gupta. 1988. “A finite element model for a higher-order shear-deformable beam theory.” J. Sound Vib. 125 (2): 193–202. https://doi.org/10.1016/0022-460X(88)90278-7.
Kant, T., D. R. J. Owen, and O. C. Zienkiewicz. 1982. “A refined higher-order C0 plate bending element.” Comput. Struct. 15 (2): 177–183. https://doi.org/10.1016/0045-7949(82)90065-7.
Kolínský, V., and K. L. Vitek. 2016. “New model for concrete creep and shrinkage prediction and its application.” Solids State Phenom. 249: 125–130.
Liu, X., M. A. Bradford, and R. E. Erkmen. 2013. “Time-dependent response of spatially curved steel-concrete composite members. I: Computational modeling.” J. Struct. Eng. 139 (12): 04013004. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000698.
Liu, X., R. E. Erkmen, and M. A. Bradford. 2012. “Creep and shrinkage analysis of curved composite beams with partial interaction.” Int. J. Mech. Sci. 58 (1): 57–68. https://doi.org/10.1016/j.ijmecsci.2012.03.001.
Manjunatha, B. S., and T. Kant. 1993. “New theories for symmetric/unsymmetric composite and sandwich beams with finite elements.” Comput. Struct. 23 (1): 61–73. https://doi.org/10.1016/0263-8223(93)90075-2.
Newmark, N. M., C. P. Siess, and I. M. Viest. 1951. “Tests and analysis of composite beams with incomplete interaction.” Proc. Soc. Exp. Stress Anal. 19 (1): 75–92.
Nguyen, Q. H., M. Hjiaj, and B. Uy. 2010. “Time-dependent analysis of composite beams with continuous shear connection based on a space-exact stiffness matrix.” Eng. Struct. 32 (9): 2902–2911. https://doi.org/10.1016/j.engstruct.2010.05.009.
Shu, C., and B. E. Richards. 1992. “Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations.” Int. J. Numer. Methods Fluids 15 (7): 791–798. https://doi.org/10.1002/fld.1650150704.
Smith, I. M., D. V. Griffiths, and L. Margetts. 2014. Programming the finite element method. Chichester, UK: Wiley.
Tarantino, A. M., and L. Dezi. 1992. “Creep effects in composite beams with flexible shear connectors.” J. Struct. Eng. 118 (8): 2063–2080. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:8(2063).
Tong, T., Q. Yu, and Q. Su. 2018. “Coupled effects of concrete shrinkage, creep, and cracking on the performance of postconnected prestressed steel-concrete composite girders.” J. Bridge Eng. 23 (3): 04017145. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001192.
Wang, X. 2015. Differential quadrature and differential quadrature based element methods theory and applications. Oxford, UK: Butterworth-Heinemann Oxford.
Wang, X., Z. Yuan, and C. Jin. 2017. “Weak form quadrature element method and its applications in science and engineering: A state-of-the-art review.” Appl. Mech. Rev. 69 (3): 030801. https://doi.org/10.1115/1.4036634.
Wang, Y., and X. Wang. 2014. “Static analysis of higher order sandwich beams by weak form quadrature element method.” Compos. Struct. 116 (Sep): 841–848. https://doi.org/10.1016/j.compstruct.2014.06.015.
Wang, Y., and X. Wang. 2016. “Free vibration analysis of soft-core sandwich beams by the novel weak form quadrature element method.” J. Sandwich Struct. Mater. 18 (3): 294–320. https://doi.org/10.1177/1099636215601373.
Wendner, R., G. Boumakis, M. Hubler, and Z. P. Bažant. 2015. “Model B4: A multi-decade prediction model for creep and shrinkage.” In Life-cycle of structural systems, 459–464. Boca Raton, FL: CRC Press.
Yu, Q., Z. P. Bažant, and R. Wendner. 2012. “Improved algorithm for efficient and realistic creep analysis of large creep-sensitive concrete structures.” ACI Struct. J. 109 (5): 665–676.
Zhu, L., and R. K. L. Su. 2017. “Analytical solutions for composite beams with slip, shear-lag and time-dependent effects.” Eng. Struct. 152 (1): 559–578. https://doi.org/10.1016/j.engstruct.2017.08.071.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 4 • April 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: May 9, 2019
Accepted: Sep 30, 2019
Published online: Feb 3, 2020
Published in print: Apr 1, 2020
Discussion open until: Jul 3, 2020
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