Cross-bracing System Research Articles

Numerical evaluation of SMA-based multi-ring self-centering damping devices

This paper introduces the innovative concept of SMA-based multi-ring (SBMR) self-centering damping devices and numerically evaluates their performance and effective design. The SBMR devices are passive metallic dampers consisting of two types of concentric circular rings with rectangular cross-section: (a) superelastic (SE) rings and (b) supplemental energy dissipating (ED) rings. The rings are tightly fitted into each other such that their diametric deformations are constrained. The SE rings are made of SE shape memory alloys (SMA) (e.g., Nitinol), thereby providing the SBMR devices with both self-centering and hysteretic damping. The ED rings are made of metals with higher hysteretic damping capacity to supplement the damping of the SE rings. The SBMR devices can resist both tension and compression (without buckling) in multiple directions, allowing their installation via cross-bracing systems. To evaluate the SBMR devices, they were simulated through 3D nonlinear finite element models. The general response/behavior of the proposed devices and the effects of brace design and orientation on their response were examined. The SBMR devices were found capable of producing more than 100% higher damping compared to single SE SMA rings, particularly under small deformations. Moreover, brace design and orientation were found to have little to no effect on the performance of the SBMR devices.

Effective length factor of a non-symmetrical cross-bracing system with a discontinuous diagonal

A non-rectangular frame panel usually contains an asymmetrical cross-bracing system with interrupted diagonals, leading to a more complicated buckling behavior than a symmetrical bracing system with continuous diagonals. There have been many studies of the stability theory of symmetrical cross-bracing systems, but few related to non-symmetrical systems. In this study, we analyzed elastic out-of-plane buckling of a general non-symmetrical cross-bracing system with a discontinuous diagonal. The discontinuous and continuous diagonals have different material and geometrical properties, and are not intersected at their mid-spans. A characteristic equation is presented to compute the critical loading of a non-symmetrical cross-bracing system when the supporting diagonal is under either compression or tension. The results show that the characteristic equation of a non-symmetrical bracing system can be transformed into a form the same as that of a geometrically mono-symmetrical system. To facilitate design applications, direct closed-form empirical equations of effective length factor are established for a general non-symmetrical cross-bracing case. The validity of the proposed empirical equations was verified by comparing predicted and theoretical results, and those from a stiffness approach.

Seismic Analysis of Irregular RC Structure with Cross-Bracing System

Seismic Analysis of Irregular RC Structure with Cross-Bracing System

Distortion-Induced Fatigue Crack Growth

Out-of-plane distortion of transverse cross-bracing systems in bridge superstructures has been known to cause localized fatigue cracking. The cracking is a result of the differential displacement of adjacent bridge girders, which causes high stress concentrations in unstiffened web-gap regions at the interface of girder and stiffener connection plates. Fatigue cracking within the web gap can occur because of cyclical loading scenarios. Rehabilitation efforts have shown to be unpredictable in preventing crack propagation once through-thickness crack profiles have developed. Therefore, understanding the mechanisms causing fatigue crack propagation in such detail is essential in developing effective repair methods. In this study, numerical analyses of typical web-gap connections are conducted using the extended FEM to characterize crack directionality and growth rate. Simulations varying the web-gap length, stress range, loading ratio, and initial crack length were used to determine the primary variables effecting crack growth in the web-gap region. Increasing the web-gap length was noted to stabilize crack propagation rates, resulting in stable growth, which can be correlated to the Paris Law. Elongation of horizontal initial crack lengths resulted in reorientation of crack growth. In stiffer web gaps, a combined high stress ratio and long initial crack length resulted in crack profiles propagating into the flange-web interface with eventual crack arrestment. The study suggests that horizontal extension of initial cracks has the potential to cause the crack to arrest, after stable propagation, without adversely compromising local structural integrity of bridge superstructures.

X-가새형 탄소섬유케이블을 이용한 중·저층 철근콘크리트 건물의 내진보강법 개발

Improving the earthquake resistance of buildings through seismic retrofitting using steel braces can result in brittle failure at the connection between the brace and the building, as well as buckling failure of the braces. In this study, a non-compression cross-bracing system using the Carbon Fiber Composite Cable (CFCC), which consists of CFCC bracing and bolt connection was proposed to replace the conventional steel bracing. This paper presented the seismic resistance of a reinforced concrete frame strengthened using CFCC X-bracing. Cyclic loading tests were carried out, and the maximum load carrying capacity and ductility were investigated, together with hysteresis of the lateral load-drift relations. Test results revealed that the CFCC X-bracing system installed RC frames enhanced markedly the strength capacity and no buckling failure of the bracing was observed.

A STUDY OF SEISMIC POUNDING BETWEEN ADJACENT BUILDINGS

Seismic pounding between adjacent buildings can cause severe damage to the structures under earthquakes, when owing to their different dynamic characteristics. During earthquake, the buildings vibrate out of phase and at rest separation is deficient to accommodate their relative motions. Such buildings are usually separated by expansion joint which is insufficient to provide the lateral movements of the buildings during earthquakes. It can be prevented by providing safe separation distances, sometimes getting of required safe separations is not possible in metropolitan areas due to high land value and limited availability of land space. If building separations is found to be deficient to prevent pounding, then there should be some secure and cost effective methods to prevent structural pounding between adjacent buildings. There are many buildings which are constructed very nearly to one another in Metropolitan cities, because everyone wants to construct up to their property line due to high cost of land. This study covers the prevention techniques of pounding between adjacent buildings due to earthquakes. Constructing new RC walls, cross bracing system and combined RC wall & bracing, with proper placement are proposed as possible prevention techniques for pounding between adjacent buildings

Stability Design of Cross-Bracing Systems for Frames

In this study, the inelastic load-carrying capacity of the compression diagonal of a typical cross-bracing system used in concentrically braced frames under gravity and wind loads is investigated, taking into consideration its interaction effect with the tension diagonal. Depending on the lateral stiffness of the tension diagonal, the compression diagonal can be fully or partially braced by the tension diagonal at their intersection point. An expression for the transition lateral stiffness, kst, that demarcates the fully and partially braced conditions is derived. When the compression diagonal is fully braced, its maximum load-carrying capacity is a function of its member slenderness, L/r, only. However, when the compression diagonal is partially braced, its load capacity is dependent upon both its member slenderness, L/r, and the lateral stiffness, ks, of the tension diagonal. Once the equations for the maximum load-carrying capacity of the compression diagonal are established, design guidelines are proposed and design examples are given to demonstrate how the proposed guidelines can be used for the design of cross-bracing systems in steel frames. The consideration of the lateral bracing effect will result in a more economical and logical design for such bracing systems.

An algorithm to simulate the one-dimensional superelastic cyclic behavior of NiTi strings, for civil engineering applications

An algorithm to model the one-dimensional cyclic behavior of NiTi strings is addressed. The NiTi alloy belongs to the shape memory alloy class of materials, therefore it presents both shape memory effect, for thermally-induced cycling, and superelasticity, for stress-induced cycles. The superelastic property has been the basis of some devices designed to mitigate the earthquake hazard level in structures. Throughout this paper the implementation of a one-dimensional cyclic behavior algorithm to model the NiTi constitutive relation is presented, supported by the thermomechanical formulation developed by Lagoudas and co-workers. The model was set up in MatLab environment and it accounts for isothermal superelastic behavior, incorporating minor hysteretic transformation loops. The definition of the transformation hardening function allowed for a better adjustment of the numerical model weighted against experimental results. Especial emphasis was given to the process of calibration of the model, regarding the definition of material parameters. The validation process consisted of the comparison between the results achieved with this algorithm and experimental tests performed at the Pacific Earthquake Engineering Research Center at the University of California at Berkeley. Quasi-static tensile tests and shake table tests of a small-scale steel structure with NiTi cross-bracing systems were used as reference. The model was able to simulate the experimental performance. This formulation can be implemented in more robust finite element analysis software, in order to perform studies in more elaborate structures.

Seismic Vibration Control Using Superelastic Shape Memory Alloys

Superelastic NiTi shape memory alloy (SMA) wires and bars are studied to determine their damping and recentering capability for applications in the structural control of buildings subjected to earthquake loadings. These studies improve the knowledge base in regard to the use of SMAs in seismic design and retrofit of structures. The results show that the damping properties of austenitic SMAs are generally low. However, the residual strain obtained after loading to 6% strain is typically <0.75%. In general, it is shown that large diameters bars perform as well as wire specimens used in non-civil-engineering applications. The results of a small-scale shake table test are then presented as a proof of concept study of a SMA cross-bracing system. These results are verified through analytical nonlinear time history analysis. Finally, a three-story steel frame implementing either a traditional steel buckling-allowed bracing system or a SMA bracing system is analyzed analytically to determine if there is an advantage to using a SMA bracing system. The results show that the SMA braces improve the response of the braced frames.

Simply Supported Curved Cellular Bridges: Simplified Design Method

The use of curved composite bridges in interchanges of modern highway systems has become increasingly popular for economic and aesthetic considerations. Bridges with a concrete deck composite with a steel multicell section can adequately resist torsional and warping effects induced by high curvature. Although current design practices in North America recommend few analytical methods for the design of curved multicell box girder bridges, economical requirements in the design process point to a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using the finite-element method, in which simply supported curved composite multicell bridge prototypes are analyzed to evaluate the moment and deflection distributions between girders, as well as the axial forces expected in the bracing system, due to truck loading as well as dead load. Results from tests on four, 1/12 linear-scale, simply supported curved composite concrete deck-steel multicell bridge models are used to substantiate and verify the analytical modeling. The parameters considered in the study are cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for moment and deflection distribution factors are deduced. Expressions for the maximum axial force in bracing members are also derived. An illustrative design example is presented.

Shear Distribution in Simply-Supported Curved Composite Cellular Bridges

Composite steel-concrete multicell box girder bridges are quite often used in modern bridge superstructures with curved alignments. They provide excellent torsional resistance as well as elegant appearance. While current design practices in North America recommend few analytical methods for the design of curved multicell box bridges, practical requirements in the design process require a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using a finite-element model, in which 120 simply-supported curved bridge prototypes are analyzed to evaluate the shear distribution in the webs due to truck loading as well as dead load. Results from tests on four 1/12 linear-scale simply-supported curved composite concrete deck-steel three-cell bridge models are used to substantiate the analytical modeling. The parameters considered in the study are: cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for the shear distribution factors for truck loadings as well as dead load are deduced. An illustrative design example is presented.

Behavior of Cross-Bracing in Latticed Towers

Cross-bracing in which the bolted steel angle members are alternately in compression and tension is widely used in latticed tower structures. Within each set of cross-bracing, the tie is generally assumed to restrain the strut at the cross-over joint. A series of 13 tests on cross-bracing systems is described, with slenderness ratios in the range of 102 to 160. Other variables include the inclination of the main legs and bracing, the number of bolts in each end connection, and the size of the main leg relative to the bracing. The measured behavior is compared with the results of a flexibility-based analysis and the formulas from the American and European transmission tower design manuals. The behavior is complex, but the importance of end eccentricity and number of bolts in the connection of the bracing to the main legs is apparent in these results. A secant-based design formulation is shown to provide accurate predictions of the strength of the cross-bracing.

Dynamic characteristics of simply supported curved composite multi-cell bridges

The use of horizontally curved composite bridges in the interchange facilities of modern highway systems has become increasingly popular for economic as well as for aesthetic considerations. Cellular steel sections composite with a concrete deck are quite suitable in resisting torsional and warping effects induced by highway curvature. However, this type of structure has inherently created design problems for the designer in estimating the level of dynamic response when subjected to moving vehicles, wind, or seismic conditions. This paper presents a summary of an extensive parametric study, using the finite-element method, in which 120 simply supported, curved composite bridge prototypes are analyzed to evaluate their natural frequencies and mode shapes. The parameters considered in the study are end-diaphragm thickness, cross-bracing system, aspect ratio, span-to-depth ratio, degree of curvature, number of lanes, and number of cells. Results from tests on four 1/12 linear-scale simply supported composite three-cell bridge models of different curvatures are used to substantiate the analytical modelling. The stipulation made in bridge codes for treating a curved bridge as a straight one is examined. Based on the data generated from the parametric study, expressions for the first flexural frequency and hence the dynamic load allowance are deduced. Recommendations for enhancing the torsional resistance to dynamic forces on curved bridges are presented. Two design examples are illustrated.

Stability of Orthogonally Intersecting Equal-Leg Angle Cross-Bracing Systems*

When a sway force acts on a cross-bracing system, one of the braces goes into a tension state while the other goes into a compression state. The tension brace helps to stiffen the compression brace through a bolted intersecting point. This paper presents an energy method for determining the improved buckling capacity of such a compression brace. The braces considered consist of equal-leg angle members that intersect orthogonally. The present problem is more difficult to solve when compared to earlier studies made on rods and tubular brace members, because angle members may buckle in a complicated flexural torsional mode rather than in a simple flexural mode.

Seismic response of braced frames with and without friction dampers

The dynamic response of friction damped bracing systems and ordinary cross-bracing systems inserted into surrounding frames without lateral stiffness is analysed in order to compare the typical behaviour of the two different bracing systems. The cyclic force-displacement relationship in the two cases is accurately modelled on the basis of experimental and related numerical models which are available in the literature, and the structural dimensionless parameters defining the shapes of the cycles are stressed. Systems having the same average period of vibration in the elastic phase of the response are assumed to be comparable with one another, which leads to a relationship linking the structural parameters of the two kinds of system. Extending the ductility concept to the friction devices, by a step-by-step integration of the equation of motion for the two systems the dimensionless structural responses are derived with variations in the strength level factor. Computing the average values of the maximum responses to five accelerograms artificially generated to be compatible with the normalized elastic spectrum proposed by Eurocode 8, the behaviour factor versus period curves are also deduced with variations in the available ductility. These curves show the different reliability levels provided by the two kinds of bracing systems considered and they are useful for practical applications. Two meaningful numerical examples, carried out by assuming an input accelerogram corresponding to an actual seismic record (EI Centro earthquake, 1940) confirm these design suggestions.

Parametric study of design variations on the vibration modes of box girder bridges

Under a moving load, a bridge undergoes deflections and stresses which significantly exceed those caused by the same load when applied statically. These dynamic deflections can cause discomfort to pedestrians using the bridge, since human response is sensitive to accelerations and to the rate of change of acceleration. Another factor affecting human response is the type of vibration in the dominant mode. People tend to react more adversely to torsional modes of vibration than to flexural modes. This paper summarizes the results of an extensive analytical investigation, which was conducted to identify key parameters affecting the changes of dominant mode types and to study the influence of diaphragms and cross bracings on dynamic responses of a twin box girder bridge. The finite element method was used to carry out these analyses. The analytical results indicate that the provision of diaphragms within the boxes at each support, or of a cross-bracing system in-between boxes, can effectively reduce peak accelerations when the dominant mode of vibration is torsional. As a result, the human discomfort and perception to vibration can be improved. Key words: vibration, human response, torsion, flexure, box girder bridge, diaphragm, cross bracing, finite element analysis.

Stiffness Requirements for Cross Bracing

In the design of roof and wall double-diagonal cross bracing, the compression diagonal is usually ignored. The possibility of bracing provided to the compression diagonal by the loaded tension diagonal is examined. It is shown that the compression diagonal may be effectively braced at midspan through its connection to the tension diagonal, thereby increasing the total capacity of the double-diagonal cross bracing system.