Plane Steel Frames Research Articles

Inelastic Analysis and Design: Frames with Members in Minor-Axis Bending

To extend previous research on obtaining designs that rely on a second-order inelastic hinge analysis to demonstrate that a structure is adequate in resisting the effects of factored loads, this paper presents a study of a series of two-story planar steel frames where all columns are subjected to combinations of axial force and minor-axis bending. Inelastic designs, which are prepared to satisfy both strength and serviceability limit states requirements, are compared to designs obtained using a conventional second-order elastic analysis in conjunction with the AISC LRFD Specification. The degree of accuracy and reliability of using a concentrated plasticity analysis to model system behavior is also established. The study indicates that for a majority of the frames investigated, a second-order inelastic hinge analysis can be used effectively to design steel structures. It is also shown that in some cases a distributed plasticity analysis may be required.

A Simplified Plastic Zone Method for Frame Analysis

Abstract: A methodology for the geometric and material nonlinear analysis of plane steel frames suitable for implementation in a microcomputer or personal computer platform is presented. The proposed procedure takes into consideration both geometric and material nonlinearities in its formulation. Geometric nonlinearity in the form of member and frame instabilities is accounted for by the use of pseudo‐joint loads derived from the geometric stiffness matrix of the structure. Material nonlinearity in the form of cross‐sectional plastification and progressive member yielding is accounted for by the use of a cross‐sectional plastification model and the concept of effective member stiffness. Since both cross‐sectional plastification and spread of yield along member length are considered in the analysis, the proposed approach is regarded as a plastic zone model. Unlike conventional plastic zone models in which intensive computations are required to obtain solutions, the proposed model employs simplified procedures by which spread of plasticity in the structural frame is accounted for in an approximate manner. Despite its simplicity, the proposed model gives reasonably accurate results when compared with other more rigorous approaches. To verify the applicability of the approach in predicting inelastic frame behavior, the proposed method was used to analyze a variety of frame structures. The results, expressed in terms of load‐deflection responses, member forces, and moments, compared well with those obtained using other more elaborate inelastic analysis methods.

Pounding of buildings during earthquakes: a Canadian perspective

The main objective of this paper is to provide information to structural engineers on how to consider and mitigate the phenomenon of pounding between adjacent structures during earthquakes. The first part of the paper reviews the problem of seismic pounding; observations of damage from pounding during recent earthquakes are described as well as the pounding potential for buildings in large Canadian cities. A review of literature on analytical and numerical studies of earthquake pounding is presented along with methods that have been proposed to mitigate pounding. In the second part of the paper, the seismic behaviour of three closely spaced, Canadian code designed, plane steel frames is investigated. Nonlinear time-step dynamic analyses and nonlinear elastic gap elements, to model pounding, are used for this purpose. Several parameters, such as separation distances, pounding locations, and ground motion characteristics, are considered. Key words: dynamics, earthquakes, impacts, pounding, seismic.

Design of steel frames for specified seismic member ductility via inverse eigenmode formulation

A new direct method of ductility design is presented for planar moment-resisting steel frames such that a set of member stiffnesses and the corresponding member strengths of a frame with realistic cross-sectional proportions are found for a specified distribution of member ductility factors under design major earthquakes. An inverse method of stiffness design is developed such that every predominant member-end strain in a frame under design earthquakes estimated on the basis of lowest eigenvibration would coincide with the specified value. A concept called ‘a set of similar cross-sections’ is introduced to make it possible to obtain a set of members with realistic cross-sectional proportions. It is then shown that this inverse formulation for specified predominant member-end strains is quite useful for developing a direct stiffness design method for specified mean maximum member-end strains under design earthquakes. It is further demonstrated that, if a frame is designed elastically for specified ductility factors based on a new concept of a ‘virtually elastic frame’ even under design major earthquakes, then the so-designed frame exhibits the desired response ductility characteristics specified for inelastic frames. Several design examples are presented to illustrate the usefulness of this design method and time history response analyses are performed to demonstrate the validity and accuracy of this design method.

Efficient numerical modelling for the design of friction damped braced steel plane frames

A novel friction damping system for the aseismic design of framed buildings has been proposed by Canadian researchers. The system has been shown experimentally to perform very well and is an exciting development in earthquake resistant design.The design of a building equipped with the friction damping system is achieved by determining the optimum slip load distribution to minimize structural response. The optimum slip load distribution is usually determined using the general nonlinear dynamic computer program DRAIN-2D, which requires extensive computer time and is not practical for most design offices.This paper describes a new, efficient, numerical modelling approach for the design of friction damped braced frames. The hysteretic properties of the friction devices are derived theoretically and included in a friction damped braced frame analysis program, which is adaptable to a microcomputer environment. The optimum slip load distribution is determined by minimizing a relative performance index derived from energy concepts. The new numerical approach is much more economical to use than DRAIN-2D and is of great value for the practical design of friction damped braced frames. Key words: braced frames, brake lining, performance index, damping, dynamics, earthquakes, energy, friction.

Nonlinear dynamic analysis of inelastic steel plane frames

A method for the nonlinear dynamic analysis of inelastic framed structures subjected to large displacements is presented. The nonlinear behavior of inelastic steel plane frames with or without initial geometric imperfections is also studied. The proposed method for dynamic analysis is based on an incremental form of equations of motion of the structures. A previously proposed member tangent stiffness matrix of an inelastic member is extended for dynamic analysis. Newmark's β-method is used as the numerical integration technique for solving the incremental form of the equations of motion. The feasibility of the proposed method is illustrated by several numerical examples on the dynamic analysis of inelastic frames.

Analysis and behaviour of flexibly-jointed frames

A method for analysing the behaviour of flexibly-connected plane steel frames is presented. Two types of elements are used in the analysis procedure: the beam-column (frame) element and the connection element. The beam-column element formulation is based on an updated Lagrangian approach. Allowance for the coupling effect of axial force and bending moments, as well as for the formation of plastic hinges in the member, is made for this beam-column element. The nonlinear behaviour of the connection is modelled by an exponential function. Both loading and unloading responses of the connections are taken into consideration in the formulation. The monotonic load-deflection response of frames with flexible connections is traced using an incremental load control Newton-Raphson iterative technique. Based on sub-assemblage and frame analyses, it is concluded that connection flexibility has an important influence on frame behaviour.

Nonlinear analysis of steel plane frames with initial imperfections

A previously proposed member tangent stiffness matrix subjected to elastic-plastic bending and derived from moment-thrust-curvature equations is extended to include the effects induced by the initial crookedness of a member. The shape of the initial geometrical imperfection of the member may be arbitrary and is expressed as an initial curvature in the formulation. A tangent stiffness matrix for initially crooked wide-flange members of elastic-plastic material is constructed and utilized for analyzing inelastic frames with initial geometrical imperfections. For the inelastic frame analyses, an incremental loading procedure is utilized to trace the load-displacement curves for the frames, and the descending branch of the load-displacement curves are obtained by using the modified arc length method of Crisfield. The technique is illustrated by several examples of plane frames loaded beyond their limit points.

Computer-Aided Analysis and Design of Steel Frames

A computer package has been developed for the analysis and design of steel plane frames. The package will, with the stiffness method, analyze a plane frame and select the leastweight wide-flange section for each member within the frame. The two modules of the package, the analysis and design, may be used independently of, or in conjunction with, one another. When used together, they interact to establish an analysis/design iteration sequence by which the least weight design is obtained. Within the analysis module, graphical displays of the structure allow for visual verification of structural data as well as analytical results. The design module minimizes data entry by making design condition assumptions, all of which can be altered. By calculating internally various design parameters, such as effective column length factors, a fast, easy design session is permitted. The package is presently being used in upper-level structural analysis and steel design courses. A student using the package has the benefit of conceptualizing the entire analysis and design process rather than the fractionized procedure often presented in texts. To enhance further the students understanding of the process, the package saves all values used in the final analysis and steel section selection for verification.

Optimal seismic‐resistant design of a planar steel frame

AbstractThis paper illustrates the design of a four‐storey, three‐bay, moment‐resisting, planar steel frame. Non‐linear step‐by‐step integration is used as the analysis technique within the design process itself rather than as a check at the end of the design process.The method of design directly quantifies the accepted seismic‐resistant design philosophy that a properly designed structure: (1) resists moderate ground motion without structural damage, and (2) resists severe ground motion without collapse. Actual ground motion accelerograms are selected and scaled to levels representing moderate and severe ground motions. Constraints quantifying structural damage and limited non‐structural damage are constructed for the case of moderate ground motion, along with constraints quantifying collapse and limited structural damage for the case of severe ground motion. In addition serviceability constraints are imposed on structural behaviour under gravity loads only. Objective functions include the minimization of structural volume as well as the minimization of response quantities such as storey drifts and inelastically dissipated energy.A sophisticated optimization algorithm is utilized to solve the resulting mathematical programming problem. Comparative results concerning the computational phase as well as performance of both preliminary and final designs are presented. The practicality and reliability of the design method are assessed.

DELIGHT.Struct: An optimization-based computer-aided design environment for structural engineering

This paper describes an expandable software system for optimization-based, interactive computer-aided design of structures. This system can be used for the design of statically and/or dynamically loaded structures which exhibit linear or nonlinear response. The software is the union of (1) an interactive base program for the management of the computeraided design process named DELIGHT, (2) a dynamic nonlinear general purpose structural analysis package named ANSR, (3) a library of optimization algorithms with corresponding interfaces for use in structural design, and (4) specialized software for the design of seismic-resistance planar steel frames. Flexibility has been emphasized in the development of this system so that a wide range of structural design problems may be considered. The user may describe a particular design problem to the system by applying a minimal amount of software or by selecting software from expandable libraries.

繰返し外力を受ける鋼構造骨組の弾塑性・大たわみ解析

In this report, the authers propose a kind of finite element method in the piece linear theory of structural analysis, the unknown displacements can be uniquely defined in tern of the relative displacements on the member coordinate axes through eachstep of loading. With the selection of relative displacement, the authers make up the shearing equations by the principle of virtural work and we calculated the plane steel frame which experimented by Dr. Wakabayashi et al. On the basis of the plastic hinge concept, the plastic hinge follow Pragers handening rule to be modified by Ziegler, it is discussed in term of generalized force-displacement expression.

Automated design of rigid steel frames including member selection

This paper outlines a new algorithm for the automated design of rigid plane steel frames having multiple loadings, displacement constraints, stress constraints and fixed geometry. The most significant contributions are, first, a method developed for incorporating into an optimization program the requirements of the specification CSA S16-1969 so that the program automatically uses realistic allowable stresses and, second, a procedure introduced for selecting actual sections that correspond to the theoretical solution. Elastic analysis is used and the optimum design is selected on the basis of minimum cost using the preliminary design factors recommended by the Canadian Institute of Steel Construction. Several examples, including a 10-storey, 1-bay frame, are included to demonstrate the capabilities of the algorithm.

Large Displacement Matrix Analysis of Elastic/Viscoplastic, Plane Frame Structures

Within the framework of lumped mass/elementary beam theory, a large displacement matrix analysis of elastic/perfectly viscoplastic plane frame structures undergoing primarily flexural deformations and following a constitutive power law is first formulated. A general purpose computer program based on the step-by-step computational procedure in conjunction with the fourth order Runge-Kutta integration technique is then developed. The computerized study is then used in an analytical/experimental correlation study of the dynamic response of a laboratory impact test problem of a mild steel plane frame dropped into a narrow rigid pole obstacle at 20 mph (32.2 km/hr); good analytical and experimental correlation results are obtained up to 2 percent of strain. An example problem of inelastic response of an automobile bumper (beam) subjected to impact loading is also given. Discussion of the results with regard to strain rate sensitivity effects on dynamic plastic behavior and comparison of the “exact” solution with those obtained under certain simplified approximations are made.

Optimal Design of Plane Frames

This paper presents an application of state space optimization techniques to the optimal design of plane steel frames. AISC Code requirements are imposed, along with displacement, natural frequency, and member size constraints. A general structural design problem is defined and is then specialized to the case of plane frames. Results for three example problems are obtained with a computer program developed for the purpose. Results are compared with solutions available in the literature. New results are presented for cases in which multiple failure modes are imposed on the structure.