Unbraced Frames Research Articles

Numerical investigation of the design of single‐span steel portal frames using the effective length and direct analysis methods

AbstractThe era of globalization enables the design, fabrication and erection of steel structures to take place in different locations far away from each other. Therefore, a widely acceptable steel design standard is required, and designers should be familiar with alternative specifications that may be considerably different from one another. This study deals with single‐span unbraced steel portal frames and makes a comparison between the design methodologies adopted by the Australian and American design provisions, in particular, the effective length method (ELM) and direct analysis method (DAM). A brief discussion on the main features of both standards is also presented. Furthermore, the results of the parametric study are portrayed, highlighting the differences between these two design standards regarding stress interaction. Finally, of the two aforementioned methods, the most applicable optimization method for the design and development of cost‐effective industrial portal frame buildings is proposed with respect to the structure geometry.

Resilient steel frames installed with self-centering dual-steel buckling-restrained brace

As one type of effective earthquake-resisting structural systems, buckling-restrained braced frames are expected to provide good seismic performance through significant plastic yielding to dissipate earthquake energy. This plastic deformation can cause significant structural damage and residual drift, leading to high retrofitting cost or even demolishment of structures after strong earthquakes. As a result, development of new systems that can not only dissipate seismic energy, but also possess self-centering ability, becomes necessary. This paper makes use of a newly proposed type of self-centering dual-steel buckling-restrained braces (SC-DBRBs). The SC-DBRB consists of a low-yield-point steel and a high strength steel, in which the low-yield-point steel mainly provides energy dissipation ability, and the high strength steel offers self-centering ability and additional energy dissipation ability during strong earthquakes. Compared with a conventional BRB (CBRB) commonly with a typical bilinear constitutive model, the SC-DBRB has a trilinear hysteretic behavior, leading to early re-yielding of the low-yield-point steel during subsequent strain reversals. This early re-yielding mechanism can greatly mitigate residual deformation of the SC-DBRB. In this paper, the constitutive model of the SC-DBRB is first established, and its correlation with main design parameters is also discussed. To demonstrate the self-centering ability of the SC-DBRB and its effect on post-earthquake performance of structures, a series of six-story and nine-story steel frames were numerically investigated using ABAQUS: unbraced frames, CBRB-equipped frames and SC-DBRB-equipped frames. Time history analysis results show that the SC-DBRB can effectively reduce residual drift.

Blast Fragility and Sensitivity Analyses of Steel Moment Frames with Plan Irregularities

Fragility functions are determined for braced steel moment frames (SMFs) with plans such as square-, T-, L-, U-, trapezoidal-, and semicircular-shaped, subjected to blast. The frames are designed for gravity and seismic loads, but not necessarily for the blast loads. The blast load is computed for a wide range of scenarios involving different parameters, viz. charge weight, standoff distance, and blast location relative to plan of the structure followed by nonlinear dynamic analysis of the frames. The members failing in rotation lead to partial collapse due to plastic mechanism formation. The probabilities of partial collapse of the SMFs, with and without bracing system, due to the blast loading are computed to plot fragility curves. The charge weight and standoff distance are taken as Gaussian random input variables. The extent of propagation of the uncertainties in the input parameters onto the response quantities and fragility of the SMFs is assessed by computing Sobol sensitivity indices. The probabilistic analysis is conducted using Monte Carlo simulations. The frames have least failure probability for blasts occurring in front of their corners or convex face. Further, the unbraced frames are observed to have higher fragility as compared to counterpart braced frames for far-off detonations.

Storey-based stability of unbraced structural steel frames subjected to variable fire loading

Structural steel has poor fire resistance properties and often requires thermal protection. Passive thermal protection systems such as insulation for steel members by application of spray-applied fire-resistance materials (SFRM) on surfaces of structural steel members are expensive and represent a significant portion of building costs for steel structures. Also, design codes around the world are progressing toward performance-based approaches rather than prescriptive-based approaches in design for fire safety. However, it is difficult to account realistically for all probable fire scenarios, and the actual fire resistance of a structure may vary significantly depending on the nature of the fire, location of origin and characteristics of the building. A means to define and identify the maximum and minimum fire loading scenarios causing instability of a given structure is therefore desirable. Presented in this paper is a novel global optimization approach for determining the highest temperature, lowest temperature, most localized, and most distributed fire scenarios causing instability for an unbraced structural steel frame. The investigation assumes that the columns are fire protected but the beams are unprotected, and may be extended to apply in other configurations and framing materials.

On the fire performance of unbraced composite frames

PurposeThe purpose of this study is to gain a deeper understanding of the structural behaviour of fire-exposed unbraced composite frames. Designers to date paid little attention to unbraced one-bay composite frames as structural system. There are two main reasons for this. First, codes lack simplified methods for the fire design of these frames due to their sway and the linked P-Δ effects when subjected to fire, which complicates the design. Second, it is demanding to construct external composite joints for the regarded one-bay frames. Thus, external joints in composite constructions are mostly constructed as steel joints. Nevertheless, these frames offer advantages. These include increased usable space and flexibility in the building’s use, large spans, fast construction times and inherent fire resistance.Design/methodology/approachTo profit from these benefits, two different external semi-rigid composite joint were developed for the considered one-bay composite frames. The first solution based on concrete-filled steel tube columns and the second on concrete-filled double skin tube columns. Furthermore, a numerical model was established to study the fire performance of unbraced composite frames. The model was validated against four fire tests on isolated composite joints and two large-scale fire tests on unbraced composite frames.FindingsOverall, the predictions of the numerical model were in good agreement with the test results. Thus, the numerical model is appropriate for further investigations on the fire performance of unbraced composite frames.Originality/valueThe sequence of construction results in significant stresses in the steel section, which creates difficulties in numerical modelling and may account for the relatively few studies carried out at room temperature. For the fire design, there was, to the best knowledge of the author, to date no numerical model available that was capable of considering the sequence of construction.

WIND-MOMENT DESIGN FOR UNBRACED FRAMES WITH BENDING ABOUT BOTH COLUMN AXES

Analysis and design of steel unbraced frames bending on both axes were performed with emphasis on stability and deflection checks. Wind-moment design is proposed to improve the stability and stiffness. The performance of the frames was checked for collapse load level at Ultimate Limit State (ULS) for 2nd order anaysis and the deflection limits at Serviceability Limit State checked for Ist order analysis. The investigation demonstrated that the frames should be restricted to less than four storeys.

Analysis of frame buckling without sidesway classification

The effective buckling length of a column in a steel frame depends on the sidesway of the frame. The classification sidesway - no sidesway of a frame depends on all members of the frame and is made on an empirical basis. A change of class leads to large changes in the effective column length, and thus affects the buckling load and the economy of the column design. In order to avoid the uncertainties of the empirical classification, it is proposed to determine the buckling load of the complete frame with a nonlinear analysis. The method is illustrated with an unbraced and a braced frame, which are analyzed for hinged as well as fixed columns at ground floor level. The forces in the columns at buckling of the frames are compared to the buckling loads of the single columns. The design of high-rise steel frames against buckling by sidesway - no sidesway categorization has been compared to the buckling analysis of the frames as a whole with nonlinear models. The results confirm the large differences between the buckling loads of braced and unbraced high-rise frames, which are well known from analytical solutions for simple portal frames.

Retrofitting of Steel Moment-Resisting Frames under fire loading against progressive collapse

Generally, fire has been one of the most important threats which can lead to the collapse of structures. Due to the high temperature caused by fire, material strength decrease significantly and finally, could lead to failure of different members of a structure. When some parts of the structure are damaged, frames without sufficient resistance and ductility can progressively collapse. In this study, the retrofitting effect of a Steel Moment-Resisting Frame (MRFs) with X and inverted-V braces are investigated using dynamic explicit analysis for frames which had previously suffer progressive collapse under fire. Simultaneously, different bracing systems and fire conditions have been used. Furthermore, the effect of stiffness and strength of bracing systems were numerically analyzed. Studies show that the unbraced moment-resisting frame (MRF) lacks an effective mechanism for transferring loads from failed parts to the neighboring parts and the frame completely collapse due to the catenary actions under fire loading in central span. Systems braced with hat truss, due to their distance from the heated columns, have limited capacity to prevent the pull-in of columns in the heated floor. However, they can directly re-distribute vertical loads which are shed by buckled columns to the neighboring columns. But, their performance in central span fire scenario seems relatively better than edge span fire scenario. On the other hand, vertical bracing systems have a good effect and with restraining the columns, it can prevent them from pull-in. Also, they are able to effectively prevent the global collapse process. Furthermore, the stronger vertical bracing system can decrease the vertical movement of the heated columns and thus, enhance the re-distribution capacity of the frame. Accordingly, with combination of hat truss bracing system and vertical bracing system, new paths can be generated for redistribution of the forces which are shed by failed columns in the frame. At the end, comparing between X bracing systems and inverted-V bracing systems indicates that the frames with inverted-V bracing systems show more ductility.

05.37: On stability of unbraced steel frames with semi‐rigid joints

ABSTRACTThe paper presents the issue of unbraced and semi‐rigid steel frames stability with special attention paid to the problem of determining buckling length Lcr of columns in these frames.The paper discusses ways of buckling length determination in frames columns with the use of selected, simplified procedure, as well as numerical method of stability analysis. The presented procedures and the analysis methods were used in calculations of certain steel frames. On the basis of presented results, it has been shown that in many practical cases, the simplified procedure of buckling length determination can give error‐prone results.The issues presented in the paper are important from the practical point of view, and therefore, they should be taken into account in the design process of such frames.

13.18: Advanced analysis of braced steel frames: Modelling accounting for the post‐limit behaviour of compressed angle braces

ABSTRACTThis paper presents a method of advanced analysis applied to steel plane load bearing systems like trusses as well as unbraced and braced frames. The effects of both material and geometrical nonlinearities on the structural behaviour are studied together with tracing the whole range of truss member behaviour. In the braced frameworks, the truss bracing model accounts for the effect of post‐limit behaviour on the inelastic redistribution of forces in frame members. Details of finite element incremental stiffness matrices for frame members and truss bracing members are briefly presented and followed by the discussion how the effects of gradual yielding, buckling and semi‐rigid joints are included. The implementation into engineering computer software is summarized and followed by certain aspects of truss and frame structural systems design according to Eurocode 3. A simple two‐bar arch truss sensitive to the elastic snap‐through buckling for which the closed form solution exists is considered as an example. Simulations of the behaviour of this truss show how the nonlinear behaviour of a single member affects the global instability of the truss. Conclusions are formulated with reference to the application of advanced analysis in direct design of steel braced frameworks.

Comparative Response Assessment of Steel Frames With Different Bracing Systems Under Seismic Effect

The field of earthquake engineering and seismology is of a great importance to structural engineers around the world. Choosing an appropriate lateral force resisting system has a significant effect on performance of the steel structure. The paper presents a comparison of the seismic response of steel frames by using different types of bracing systems. The bracing systems are X-braced frames, V braced frames, inverted V braced frames, Knee braced frames and zipper braced frames. The steel frames are modeled and analyzed in four different height levels. Nonlinear static and dynamic analyses were performed. The frames consist of three bays and steel braces were inserted in the middle bay of each frame. The structural responses of frames are studied in terms of capacity curve, drift ratio, global damage index, base shear, storey displacements, roof displacement time history and plastification. The results showed a good improvement in the seismic resistance of frames with the incorporation of bracing. The results revealed that the bracing elements were very effective in diminishing drifts since the reduction of inter-storey drifts with respect to unbraced frames were on the average 58%. Also steel braces considerably reduced the global damage index.

Behaviour of bolted end-plate connections to concrete-filled steel columns

This research aims to investigate the cyclic behaviour of composite joints consisting of concrete-filled steel tubular (CFST) columns, steel beams, and through-bolt connections. A total of 10 specimens, including 5 specimens with square CFST columns and 5 specimens with circular CFST columns, were tested under lateral cyclic loading with horizontal displacements imposed at the top of the column. The main experimental parameters were the cross-sectional type of the column, the axial load level in the column and the cross-sectional configuration of the beam. The experimental results are analysed in this paper to evaluate the performance of the through-bolt connections. Based on numerical analysis, the performance of the bolted joint is further compared with that of the counterpart with external diaphragm. In general, the initial stiffness of the bolted end-plate CFST connections investigated is greater than 8EIb/Lb, so a fixed connection can be assumed in modelling non-sway frames. However, the connection rotation in unbraced frames may need to be considered to minimise the modelling error since the initial connection stiffness is usually smaller than 25EIb/Lb.

Buckling Analysis of Steel Frames Exposed to Natural Fire Scenarios

The fire design of a steel frame is defined according to Part 1.2 of Eurocode 3 (EN 1993-1-2). It is based on security check to standard ISO 834 fire, where the structure must resist to fire during time set by regulation. For a natural fire, the structural resistance is ensured in the way that the collapse does not occur during the fire, including fire decline phase, or alternatively for a certain period. The Eurocode makes it clear that to check the standard fire resistance requirements it is enough to perform analysis of elements but does not report if such analysis is sufficient for a natural fire design and some uncertainties remain.This study focus on the clarification of the use of the simplified design methods for assessment of the fire resistance of steel frames exposed to natural fire scenarios. Special attention is drawn to the use of the buckling lengths suggested in EN 1993-1-2 for the fire design of columns in braced frames and a recent proposal for unbraced frames suggesting the use of a buckling length of 1.0L for all columns except those belonging to the first storey of pinned frames where 2.0L should be taken instead.Finally, a comparison is made between simple and advanced calculation models and it is demonstrated that the simple design methods, using the suggested buckling lengths to calculate the fire resistance of the frames are safe sided when compared to the use of more advanced calculations by means of the finite element method (FEM).

Anchored blind bolted composite connection to a concrete filled steel tubular column

A new type of moment-resisting bolted connection was developed for use in composite steel- concrete construction to connect composite open section steel beams to concrete filled steel square tubular columns. The connection was made possible using anchored blind bolts along with two through bolts. It was designed to act compositely with the in-situ reinforced concrete slab to achieve an enhanced stiffness and strength. The developed connection was incorporated in the design of a medium rise (five storey) commercial building which was located in low to medium seismicity regions. The lateral load resisting system for the design building consisted of moment resisting frames in two directions. A major full scale test on a sub-assembly of a perimeter moment-resisting frame of the model building was conducted to study the system behaviour incorporating the proposed connection. The behaviour of the proposed connection and its interaction with the floor slab under cyclic loading representing the earthquake events with return periods of 500 years and 2500 years was investigated. The proposed connection was categorized as semi rigid for unbraced frames based on the classification method presented in Eurocode 3. Furthermore, the proposed connection, composite with the floor slab, successfully provided adequate lateral load resistance for the model building.

Prediction of lateral stiffness and fundamental period of concentrically braced frame buildings

In this paper, a simple hand calculation method to predict lateral stiffness and fundamental period of concentrically braced frame buildings with either fixed or pin base, which can also be used for unbraced frame buildings, is theoretically derived. To verify the reliability of the developed equations, the estimated lateral stiffness and fundamental periods are compared with the corresponding values obtained from pushover and Eigenvalue analyses for a wide range of low to medium rise buildings (i.e. up to ten storeys) with varying geometrical configurations. Systematic investigation of parameters affecting the fundamental period of frame buildings is also carried out. Although the basic formulation considers X and chevron brace configurations explicitly, its applicability to other types of brace configurations is also investigated. The suitability of the proposed equation for the braced frames with linear variation of section properties along the building height and pin beam-column connections is also scrutinized. Reliability of the developed hand calculation method is verified using the experimental test and numerical analysis results available in the literature. Finally, a flowchart and two worked examples are provided to explain the sequence of steps to calculate the fundamental period of concentrically braced frame buildings.

Seismic performance of a reinforced concrete frame equipped with a double-stage yield buckling restrained brace

Summary In this paper, a double-stage yield buckling restrained brace (DYB) is proposed to prevent soft story collapse in structures subjected to strong earthquakes. The DYB consists of two conventional buckling restrained braces (BRBs) with different yield forces: a large BRB and a small BRB. The deformation of the small BRB has an upper threshold value, controlled by a special mechanical mechanism. Once the force acting on the DYB exceeds the yield force of the small BRB, the small BRB yields and the deformation concentrates on the small BRB. When the deformation of the small BRB reaches the threshold value, the small BRB stops deforming. If the force of the DYB continues to increase and exceeds the yield force of the large BRB, the large BRB yields and most of the deformation takes place in the large BRB. In this way, the DYB achieves a double-stage yield mechanism. To demonstrate the effectiveness of the DYB, a model of a six-story reinforced concrete frame equipped with DYBs was constructed using the finite element software ABAQUS, and its seismic performance was analyzed. The double-stage yield mechanism of the DYB was simulated by a gap element. To investigate the effect of DYBs on the seismic performance of the structure, four different models were built: an unbraced frame, frame with DYB, frame with small BRB, and frame with large BRB. The results of the pushover and time-series analyses showed that the DYB effectively controlled the deformation pattern of the structures, and prevented weak story collapse.

Seismic Optimum Design of Steel Structures Using Gradient-Based and Genetic Algorithm Methods

Optimum design of structures under time-variable loadings is a difficult task. Time-dependent behavior of constraints and cost of gradients calculations could be mentioned when applying time history loadings in the optimization problems. To overcome these difficulties, the response spectra as a seismic demand are used instead of using time history acceleration in the structural modeling. In this paper, the P-Delta effects are considered in the finite-element modeling of the frames. Furthermore, many practical constraints are included in the optimization formulation according to the Iranian national building code (Standard N. 2800). The developed MATLAB-based computer program is utilized for optimization of the low, intermediate- and relatively high-rise braced and un-braced steel frames. The obtained results of sequential quadratic programing (SQP) method are compared with the results of genetic algorithm (GA) technique for guarantying the global optimal designs. Because of the inexpensive costs of SQP method in comparison with genetic algorithm technique, SQP method could be confidently applied for obtaining the global optimum designs of the steel frames.

A STUDY ON THE PUSHOVER TEST AND NUMERICAL ANALYSIS OF GFRP FRAMES

This paper presents the use of glass fiber reinforced plastic (GFRP) composite material to produce a structure frame; the behaviors of the GFRP frames were analyzed by using pushover test and a numerical analysis software. Double-web FRP I-beams are used for the beams and columns of the frame, and joints made from metal and FRP. Three types of frame specimens were involved: an un-braced frame, a compression-braced frame and a tension-braced frame for each joint type. The joints were bonded to the frame components using epoxy resin but also adding bolts in the beam-column joint. The pushover test was used to investigate the mechanical behaviors and failure modes of the GFRP frames. The analysis software SAP2000 was used for the pushover analysis of the GFRP frames, and it was shown that the ultimate strength and force-displacement relationships of the analytical results were similar to that of the experimental ones.

Improvement of progressive collapse resistance potential of semi-rigid jointed steel frames through bracings

Progressive collapse studies of both unbraced and braced semi-rigid jointed steel frames have been carried out to evaluate the contribution of bracings in improving progressive collapse resistance potential. Numerical models of 10-story frames with different types of semi-rigid connections have been developed using SAP2000. Progressive collapse potential of semi-rigid frames is first investigated without bracings. Bracings are then included in a systematic manner, and response of the braced frame is compared with that of unbraced frame to evaluate the contribution of bracings. Two different arrangements of bracings, that is, bay-wise and floor-wise arrangements, are considered to find out a preferred arrangement of bracings. Parametric studies include eight column removal conditions at center and corner locations of different floors. Development of catenary action has also been considered as it gives additional resistance, especially to braced frame. Apart from nonlinear static analysis, effects of bracings are evaluated also through nonlinear dynamic analysis and the responses of the frames in nonlinear dynamic analysis are compared with those of nonlinear static analysis. From the study, it is found that provision of bracings significantly improves the progressive collapse resistance potential of the semi-rigid frames under different column removal conditions. Floor-wise arrangement of bracings is much effective as compared to bay-wise arrangement.

Systems Reliability for 3D Steel Frames Subject to Gravity Loads

The system-based design of steel structures using advanced analysis leads to a more efficient structural design process and achieves a more uniform level of structural system reliability. The main impediment to adopting this method in practical applications is the apparent difficulty in assigning an appropriate resistance factor to structural systems. In this paper, the reliability assessment and derivation of system resistance factors for a series of 3D low-to-mid-rise steel frames are presented, taking into account the inherent uncertainties in material and geometric properties, and the model uncertainty of advanced analysis. Braced and unbraced (sway) frames with regular and irregular configurations are analysed under gravity loads and the system resistance factors are derived for different target reliability levels. The frames are selected to provide different system failure modes such as sway instability and/or member failure. Recommendations are made for the appropriate target reliabilities and associated system resistance factors for use in designing 3D steel frames at system level by advanced analysis.