Rigid-jointed Frames Research Articles

Evaluation on story-based stability in multistory frame under various restraining conditions

To estimate the critical buckling load, the effective length approach isolates a critical column inside a frame and analyses the rotational and translational stiffness of its end restraints. Although designers proportion leaning columns with K = 1, which is the correct K-value based on the column failure mode, buckling analysis fails to predict these values due to the influence of nearby columns and beams. In current design practise, beam-to-column and column-base connections in steel frames are typically idealised as wholly pinned or totally stiff connections. Various studies have demonstrated, however, that the semi-rigid behaviour of the systems beam-column connections affects the internal efforts in the structural parts, therefore the buckling critical loads and corresponding effective lengths of the compressed elements were also taken into account. In this study, a numerical analysis of the Effective length of column in multi-storey frames with single bay and dual storey (G + 2) is tried with variation in storey heights using rigid and semi-rigid jointed frames with rigid and semi-rigid jointed frames is undertaken. Webber's empirical equations are efficient in rigid frame systems for calculating the effects of adjoining columns and their critical buckling loading of the isolated column. The effective length K factor with the variance in critical length with different storey heights acquired a greater value when compared to other models. Moment rotations in semi-rigid jointed frames were influenced by differences in fixity factors in semi-rigid frames. The rigidity coefficient dropped as the stiffness coefficient increased, leading in an increase in the effective length factor.

Reverse Cyclic Loading Effect on RCC Wall‐Floor Slab‐Deep Beam Connection

High‐rise structures are more vulnerable when subjected to lateral loading. Generally, the shear walls function as the main lateral load resistant system in high‐rise structures. In the case of high‐rise structures with an open ground story, the shear wall‐floor slab‐deep beam acts together as a rigid jointed frame connection to withstand gravity and lateral force induced by external loadings like earthquakes and wind. The wall‐floor slab‐deep beam connection will be subjected to a higher concentration of stresses, which is a more vulnerable area in any high‐rise structure. Hence, it is necessary to design this connection with more ductility. This article presents the experimental investigations carried out to study the behavior of three different reinforcement detailing in RCC wall‐floor slab‐deep beam connections, such as (1) 90° bend up bars connection as per Indian Standard Code (Conventional connection), (2) U‐hooks connecting the core region as per Euro code 2, and (3) proposed U‐hooks with additional reinforcement in the core region transverse to the beam orientation. The additional reinforcement is provided at a distance of 50 mm from the face of the shear wall. The parameters considered for this study are load‐carrying capacity, energy dissipation, ductility, and stiffness. The results were then compared with that of the conventional connection. It was found that the proposed U‐hook with additional reinforcement performed better than that of the conventional connection and type 2 connection.

Simplified Procedure to Calculate by Hand the Natural Periods of Semirigid Steel Frames

AbstractCurrent seismic design codes provide empirical equations for the calculation of the fundamental period of a framed structure primarily as a function of height, and do not consider the effect of beam-column joint stiffness. In the literature, far too little attention has been paid to incorporate this effect in approximate formulas to calculate by hand the natural periods of semirigid steel frames, which is the aim of this paper. The proposed formulas have been developed after modifications of existing formulas in the literature for rigid-jointed plane steel frames. Then, the accuracy of these approximate formulas was verified by a finite element analysis using ABAQUS software. Finally, a parametric study was conducted to highlight the effect of semirigid connections on the natural periods of vibration of plane steel frames.

Effect of Slab Shear Reinforcement on the Performance of the Shear Wall–Floor Slab Connection

AbstractThe floor slabs and shear walls together act as a rigid jointed frame in resisting gravity loads and lateral forces caused by wind and earthquake. The junction between the wall and slab is a key force-resisting element that is subjected to severe stress concentration. The performance of the connection can influence the pattern and distribution of lateral forces among the vertical elements of the structure. In the current study, two different reinforcement detailing adopted, such as (1) conventional joint with the provision of U hooks connecting shear wall and slab and (2) slab bars bent 90° at the core region along with the provision of shear reinforcement in the slab. Analytical investigations were carried out to study the performance of the shear wall–slab connection with these detailings. The RC model consists of a material model to predict the failure of brittle materials, applied to a three-dimensional solid element in which reinforcing bars may be included. Good energy dissipation capacities...

Serviceability design of a cold-formed steel portal frame having semi-rigid joints

Details are given of a cold-formed steel portal framing system that uses simple bolted momentconnections for both the eaves and apex joints. However, such joints function as semi-rigid and, as a result, the design of the proposed system will be dominated by serviceability requirements. While serviceability is a mandatory design requirement, actual deflection limits for portal frames are not prescribed in many of the national standards. In this paper, a review of the design constraints that have an effect on deflection limits is discussed, and rational values appropriate for use with cold-formed steel portal frames are recommended. Adopting these deflection limits, it is shown through a design example how a cold-formed steel portal frame having semi-rigid eaves and apex joints can be a feasible alternative to rigid-jointed frames in appropriate circumstances.

Errata for “Explicit Kinematic Solution for Tall Rigid-Jointed Frames” by Carl A. Nelson

Errata for “Explicit Kinematic Solution for Tall Rigid-Jointed Frames” by Carl A. Nelson

立体ラーメンの微小変位応力解析 : その1 基礎式,変位法

The purpose of this study is to propose a systematic solution of the displacement method and stress method about the small displacement analysis of spatial rigid-jointed frames. Matrix method of structural analysis has already been described by many researchers, but most is based on potential energy theory. In this paper, we formulate compatibility equation and equilibrium equation and constitutive equation which made use of the characteristic of spatial rigid-jointed frame composed by line members. And, as combination of these fundamental equations, we propose a displacement method which makes displacement an unknown quantity.

Explicit Kinematic Solution for Tall Rigid-Jointed Frames

A new set of equations for linear elastic analysis of tall rigid-jointed frames loaded at the joints is derived. These are simultaneous difference equations involving four local kinematic quantities, with story level as the single independent variable. They may be solved explicitly for certain classes of frames of practical interest. The solution is nontrivial and employs techniques that are of general interest in the kinematic and static analysis of periodic elastic structures. Application to an eight-bay, 40-story frame under lateral loading yields topmost story drift within 6% of the exact finite-element solution. The solution represents a vertex of the subspace of kinematically admissible states. Thus, it may be used in the hypercircle formulas of Prager and Synge to obtain bounds on displacement and stress, or as a stand-alone analysis and design tool for tall planar frames. The current solution may be implemented easily in commercial spreadsheet software, offering a significant advantage to the stru...

Evolutionary structural optimisation (ESO) for combined topology and size optimisation of discrete structures

The single most researched and analysed topic in the field of structural optimisation in the last 40 years has been that of size optimisation for pin- and rigid-jointed frames. Much of the effort has been in developing the search engines that will find a global weight/volume minimum in the presence of multiple constraints, not all of which may be active at the minimum. Most of the algorithmic developments have followed formal mathematical programming techniques. Recently more heuristic methods have emerged for structural optimisation such as genetic algorithms, simulated biological growth and evolutionary algorithms. The authors have been researching the latter mentioned evolutionary structural optimisation (ESO) method for the last six years and have found it to be most efficacious for the full range of structural situations; topology, shape and size optimisation with stress, stiffness, frequency, stability constraints in 2D and 3D with single or multiple loads and support conditions. In the present work is a summary of some of our ESO research for pin and rigid-jointed 2D and 3D frames with or without multiple loads. The paper presents the simple evolutionary algorithm and gives examples covering the range of applications. Attention is also given to benchmarking the algorithms and to their reliability and robustness.

Theory of Combined Sway and Nonsway Frames Buckling

Conventional design procedures for rigid jointed frames encourage a situation in which more than one buckling mode could occur simultaneously. Even though this practice is known to often give rise to increased sensitivity of buckling loads to small initial imperfections, current design practice is usually lacking in explicit design guidance. This paper seeks to explore the extent to which buckling loads in framed structures are reduced by the effects of modal interactions arising when designs are optimized. It takes, as a specific example, the situation where the buckling and bending planes for a rigid-jointed frame coincide and for which sway and nonsway buckling modes occur at similar load levels. It explores the extent to which elastic-plastic buckling loads may be affected by interactions of sway and nonsway modes and compares predictions with results from a recently conducted test program. It is suggested that the theoretical approach described has the potential to provide an extended and improved alternative to existing design practice.

Limiting Sway For Unbraced Steel With Column Bending On Minor Axis

The proposed method is presented for the design of multi-storey steel frames to limiting values of horizontal sway deflection. The frame is divided into statically determinate sub-frames by assuming points of contraflexture. Allowance for steelwork costs is then used, together with slope deflection analysis, to derive equations for optimum design. This method is suitable for hand calculation. A series of rigid jointed unbraced steel frames was studied with column bending on minor axis. The accuracy of the design equation was found to be good by comparison with linear elastic computer analysis. Ultimate limit state and serviceability limit state were checked for the frames.

The analysis of a three-dimensional rigid-jointed rectangular plexus frame

The investigation of a three-dimensional rigid-jointed rectangular plexus frame under a general static loading is presented. Since the matrices involved in the exact elasticity solution are of maximum dimensions equal to the square of the number of the nodes of the frame, the proposed methodology is more convenient in comparison to existing methods because it requires less memory space and computer coding.

Finite Element Stability Analysis of a Glulam Dome

The paper centres on stability investigations of a glued-laminated timber (glulam) dome under several snow load conditions. The dome consists of a triangulated network of curved glulam beams, a decking supported by curved purlins, and a steel tension ring. The dome is represented by two different models. The first model is a rigid-jointed space frame composed of curved beam elements. The second model consists of straight beam elements, with rigid or flexible joints, and a bracing to simulate the lateral support of the beams provided by the decking. Two finite element methods are presented and used in the analyses: A nonlinear method that computes the buckling load and a combined nonlinear/linear eigenvalue method that provides estimates of the buckling load. The results presented include buckling pressures, buckling modes, effects of joint stiffness and bracing on the stability of the dome, and the status of the material prior to buckling.

The effect of isochoric changes of portal frames on their natural frequencies

Abstract The effect of geometrical changes of symmetric rigid-jointed portal frames on their natural frequencies is analysed. Discussed are the following issues: (a) the sensitivity of the frequencies to selected shape variables; (b) the variation of the three lowest frequencies ω1, ω2 and ω3 as functions of the shape variables in a prescribed domain; and (c) the occurrence of the repeated lowest frequency ω1.

The In-Plane Stability of a Frame Containing Pin-Based Stepped Columns

This paper presents five graphs and a simple formula from which the in-plane buckling load of a pin based stepped column, forming part of a rigid-jointed frame, can be calculated. These analytical aids were derived from a parametric study of the problem using a proven finite-element stability analysis program. They account for the rotational and translational restraints within the frame system, and enable the designer to readily determine the most critical disposition of the crane loads. The method is illustrated by an example.

Virtual Large Displacement Theorem for Framed Structures

This paper formulates a new theorem of virtual work for finite deformation with the following qualities: (1) Any actual large displacement in a body may be adopted as the virtual displacement; and (2) the internal virtual work is composed in terms of the physical components of stresses and their conjugate finite virtual strains in the Lagrangian description plus the additional terms. These terms become the rigid-body rotations for axial strains and the corrections due to elongations for shear strains. Fundamental matrix equations are derived for the finite deformation analyses of pin-jointed trusses and rigid-jointed frames on the basis of the present theorem. These formulations are simpler than previous approaches and lead to the exact solutions of nonlinear analyses, particularly for plane and space pin-jointed trusses. Further, when using these equations, the larger increments of load and displacement can be accommodated in the numerical computations. This theorem unifies the principle of virtual work and the principle of complementary virtual work for finite deformation.

Seismic design in reinforced concrete

Highlights of the evolution over the past two decades of a seismic design strategy, used in New Zealand for reinforced concrete buildings, are reviewed. After a brief outline of some philosophical concepts of the capacity design methodology, the main features of its application with respect to ductile rigid jointed frames, structural walls and hybrid structural systems are sketched. Another aim of this strategy, complementary to ductility requirements, is to strive for high quality in detailing. Numerous examples are presented to illustrate how this can be achieved. A specific intent of this state of the art review is to report on features of design and detailing which are considered to have originated primarily in New Zealand.

Efficiency and accuracy of linearized postbuckling analyses of frames based on elastica

The efficiency, accuracy and ease in use of linearized stability analyses for establishing the postbuckling response of rigid jointed frames is discussed using as a model a simple rectangular frame. This is accomplished by comparing a variety of results of the linearized stability analyses with those of the exact elastica analysis the governing equations of which appear for the first time in the technical literature; important conclusions on the accuracy and range of applicability of the foregoing linearized stability analyses are drawn. It is found that the completely linearized stability analysis, corresponding to a linear boundary-value problem, furnishes very reliable results which are quite near to those of the widely used non-linear kinematic stability analysis and much more accurate than those of the standard (incompressible) elastica; thus the former analysis, being the simplest possible postbuckling analysis, constitutes, for structural design purposes the most powerful method for determining the initial postbuckling response of frames.

Interaction of multi-storey and multi-column rigid-jointed frames supported on an elastic foundation under static loading

In this investigation an exact matrix solution for the static analysis of a multi-storey and multi-column rectangular plexus frame on an elastic foundation is presented in the most general case of response and loading. Furthermore, based on the formulation and proof of a convenient corollary and proposition, associated with the existing closed-form solution of the matrix equation of the type AX + XB = C, the problem of interaction between an elastic soil and the frame is completely solved. The entire procedure is illustrated by a comprehensive example concerning a four-storey and four-column plexus frame supported on an elastic foundation. Several numerical results are also given. As the obtained closed-form formulae, giving the structure redundants, include matrices of dimensions equal to the number ( m × n) of the nodes of the frame, the proposed solution methodology is more convenient in comparison with those in the existing literature, because it requires less memory space and coding.

Internal Force Distribution Effect on Framework Stability

The exact stability matrix approach is used to study the internal force distribution effect on the elastic critical load and subsequently on the failure load of planar frameworks. In particular, three options are considered. The first option utilizes an assumed axial load distribution in the structure, while in the second option an iterative procedure is employed to find the exact distribution of the axial load. The third option accounts for second order effects. A parametric study is conducted to determine the elastic critical load of various rigid-jointed frames by these three options. Also, the aforementioned options are compared on the basis of accuracy and efficiency.