Introducing openings/holes in joists/beams of flooring systems is usually necessary to pass through building services without increasing the floor-to-floor height. In timber beams, the openings reduce the stiffness and limit the ultimate load-carrying capacity by promoting tensile stresses perpendicular to the grain and longitudinal splitting shear stresses. Furthermore, quasi-brittle failure of the timber in shear and tension (promoted by openings) leads to localisation of strain, spurious sensitivity of finite element (FE) simulations with respect to mesh size and orientation and ultimately poor or erroneous damage initiation and failure load predictions. Moreover, the interaction between the openings in the web and slabs of timber-timber composite (TTC) floors which have gained popularity in recent decade, remain largely unexplored in terms of experimental results, and numerical simulations, and design provisions are only limited to bare timber beams without slabs. Accordingly, this research project aims at producing benchmark experimental data and developing reliable FE models for assessing the effect of geometrical irregularities such as notches and openings on the failure mode and load carrying capacity of the timber and TTC beams.
The research project consists of an experimental program and a numerical (FE) simulation that involves derivation, computer implementation and application of a nonlocal continuum-damage model for timber. In the first stage of laboratory testing, pushout tests were performed on symmetric LVL-CLT and GLT-CLT joints with coach screw shear connectors to establish the load-slip behavior, stiffness, and peak load of the coach screw shear connectors. In the second stage, laminated veneer lumber (LVL) and glued laminated timber (GLT) beams with symmetric circular and square openings were tested under three-point bending tests to establish the governing failure mechanism, produce the load-mid span deflection curve and determine the reduction in stiffness and peak load of the LVL and GLT beams due to openings. In the final stage of laboratory experimentations, TTC beams were fabricated by connecting CLT slabs to LVL and GLT beams using coach screw shear connectors and then three-point bending tests were performed on the fabricated LVL-CLT and GLT-CLT composite beams with web opening size, shape, and location identical to the LVL and GLT beams tested in the second stage of the testing program. The digital image correlation (DIC) results acquired during stages two and three of the experimental programs shed light on the mechanism of strain localisation and failure promoted by the openings. Moreover, the test results elucidated the major contribution of the coach screw shear connectors in conjunction with CLT slabs to the failure mode and load-carrying capacity of the TTC beams with web openings. After the experimental program, the existing design criterion for evaluating the ultimate load-carrying capacity of the bare timber beams with holes was modified and applied to TTC beams with web openings. In this regard, an analytical Timoshenko composite beam model was utilized to estimate the shear stress and normal stress profiles in the joist (web) cross-sections and accordingly, the relevant terms in existing design criterion were modified to take into account the composite action between the slab and joist and the reinforcing effects of the screws around the opening areas. The proposed modified design equation had a great agreement with the experimental results.
The numerical part of this research project focused on development, implementation, and validation of a constitutive law for nonlinear FE analysis of timber beams with stress concentrators such as notches and openings. The complex orientation-dependent behaviour of timber accompanied with nonlinear ductile hardening and brittle softening of the timber in compression, tension and shear were captured by an enriched 3D multi-surface continuum damage model. To alleviate the localisation of strain and spurious FE mesh sensitivity associated with brittle/quasi-brittle behaviour of the timber in tension and shear, a nonlocal integral model was developed and incorporated into the 3D continuum damage material model of timber. Apart from a standard attenuation function that suffers from boundary effects at the edges of notches and openings, a symmetric attenuation function was adopted in the nonlocal integral model to minimise the boundary effects in the nonlocal FE simulations. The developed symmetric nonlocal material model was implemented as a user-defined material subroutine (UMAT) in ABAQUS software, and the nonlocal FE simulations of the tested timber and TTC beams with openings were carried out to demonstrate the adequacy and accuracy of the nonlocal FE model for predicting the failure mode, load-displacement, and peak load of the timber beams in the face of strain localisation.
The results of experimental program and numerical simulations revealed that the CLT slab thickness and penetration length of screw shear connectors around the opening areas have major impact on the structural behaviour of the perforated timber beams. It was demonstrated experimentally that different opening shapes of equal area could result in similar reduction of the loading capacity in the perforated timber beams. In addition, the numerical models revealed that local constitutive models cannot simulate the failure of timber materials. Indeed, the local material models must be enriched with a strong localization limiter to prevent strain localization and mesh dependency associated with quasi-brittle failures (softening behaviour) of timber. In the numerical simulations, it was shown that adopting nonlocal integral technique in the material model of timber effectively resolves the strain localization and mesh sensitivity issues.