Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators
Abstract
In the paper, the analysis of composite and prestressed beams using the matrix stiffness method is presented. The stiffness matrix for the frame element with a moment release at one end and the vector of equivalent nodal forces for the frame element with and without a moment release are derived. In the presented method, concrete is assumed to behave as viscoelastic material and the relaxation of the prestressing steel is also considered. Therefore, the relations between the generalized element displacements and the generalized element forces are integral and, here, are presented using the mathematical operators. Applying the linear integral operators, the solution to the problem is derived without introducing additional mathematical approximations and simplifications, besides the inevitable approximations related to the rheological properties of constitute materials, i.e., steel, concrete, prestressing and reinforcement steel. The derived relations can be applied with any concrete cree...p functions and for the element with a variable cross section.
Keywords:
Composite beam / End moment release / Viscoelastic analysis / Creep / Shrinkage / Linear integral operators / Stiffness matrix / Equivalent nodal forcesSource:
Archive of Applied Mechanics, 2015, 85, 12, 1961-1981Publisher:
- Springer Verlag
Funding / projects:
- Energy efficiency enhancement of buildings in Serbia and improvement of national regulative capacity for they are certification (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-42012)
DOI: 10.1007/s00419-015-1030-7
ISSN: 0939-1533
WoS: 000363536600012
Scopus: 2-s2.0-84945451818
Institution/Community
GraFarTY - JOUR AU - Deretić-Stojanović, Biljana AU - Kostić, Svetlana M. PY - 2015 UR - https://grafar.grf.bg.ac.rs/handle/123456789/719 AB - In the paper, the analysis of composite and prestressed beams using the matrix stiffness method is presented. The stiffness matrix for the frame element with a moment release at one end and the vector of equivalent nodal forces for the frame element with and without a moment release are derived. In the presented method, concrete is assumed to behave as viscoelastic material and the relaxation of the prestressing steel is also considered. Therefore, the relations between the generalized element displacements and the generalized element forces are integral and, here, are presented using the mathematical operators. Applying the linear integral operators, the solution to the problem is derived without introducing additional mathematical approximations and simplifications, besides the inevitable approximations related to the rheological properties of constitute materials, i.e., steel, concrete, prestressing and reinforcement steel. The derived relations can be applied with any concrete creep functions and for the element with a variable cross section. PB - Springer Verlag T2 - Archive of Applied Mechanics T1 - Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators EP - 1981 IS - 12 SP - 1961 VL - 85 DO - 10.1007/s00419-015-1030-7 ER -
@article{ author = "Deretić-Stojanović, Biljana and Kostić, Svetlana M.", year = "2015", abstract = "In the paper, the analysis of composite and prestressed beams using the matrix stiffness method is presented. The stiffness matrix for the frame element with a moment release at one end and the vector of equivalent nodal forces for the frame element with and without a moment release are derived. In the presented method, concrete is assumed to behave as viscoelastic material and the relaxation of the prestressing steel is also considered. Therefore, the relations between the generalized element displacements and the generalized element forces are integral and, here, are presented using the mathematical operators. Applying the linear integral operators, the solution to the problem is derived without introducing additional mathematical approximations and simplifications, besides the inevitable approximations related to the rheological properties of constitute materials, i.e., steel, concrete, prestressing and reinforcement steel. The derived relations can be applied with any concrete creep functions and for the element with a variable cross section.", publisher = "Springer Verlag", journal = "Archive of Applied Mechanics", title = "Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators", pages = "1981-1961", number = "12", volume = "85", doi = "10.1007/s00419-015-1030-7" }
Deretić-Stojanović, B.,& Kostić, S. M.. (2015). Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators. in Archive of Applied Mechanics Springer Verlag., 85(12), 1961-1981. https://doi.org/10.1007/s00419-015-1030-7
Deretić-Stojanović B, Kostić SM. Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators. in Archive of Applied Mechanics. 2015;85(12):1961-1981. doi:10.1007/s00419-015-1030-7 .
Deretić-Stojanović, Biljana, Kostić, Svetlana M., "Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators" in Archive of Applied Mechanics, 85, no. 12 (2015):1961-1981, https://doi.org/10.1007/s00419-015-1030-7 . .