ASSESSMENT OF THE STRESS–STRAIN STATE OF REINFORCED TIMBER BEAMS STRENGTHENED WITH WOOD–METAL ELEMENTS

Abstract

The study investigates three variants of the stress–strain state of reinforced glued-laminated timber beams subjected to bending, highlighting the mechanical interaction between the timber and the reinforcing elements in each case. The reinforcement strategies considered include vertical stiffening members, a combination of vertical and horizontal reinforcement elements, and vertical members combined with FRP (fiber-reinforced polymer) strips, enabling a comprehensive assessment of the structural efficiency of different reinforcement schemes. The paper presents the derivation and generalization of fundamental equilibrium and compatibility equations for determining internal stresses as functions of deformations, accounting for layer interaction, stiffness characteristics, and the nonlinear behavior of wood and composite materials. Particular emphasis is placed on the methodology for constructing moment–curvature diagrams for each reinforcement variant, allowing identification of the elastic limit, cracking moment, plastic redistribution region, and ultimate limit state. These diagrams serve as a crucial tool for evaluating the load-bearing capacity and flexural stiffness of combined reinforced elements and for optimizing reinforcement parameters in structural design calculations. The conducted analysis enables the determination of the most effective reinforcement schemes in terms of enhancing stiffness, crack resistance, and overall structural durability, providing a scientific basis for developing regulatory guidelines and methodological approaches for the strengthening of timber beams in buildings of various functional purposes.