Bending of simply-supported circular timber beam strengthened with fiber reinforced polymer

• Published in: Applied mathematics and mechanics Vol. 35; no. 3; pp. 297 - 310
• Main Authors: Yang, Xiao, Yang, Zheng, Wen, Qun
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University 01.03.2014; Department of Civil Engineering, Shanghai University, Shanghai 200072, P.R.China
• Subjects: Applications of Mathematics; Beams (structural); Bending; Carbon fiber reinforced plastics; Classical Mechanics; Deflection; Fiber reinforced plastics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinearity; Partial Differential Equations; Timber; circular timber beam; 65L06; 34B15; bending moment-curvature relation; failure mode; nonlinear bending; TU323.3; O341; fiber reinforced polymer (FRP) reinforcement
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-014-1792-x

The bending behavior of the circular cross-section timber beam strengthened with a fiber reinforced polymer (FRP) sheet is investigated. The tight bonding is on the interface between the surface of a timber beam and the reinforcement layer of the FRP sheet. An analytical expression for the bending moment-curvature relation is presented, and its failure modes are analyzed. The governing equation for nonlinear small deflection of the FRP-strengthened circular timber beam is established, and the corresponding numerical method is given. The bending deformation of the simply-supported circular timber beam strengthened with the carbon fiber reinforced polymer (CFRP) sheet subject to a uniform load is studied numerically. The influence of the angle and thickness of the CFRP layer as well as the timber strength on the bending deflection of the FRP-strengthened circular timber beam is examined. It is revealed that, with the increases of the thickness and angle, the deflection of the CFRP-strengthened circular timber beam is decreased, and its carrying capacity and ductility are increased. However, when the angle of the layer reaches a certain value, the deflection will no longer decrease with the increase of the angle. At the same time, the nonlinear bending moment-curvature relation of the CFRP-strengthened circular timber beam is simplified as an approximate bilinear constitutive model. The approximate deflections of the simply-supported circular timber beam strengthened with the CFRP sheet are obtained. The results are compared with the linearly elastic bending and nonlinear bending models, showing that the mid-span deflections of a CFRP-strengthened circular timber beam with the approximate bilinear constitutive model are greater than those with the nonlinear constitutive model. The results of its stiffness analysis are on the safe side.