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Elastodynamic Green’s function for reinforced concrete beams |
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| Institution: | 1. Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India;2. Department of Civil Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 5V6;1. Octav Mayer Institute of Mathematics, Romanian Academy, Bd. Carol I, nr. 8, 700506 Ia?i, Romania;2. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Terrassa, Barcelona, Spain;1. Department of Energy Conversion and Storage, Technical University of Denmark – DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark;2. Swiss Light Source, Paul Scherrer Institut (PSI), 5232 Villigen PSI, Switzerland;1. Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia;2. Center for Aerospace Research & Education, University of California, Irvine, CA, USA;1. Department of Mathematical and Physical Sciences, Nizwa University, Nizwa -611, P.O. Box 1357, Oman;2. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt;1. Applied Mechanical Dept., Universidad Nacional del Nordeste, Las Heras 727, Resistencia, Chaco, Argentina;2. Applied and Computational Mechanical Center (CEMACOM), Federal University of Rio Grande do Sul., Av Osvaldo Aranha 99, 3° Andar, Porto Alegre (RS), Brazil;3. CONICET, Argentine Council for Science and Technology, Argentina |
| Abstract: | A semi-analytical solution procedure for three dimensional wave propagation in reinforced concrete (RC) beams has been presented in this paper. Elastodynamic Green’s function has been derived by employing the compatibility conditions and utilizing the symmetry conditions at the loaded cross section. Numerical procedure developed for the Green’s function has been validated using results available in the literature for an infinite laminated composite plate. Three-dimensional wave propagation analysis has been performed for reinforced concrete beam sections of T and L shapes which are common forms of structural elements. Steel reinforcement has been modeled in the finite element mesh. Effect of corrosion has also been included in the finite element model. Green’s function for reinforced concrete sections affected by corrosion of steel unit normalized frequency has been evaluated for illustration. Accuracy of the solution technique has been evaluated in terms of the percentage error in energy balance between the input energy of the applied unit load and the output energy carried by the propagating wave modes. The percentage error has been found to be negligible in all the cases considered here. A simple and accurate numerical method has been presented here as a tool to evaluate Green’s function for RC beams and can be used to detect corrosion. |
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