Structural Analysis Of Three Dimensional Space Frames With Dynamic Loadings

Doctoral Thesis / Dissertation from the year 2014 in the subject Engineering - Civil Engineering, grade: 9, , course: Advanced Steel Structures, language: English, abstract: This dissertation presents three various advanced analysis approaches which can capture accurately and efficiently the ultimate strength and behavior of steel framed structures with nonlinear beam-to-column connections subjected to static and dynamic loadings. Three major sources of nonlinearity are considered in the analyses as follows: (1) material nonlinearity; (2) geometric nonlinearity; and (3) connection nonlinearity. Three types of nonlinear beam-column element formulation considering both geometric and material nonlinearities are coded into two nonlinear structural analysis programs: (1) Nonlinear Structural Analysis Program (NSAP) – 2-D plastic-zone finite element; (2) Practical Advanced Analysis Program (PAAP) – 3-D refined plastic-hinge element and 3-D plastic-fiber element. Three types of steel frames analyzed by the proposed program are: (1) rigid frames – beam-to-column connections are fully rigid; (2) linear semi-rigid frames – beam-to-column connections have constant stiffness; and (3) nonlinear semi-rigid frames – beam-to-column connections have continuously variable stiffness. Three types of analysis can be performed are: (1) nonlinear inelastic static analysis; (2) nonlinear elastic and inelastic time-history analysis; and (3) free vibration analysis. Three main resources of damping are taken into account in the proposed programs are: (1) hysteretic damping due to inelastic material; (2) structural viscous damping employing Rayleigh damping; (3) hysteretic damping due to nonlinear beam-to-column connections. Two computer programs are developed: (1) Nonlinear Structural Analysis Program (NSAP) – written in the C++ programming language; (2) Practical Advanced Analysis Program (PAAP) – written in the FORTRAN 77 programming language. They are verified for accuracy and computational efficiency by comparing predicted results with those generated by the commercial finite element analysis packages of ABAQUS and SAP2000, and other results available in the literature. Through several numerical examples, the proposed program (PAAP) proves to be a reliable and efficient tool for daily practice design in lieu of using costly and time-consuming commercial software.

This report presents the theoretical basis for CTABS80, a computer program for the linear three-dimensional structural analysis of multistory frame and shear wall buildings subjected to static or dynamic loadings. In CTABS80, the building is idealized as an assemblage of vertical independent frame and shear wall systems interconnected by horizontal floor diaphragms which are rigid in their own plane. The frame and shear wall systems must basically be of rectangular geometry (in elevation) with vertical columns (or piers) and horizontal beams (or spandrels). However, with special modeling techniques, very complex situations may be considered. A special shear panel element is developed to enable modeling of discontinuous shear walls and shear walls with arbitrary openings. A diagonal bracing system to model braced frames (X-braced, K-braced, or eccentrically braced systems) is also presented. The column, shear panel, and diagonal formulations include the effects of bending, axial, and shear deformations. Bending and shear deformations are also included in the beam formulation: however, the effects of axial deformations are neglected. The effects of the finite dimensions of the beams and columns on the stiffness of a frame or shear wall system are automatically included. The buildings may be unsymmetrical and nonrectangular in plan. Torsional behavior and interstory compatibility are accurately reflected in the results.

The first objective of this dissertation is the development of a three-dimensional hysteretic model capable of representing the behavior of typical frame members. A macro-modeling approach is adopted, the essence of which is to define the constitutive relations at a control section directly in terms of stress resultants and strains. The derivation relies on the premise that the underlying material behavior can be represented by a parallel-plasticity model. The connection between the fundamental stress-strain law and the section stress resultant-strain relations is rationalized from that perspective. The model is designed as a constitutive relation with internal variables. The evolution equations are postulated using non-associated flow rule with the ultimate-yield locus of the section serving as a plastic potential function. The latter is represented by an axial force-biaxial moment interaction surface in hysteretic force space. A new parametric equation of a general interaction surface is introduced to provide a versatile tool for modeling triaxial effects in frame members. It is also demonstrated that several popular one- and two-dimensional hysteretic models can be regarded as particular cases of the proposed model. The loading/unloading criteria of the two-dimensional versions are shown inadequate and a new loading/unloading criterion is proposed. The constitutive model is then used to define the behavior at the control sections of a nonlinear beam-column element. The principle of virtual forces is employed to derive the nodal force-displacement relationship embodied by the flexibility matrix. This approach exploits the internal determinancy of frame members under any boundary conditions - a quality allowing exact interpolation of the element force field from the nodal actions. The element is developed in the setting of a stiffness-based incremental solution of the governing equations. The specific contribution is the introduction of a novel aspect in the state determination procedure. The main idea is to merge the equilibrium unbalances at the control sections from the current global iteration with the incremental internal forces in the next one. Another goal of the dissertation is the conceptual design of an algorithm for solving finite-element problems in state space. The key concept is to solve the structure equations of motion and the element constitutive relations simultaneously in time. Specific advances are made toward systematizing the task of defining the state of a general element and postulating its evolution. Guidelines are provided for selection of state variables for various combinations of formulation types and constitutive models. The concepts involved in the creation of a new element are illustrated through the definition of an inelastic frame member model, operating in the setting of the state-space method. The final chapter of this dissertation presents analytical studies of a typical long multi-span highway bridge for spatially varying ground motion of the 1994 Northridge earthquake. The primary objective of the study is to qualify and quantify the effects of the non-synchronous excitation. The numerous cases involved in the study are analyzed using the modeling and analysis tools of the computational platform IDARC-BRIDGE. Based on these results, the relative importance of factors that have been shown to affect the behavior of highway bridges is weighed and the dominant influence on the response is identified.

First published in 1991. This volume contains the proceedings of the first European Conference on Structural Dynamics (Eurodyne 90) held at the Ruhr University, Bochum, FRG in June 1990. Volume one (169-9) covers impact, dynamic stability, soil dynamics, system identification, earthquake engineering, earthquake engineering R/C structures, and earthquake engineering for steel structures.

This book is devoted to the discussion and studies of simple and efficient numerical procedures for large deflection and elasto-plastic analysis of steel frames under static and dynamic loading. In chapter 1, the basic fundamental behaviour and philosophy for design of structural steel is discussed, emphasising different modes of buckling and the inter-relationship between different types of analysis. In addition to this, different levels of refinement for non-linear analysis are described. An introduction is also given to the well-known P-&dgr; and P-&Dgr; effects. Chapter 2 presents the basic matrix method of analysis and gives several examples of linear analysis of semi-rigid pointed frames. It is evident from this that one must have a good understanding of first-order linear analysis before handling a second-order non-linear analysis. In chapter 3, the linearized bifurcation and second-order large deflection are compared and the detailed procedure for a second-order analysis based on the Newton-Raphson scheme is described. Chapter 4 introduces various solution schemes for tracing of post-buckling equilibrium paths and the Minimum Residual Displacement control method with arc-length load step control is employed for the post-buckling analysis of two and three dimensional structures. Chapter 5 addresses the non-linear behaviour and modelling of semi-rigid connections while several numerical functions for description of moment versus rotation curves of typical connection types are introduced. The scope of the work in chapter 6 covers semi-rigid connections and material yielding to the static analysis of steel frames. Chapter 7 studies the cyclic response of steel frames with semi-rigid joints and elastic material characteristics. In the last chapter the combined effects of semi-rigid connections and plastic hinges on steel frames under time-dependent loads are studied using a simple springs-in-series model. For computational effectiveness and efficiency, the concentrated plastic hinge concept is used throughout these studies.

The general philosophy of design of a space frame is discussed from both an architectural and structural point of view. A number of approaches to the method of structural analysis are briefly reviewed, then one method, that of stiffness coefficients, is trated in more detail. Engineering and construction details showing the extensive use of tubular members are presented. Field investigation of actual stresses and deflections is treated with specific reference to the National Cash Register Pavilion at the New York City 1964-1965 World's Fair.