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Generalized Formulation for the Behavior of Geometrically Curved and Twisted Three-Dimensional Timoshenko Beams and Its Isogeometric Analysis ImplementationAbstract This article presents a novel derivation for the governing equations of geometrically curved and twisted three-dimensional Timoshenko beams. The kinematic model of the beam was derived rigorously by adopting a parametric description of the axis of the beam, using the local Frenet–Serret reference system, and introducing the constraint of the beam cross ection planarity into the classical, first-order strain versus displacement relations for Cauchy’s continua. The resulting beam kinematic model includes a multiplicative term consisting of the inverse of the Jacobian of the beam axis curve. This term is not included in classical beam formulations available in the literature; its contribution vanishes exactly for straight beams and is negligible only for curved and twisted beams with slender geometry. Furthermore, to simplify the description of complex beam geometries, the governing equations were derived with reference to a generic position of the beam axis within the beam cross section. Finally, this study pursued the numerical implementation of the curved beam formulation within the conceptual framework of isogeometric analysis, which allows the exact description of the beam geometry. This avoids stress locking issues and the corresponding convergence problems encountered when classical straight beam finite elements are used to discretize the geometry ofmore »Free, publicly-accessible full text available July 1, 2023
Abstract Rising global emission have led to a renewed popularity of timber in building design, including timber-concrete tall buildings up to 18 stories. In spite of this surge in wood construction, there remains a gap in understanding of long-term structural behavior, particularly wood creep. Unlike concrete, code prescriptions for wood design are lacking in robust estimates for structural shortening. Models for wood creep have become increasingly necessary due to the potential for unforeseen shortening, especially with respect to differential shortening. These effects can have serious impacts as timber building heights continue to grow. This study lays the groundwork for wood compliance prediction models for use in timber design. A thorough review of wood creep studies was conducted and viable experimental results were compiled into a database. Studies were chosen based on correlation of experimental conditions with a realistic building environment. An unbiased parameter identification method, originally applied to concrete prediction models, was used to fit multiple compliance functions to each data curve. Based on individual curve fittings, statistical analysis was performed to determine the best fit function and average parameter values for the collective database. A power law trend in wood creep, with lognormal parameter distribution, was confirmed by themore »