Multi-span Frame Research Articles

BUCKLING STRENGTH OF COLUMNS IN LOW-RISE MULTI-SPAN FRAMES EVALUATED BY THE STABILITY INDEX

The objective of this study was to investigate the validity of the effective length factors for low-rise multi-span frames obtained by the stability index (SI) method, and SI is defined by the ratio of PΔ moment to story moment. The SI method calculates the buckling load based on the condition that the story with the maximum stability index is the first to lose its stiffness compared with the other stories at the time of buckling. The analytical parameters used in the present study were the stiffness ratios of beams and columns. The effective length factors obtained by the SI method were compared with the exact effective length factors provided by the buckling slope-deflection method. The story displacement Δ of the PΔ moments was calculated by the application of horizontal forces at the top of the column of each story. This paper outlines a valid process to evaluate the effective length factors using the SI method and demonstrates the impact of the horizontal force distribution and Pδ moments on the accuracy of the SI method in low-rise, multi-span frames.

Analytical Study on Lateral Strength of Multi-Span RC Frame with Masonry Infill

Abstract A simple and accurate analytical model for defining the lateral strength of the multi-span RC frame with masonry infill has been developed in this study. This model is developed due to the limitation of the current analytical model which only can be applied to the single-span RC frame. Meanwhile, the structure in the building also is in a multi-span frame and masonry infill greatly impacts the portal structure. In the existing building, this analytical method is needed to calculate the lateral strength of the RC frame. Besides, the analytical method was developed based on the lateral strength analysis method of a single-span RC frame in which the modeling of a multi-span RC frame with masonry infill along with uniform span spacing was applied. Furthermore, an equivalent diagonal strut with the same thickness and material as the masonry panels was used instead of masonry infill in the frame structure. The external column has diagonal compressive forces on the top or bottom of the column. On the other hand, diagonal compressive forces work at the top and the bottom of the column in the internal column. The lateral strength of the infill was determined based on the frame infill contact length. Furthermore, in order to obtain the lateral strength of the structure, the experimental study of a multi-span RC frame with masonry infill under cyclic load was also tested. Applying the analytical model has shown promising results even after being compared with the results of the experimental work.

Seismic Performance of Precast Multi-span Frame System Integrated by Unbonded Tendons

Seismic Performance of Precast Multi-span Frame System Integrated by Unbonded Tendons

TITLE: CALCULATION OF MULTISPAN FRAME STABILITY WITH REGARD TO GEOMETRIC NONLINEARITY

The paper considers the methodology of determining the critical value of the load acting on a flat multi-span frame, taking into account geometric nonlinearity. The elements of the frame have arbitrary stiffnesses constant along the length. The problem is solved in two stages. At the first stage, the strain calculation of the frame is performed, the main goal of which is to obtain the values of longitudinal forces in the struts. At the second stage, loss of stability of the first kind is considered in relation to the longitudinal bending of the props under the action of vertical forces. In both calculations, practically the same system of nonlinear equations of displacement method is solved. The compact notation of generalized stiffness matrix coefficients obtained earlier by the authors facilitates the development of the algorithm and computer programs designed for solving the problems set in the paper. The algorithm is implemented in Excel spreadsheets. To verify the obtained results, test calculations for both stages of the calculation have been performed. Using the proposed methodology, the stability of a flat free one-story frame with a periodic structure has been calculated. In the ANSYS software package, the calculations of this frame according to the deformed scheme were performed, with the subsequent determination of the value of critical longitudinal force in the struts. Comparison of the results of calculations by the offered technique and in the ANSYS program complex shows their practically complete coincidence: the difference in the values of longitudinal forces in the frame struts with allowance for geometric nonlinearity is less than 0.01 %; the calculation results of the first two critical forces differ by 0.06 %. The proposed methodology allows us to use a unified approach to the formation of systems of solving nonlinear equations, both in the strain calculation and in the calculation of stability. In addition, this approach releases from the use of expensive computer programs, the use of which requires special training.

Possibilities of Using Frame Structures of Industrial Buildings for Placing Wind Energy Generating Devices

The article deals with the highly relevant problem of finding additional sources of energy supply for industrial enterprises using alternative energy-saving energy sources. The author considers the possibility for using the energy potential of surface wind flows with the formation of a wind profile to fit conditions of applications in industrial buildings, as the central idea. The proposed concept is substantiated by the possibility of effective use of outdoor wind generators in construction of the supporting frame of industrial building. The method of integrating wind-driven generators into the structure of a multi-span industrial building is illustrated by the author in the case study of a completed pilot project. The author proposes a solution for a multi-span frame with the formation of a wind-driven transverse profile of the building. A new architectural & constructive solution fundamentally provides a possibility for rational placement of a supporting frame of additional wind-driven power plant with the use of wind turbines in a single integral configuration. Efficient types of turbogenerators were used in the form of built-in multi-row sections configured in the upper zone of the production building, with comprehensive maintenance of the said sections provided. The research results are recommended for wide implementation of such wind generator plants in design and upgrade of industrial buildings for multiple purposes with energy-efficient use of the structural features of their supporting frame. The author has substantiated the prospects for further comprehensive research.

Calculation of a multi-span frame for stability

The loss of stability of the first kind as applied to the longitudinal bending of the supports of a flat one-story free multispan frame under the action of vertical forces is considered. The elements of the frame have arbitrary stiffnesses constant along the length of the elements. The system of nonlinear equations of displacement method is solved. The matrix of coefficients of the system of equations is presented in block form. Formulas of generalized coefficients for each block of matrix are determined, and then one or another element of general stability equation matrix. A slight correction of generalized coefficients formulas makes it possible to extend the methodology to calculate the stability of non-free frames (overpasses). Compact notation of generalized coefficients of stability equation matrix makes it possible to considerably simplify development of algorithms and computer programs designed for solution of such tasks. The algorithm is implemented in Excel. To verify the obtained results, test calculations of stability frames for which the exact solution is known have been performed. Stability calculation of plane frame of periodic structure has been done by the suggested method. The diagram of the boundary curve has been made and the areas of frame stability and instability under the action of the given system of forces have been determined. Stability calculations of the model in the software package ANSYS, with subsequent comparison of the calculation results, have been performed.

Optimal Design of Pitched Roof Rigid Frames with Non-Prismatic Members Using Quantum Evolutionary Algorithm

The weight and shape of the gable and multi-span frames (mono and two-span pitched roof) with tapered members, as a familiar group of the pitched roof frames, are highly dependent on the properties of the member cross-section. In this work a quantum inspired evolutionary algorithms, so-called Quantum evolutionary algorithm (QEA) [1], are utilized for optimal design of one gable frame and a multi-span frame in five alternatives with tapered members. In order to optimize the frames, the design is performed using the AISC specifications for stress, displacement and stability constraints. The design constraints and weight of the gable and multi-span frames are computed from the cross-section of members. These optimum weights are obtained using aforementioned optimization algorithm considering the cross-section of members and design constraints as optimization variables and constraints, respectively. A comparative study of the QEA and some recently developed methods from literature is also performed to illustrate the performance of the utilized optimization algorithm and its featuring. Furthermore, optimal design of a multi-span frame is compared with the solution of other methods including the same conditions and constraints. This study indicates the power of QEA in exploring and exploitation due the search space with using Q-gate and binary code for individual representation and updating. Binary code helps the QEA to find optimal solution even with minimum number of Q-bit individuals. High speed of this method is because of such a feature.

Column Analogy in Multi-Span Hinged Frames

A procedure is presented in which the method of column analogy, normally applicable to the analysis of single-span and closed frames, is extended for the analysis of multi-span frames with columns hinged to the ground. The extension involves consideration of conditions of rotations at the hinges. For illustration, a two-span hinged frame issolved in details. Results are in excellent agreement with values obtained using classical structural methods.

Analysis of nonlinear soil-structure interaction effects: 3D frame structure and 1-Directional propagation of a 3-Component seismic wave

In this paper, a finite element modeling technique, taking into account the effects of soil-structure interaction (SSI) is proposed for structural analysis and design. The one-dimensional model of a nonlinear multilayered soil profile is assembled with a multi-story multi-span frame model and the dynamic equilibrium problem is solved directly. The one-directional propagation of three-component seismic waves (1D-3C) is modeled taking into account the SSI, in the case of rigid shallow foundation and negligible rocking effects.The 1D-3C wave propagation model provides the three components of motion at the base of the frame structure, allowing the reduction of mesh size and computation time, compared with a fully three-dimensional model, and avoiding modeling difficulties to realize a reliable three-dimensional soil domain, related among others to boundary conditions.The proposed model allows the analysis of those structural dynamic features, seismic wave and local soil stratigraphy, that produce changes in the ground motion at the surface. The model reproduces well expected phenomena, in the case of layered soil with increasing nonlinearity and for different inertia distribution in the frame structure. SSI combined with seismic site effects is analyzed in a Japanese soil profile, using as seismic loading a 3C record of 2011 Tohoku earthquake.

Realistic behavior of infilled steel frames in seismic events: experimental and analytical study

An experimental and analytical study is carried out to investigate the effects of lateral loading type on the behavior of masonry infilled steel frames. During earthquake the lateral load is applied as distributed loading to the top beams and columns through rigid floors; however, in most available experimental studies the lateral loading is applied as concentrated loading. In this study, two identical specimens are tested and their behavior is compared under distributed and concentrated lateral loadings. Finite element models of the specimens are also developed and validated against the experimental results. To have a better view, the influence of loading type is studied on another experimental specimen having concentrated loading. A parametric study is also conducted on the influence of loading type in multi-span frames and infills with different aspect ratios. The obtained experimental results show that the distributed loading results in 18.5 and 29% increase in the strength and stiffness of Infilled frames, compared to the case with concentrated loading. Less strength and stiffness in specimens subjected to concentrated loading is a result of stress concentration at the infill corner near the loading point which leads to premature corner crushing. Therefore, it is believed that the codes’ formulas, mostly based on specimens with concentrated loading, are conservative, underestimating the real ultimate strength and stiffness of masonry infilled steel frames.

大断面横架材を有する2スパン伝統木造軸組の耐震要素配置と力学特性

In seismic evaluation methods based on limit strength calculation, a shear force with a one-to-one correspondence with a load-bearing element is defined, and the shear force of construction only adds the restoring forces of the element. However, the specifications of traditional joints and element position may vary, and the calculation method does not depend on these specifications. Some previous studies have considered the specifications of traditional joints such as column-to-beam (Sashigamoi) joints based on element experiments and simulation analysis. However, the influence of element position on the structural properties and the behavior of traditional wooden frames with large section beams (Sashigamoi) based on multi-span frame experiments has been addressed in few studies. Japan has experienced numerous earthquakes, and there are many reports of traditional wooden structures collapsing because of earthquakes. However, many traditional wooden structures remain sound and unaffected and are extremely interesting. Evaluation of the seismic performance of such traditional wooden buildings may be significant in preventing damage to buildings and ensuring safety. Against this background, this paper presents the results of static cyclic loading tests and simulation analysis for four traditional wooden frames in order to understand the seismic performance of frames with uneven large section beams (Sashigamoi) and to clarify the influence of the beams and shapes of fitting-type joints on the behavior of the whole frame. Major findings of the present work are as follows: (1) First, static cyclic loading tests were conducted on four traditional wooden frames; the number of frame spans, the presence or absence of large section beams (Sashigamoi), and the position of beams were considered as the parameters. Two-span frames underwent column splitting or column breaking more readily and with smaller deformation than in the case of one-span frames. In addition, the shear forces exhibited directional dependence, which is attributed to the asymmetry of the frames or the shapes of the column-beam joints. (2) Second, a method for modeling traditional fitting-type joints was developed. This method can be used to analyze traditional wooden frames with large section beams (Sashigamoi). Simulation analysis results were in good agreement with the test results. (3) Finally, a parameter study about the aspect ratio of the frame, large section beam position, and beam height distance was carried out, and the restoring force was verified. The smaller the beam height distance, the smaller was the difference in the restoring force with the loading direction.

Simultaneous identification of excitation time histories and parametrized structural damages

This paper presents and experimentally verifies an effective method for simultaneous identification of excitations and damages, which are two crucial factors in structural health monitoring and which often coexist in practice. The unknowns are identified by minimizing a time-domain square distance between the measured and the computed responses. Even though both damage and excitation are unknown, only damage parameters are treated here as the optimization variables: given the damage, the excitation is uniquely determined from the measured responses. As a result, all unknowns are of the same type, which allows standard optimization algorithms to be used and obviates the need for two-step procedures. The sensitivity analysis is facilitated by interpolating in each iteration the relation between structural responses and damage parameters. The numerical costs are further decreased by the fast reanalysis approach of the virtual distortion method (VDM), which is used to compute exact impulse responses of the damaged structure. The proposed methodology is verified both numerically (using a multi-span frame) and experimentally (using a cantilever beam). Stiffness-related damages and mass-related modifications are identified successfully together with the three tested types of external excitation.

Dynamic stability of multi-span frames subjected to periodic loading

In this study, in-plane dynamic stability analysis of multi-span frames, which are composed of columns and beams and subjected to periodic loading, is investigated by using the Finite Element Method. Periodic loading is considered to be applied to each column member as an axial load and no loading is applied on the beams. The effects of beam to column length ratio, beam to column cross-section ratio and beam to column moment of area ratio are investigated for in-plane frames. In addition, the effect of the number of span and static and dynamic load parameters on the free vibration, buckling and dynamic stability analysis is also investigated. The results are compared with the recent literature in terms of the fundamental natural frequency and critical buckling load.

Numerical Simulation on Framed Anti-Sliding Piles

As a new bracing structure, the framed anti-sliding piless based on spatial framework structure, which have the advantages of less displacement in the top of the piles and large anti-force, are developed as a new retaining structure, and can be used to reduce the piles deformation. However, the previous calculation models of double-row piles ignored the deformation coordination action between linking beams and ring beams, the interaction between piles and beams. Further more the calculation results based on the models are not accurate enough. In this paper, a spatial force model of the framed anti-sliding piles is presented. Taking framed anti-sliding piles as a single-layer multi-span frame affected by piles, beams and soils, the spatial synergic interaction between top ring beam and linking beam, as well as the affection of soil-arch on the frame are analyzed. The horizontal displacement in front of the framed anti-sliding piles and distribution of axial force and moment of piles are studied by Finite element method. The results reflect commendably the stress and distortion character of the framed anti-sliding piles. Finally, some rules about the pile-beam-soil interaction in the pile structure are summarized.

Considerations about Load Inclination Effect on Seismic Bearing Capacity Factors of Strip Foundations

Assessment of seismic bearing capacity of strip foundations has been the concern of only few researchers in the field of geotechnical earthquake engineering during the last decades. The previous works have mostly assumed that in the presence of a horizontal earthquake acceleration (kh.g) besides the body force due to gravity, the ratio of the shear stresses to the normal stresses along the ground surface is equal to kh and the load inclination beneath the footing with respect to vertical equals to tan-1(kh). But this assumption does not seem to be always correct. For example in the case of multi span frames where only some spans may be braced and the support conditions at the end of the columns may not be uniform, the load inclination beneath some footings may not be equal to tan-1(kh). This paper presents the seismic bearing capacity factors Nγ, Nq and Nc of a rigid strip foundation resting on a horizontal ground surface, when the load inclination beneath the footing is not equal to tan-1(kh). All calculations are executed by the well known stress characteristic method, commonly referred to as the slip-line method. It is assumed that the soil behaves rigid perfectly plastic and obeys the well known Mohr-Coulomb failure criteria under plane strain conditions. It is assumed that the state of the stress everywhere in the neighborhood of the foundation is at failure. It is also assumed that everywhere along the surface of the foundation, the ratio of the shear to the normal stress is equal to the horizontal earthquake acceleration coefficient (kh). The Nγ parameter was calculated based on the both-sides failure mechanism, whereas the Nq and Nc parameters were calculates based on the single-side failure mechanism. The Nc parameter for cohesive media was calculated using the rule of equivalent states. Some graphs and tables are presented that could be used in order to assess the seismic bearing capacity factors of rigid strip foundations obtained by the stress characteristic method for various load inclinations. It is shown that the seismic bearing capacity factors, just like the static bearing capacity factors, increase considerably with reduction in the load inclination and vice versa. Further, this important outcome of some previous research works has been confirmed once again that the earthquake's effect on each of the body force as well as the overburden is as important as the earthquake's effect on the load inclination which should not be neglected. It is also shown that because of the non-symmetric nature of the seismic loading, the disposal of the characteristic lines as well as the pressure distribution below the foundation is non-symmetric. In other words, the foundation would be subjected to a moment in addition to the vertical and horizontal reactions, as a result of the non-symmetric soil pressure distribution during earthquakes.

Vector Form Intrinsic Finite-Element Analysis of Steel Frames with Semirigid Joints

This study uses the vector form intrinsic finite-element (VFIFE) method to investigate the inelastic large deflection behavior of steel frames with semirigid joints. The structural connections are modeled by the two-node, multidegree-of-freedom spring system and dummy element with stiffness but without actual mass and length. The proposed model is first verified by comparing its numerical solutions with the published results. The various structural behaviors, such as the bifurcation instability, the snap-through buckling, and the inelastic structural response with beam element fracture, are then fully studied. The numerical results show that the semirigid joint reduces the global stiffness of structure. Therefore, as expected, the simplified rigid joint will over estimate the loading capacity of the structure. The fracture analysis of the multi span frame shows that when the beam fractures, the structure elements would absorb more energy and thus, the reduction ratio of loading capacity after beam fractur...

PRIMARY STUDIES ON POST-LATERAL BUCKLING BEHAVIOR OF STEEL RIGID FRAME SUBJECTED TO HORIZONTAL FORCE

In this numerical study, the behavior of one-story steel rigid frame subjected to horizontal force is presented, involving the post-lateral buckling of beams in the frame. It is well known that the strength of a beam remarkably deteriorates after the lateral buckling occurred. However, the numerical analysis results show that the strength of frame does not deteriorate very much, even if the lateral buckling occurs to beams constituting multi-span frame. The behavior of frame is considerably stable after the lateral buckling of beams.

Column effective lengths considering inter-story and inter-column interactions in sway-permitted frames

The physical meaning of the traditional effective length coefficients (ELCs) in a sway permitted frame is first explained. It is found through an example that the critical loads of columns in a story have the same percentage increase or decrease after considering the inter-story interaction. It is also pointed out that the ELCs obtained by an overall buckling analysis are applicable only in the weakest story, for the other stories their ELCs simply implied the proportional loading assumption. With three assumptions of the conventional effective length approach discarded, this paper presents a mergence approach for buckling analysis of frames in which the column linear rigidities and axial loads are summed up, and the rotational restraints provided to columns by beams are summed at the merged beam-to-column joints. Effective lengths considering both inter-story and inter-column interactions are determined in unbraced two-story and three-story frames by simple algebraic operations. For frames with more than three stories, a three-story sub-assemblage, which includes beams at far ends of the columns above and below the story under consideration, is used to find the effective lengths of columns in the middle story. For frames with different bases, a equivalence procedure transforms the frames into those with the same type of bases before the mergence. For multi-span frames, the mergence approach overestimate the story lateral stiffness, a modification is proposed to eliminate this overestimation. Although overall buckling analysis of frames is easily carried out today, the findings and the proposed method of this paper will help to understand the inter-column and the inter-story interactions in frames.

設計用水平力を受ける建築骨組の構造重量と保有水平耐力を指標とした満足度指定設計法

Specified grade design of multistory multispan frames under a set of horizontal loads is formulated Thls problem is an α-Levelfuzzy optlmum design problem in which both the fuzzy constraint relating to plastic collapse load factor and the fuzzy objective function relating to the weight of the structure are adopted. The above fuzzy design problem is verified to be a problem for mathematical programming, analogical to the crisp minimum weight design problem And an analogical method is proposed for derivation of exact closed form solutions to the fuzzy design variables of that problem The closed form solutions are very useful for determining members of a structure at the design process, as designers have only to select the members whose dimensions are within the range of fuzzy design variables

Moment Redistribution Caused by Beam Fracture in Steel Moment Frames

This paper presents an analytical study on static moment redistribution and resultant reduction of lateral resistance caused by sudden beam fractures in steel moment frames. A numerical example is presented for a simple multispan frame, and the step-by-step processes of beam fractures, moment redistribution, and loss in resistance under statically increasing lateral deflection are examined. The mechanism of moment redistribution is interpreted using the three-moment equations, and the possibility of sequential fractures in the course of static moment redistribution is investigated. A sudden fracture of a beam changes moment distribution rather locally, particularly when plastic hinges are already formed in beams by the time of the fracture. Sequential fractures are less likely to occur during static moment redistribution when rotations corresponding to fracture are large (to simulate fractures after significant plastification) and vary from plastic hinge to plastic hinge (to allow for the random nature of fractures). It should be carefully noted that the above observations are applicable for static moment redistribution, and do not necessarily represent the effects of beam fractures on dynamic responses.