Bracing Requirements for Multi-column Systems with Nonuniform Stiffness and Semi-rigid Connections
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Date
2023-01-12
Authors
Zhang, Linbo
Journal Title
Journal ISSN
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Publisher
University of Waterloo
Abstract
For a structural system consisting of multiple columns, horizontal discrete braces are often used to increase the system's load-carrying capacity by reducing the columns' effective length. Over the past several decades, Winter's model has been extensively adopted to investigate the stiffness and strength requirements of bracing for multi-column systems. However, as Winter's model simulates the column as two perfectly-straight rigid members pin-connected at ends, it neglects the column's flexibility and initial curvature as well as the stiffness of end connections. As a consequence, the pertinent research and standards are limited to multiple columns with pin ends and may yield unconservative results due to neglecting the column initial curvature. In addition, the specifications in current standards are based on the cases in which the column sizes, applied loads, and braces are the same (referred to as uniform stiffness), which restrains its practical application scenarios. Therefore, the effect of nonuniform stiffness, i.e., different column sizes, applied loads, or brace stiffness, on the bracing requirements for multi-column systems has not been investigated.
A new analytical model (half-length column model) is proposed in this thesis to consider the aforementioned factors neglected in Winter's model. The bracing requirements for a single semi-rigidly connected column with a lateral brace at the mid-height obtained by employing the proposed model are investigated and compared with those obtained by following current standards. It is found that considering the column initial curvature will magnify the additional lateral displacement induced by the applied load and subsequently increase the brace force, as expected. Hence, the bracing requirements for a single column specified in current standards may be underestimated in some cases.
By extending the proposed half-length column model to multiple columns, an analytical method is proposed to evaluate the ideal brace stiffness and brace forces for multi-column systems with nonuniform stiffness by formulating the stiffness interaction among columns and braces. Explicit solutions and empirical equations are attained to evaluate the ideal brace stiffness and maximum brace force for systems with uniform column stiffness. The results of the presented numerical examples indicate that the design equations in current standards are not applicable to cases with nonuniform column stiffness.
Due to the interactive relationship between the brace stiffness and brace force in multi-column systems, the design process of evaluating the maximum brace force and column lateral displacement with presupposed brace stiffness may require cumbersome iterations and overestimate the bracing requirements. Therefore, instead of presupposing the brace stiffness to calculate the brace forces and column lateral displacements, the bracing requirements are converted to preconditions and incorporated into the formulations established in the proposed method to assess the minimum brace area for a single column and multi-column systems, thus circumventing the iteration process.
Instead of assuming all the brace stiffness to be uniform, the effect of nonuniform brace stiffness on bracing requirements is also investigated. The effect of solid blocking on bracing requirements for cold-formed steel bearing walls is assessed, indicating that considering solid blocking will always reduce the bracing requirements, which is not considered in the current standards. An optimization problem is proposed to investigate alternative bracing patterns that are more economical than the uniform bracing pattern.
As building fires are responsible for momentous losses of property and life, fire safety has become an inseparable part of structural design, especially for steel structures. Also, it has reached a consensus in the structural fire research community that the creep effect should be considered when evaluating the fire resistance of steel members because it will decrease the material stiffness, thus leading to larger deformations and premature failure. A numerical method is established in this thesis to assess the column's mid-height deflection at elevated temperatures induced by the creep effect. The method is validated against the creep buckling tests on steel columns at elevated temperatures. In particular, it has been found that the creep-induced deflection of the steel column is led by the nonuniform strain and stress distributions on the cross-section, which is triggered by the initial imperfection.
As the assumptions adopted in the proposed numerical method are experimentally verified to be reasonable, a simplified formulation is proposed to evaluate the creep effect on the column lateral stiffness at elevated temperatures. Analytical expressions are proposed to attain the additional column lateral displacements and internal forces induced by the thermal expansions of braces. The modified plastic-hinge method is adopted to account for the adverse effect of partial yielding on the lateral stiffness of steel columns at elevated temperatures. Finally, a numerical method is established incorporating the effects of thermal expansions of braces, and partial yielding and creep of columns, to evaluate the critical temperature of multi-column systems.
As necessary, finite element modelling is used to validate the theoretical accuracy of the proposed methods. Overall, the proposed model and analytical methods in this study are comprehensively applicable to assessing the bracing requirements for multi-column systems, providing certain reference significance for researchers and engineers.
Description
Keywords
Brace design, Ideal brace stiffness, Brace force, Storey-based stability, Initial curvature, Semi-rigid connection, Nonuniform stiffness, Multi-column system, Creep buckling