Bending Moment Of Columns Research Articles

Assessing the significance of nonlinear rotational behavior in high damping rubber bearings for seismic performance of base‐isolated RC frame building

AbstractUtilizing high‐damping rubber bearings (HDRBs) for seismic isolation significantly enhances building seismic performance. However, previous studies have often neglected the nonlinear rotational behavior of these bearings when assessing base‐isolated systems using HDRBs. This study introduces two numerical models of the HDRBs, each comprising six springs. The first model, referred to as the BIL model, assumes linear behavior for the rotational degrees of freedom of the bearings. The second model, referred to as the BINL model, accounts for the nonlinear rotational behavior. The parameters of the bearing shear springs and the rotational springs of the two models are calibrated using experimental data. In order to investigate the influence of nonlinear rotational behavior of HDRBs on the seismic performance of base‐isolated buildings, nonlinear time history analysis is conducted on a six‐story base‐isolated RC frame building. Comparative analysis between the BIL model and the BINL model covers bearing behavior, superstructure response, and energy dissipation distribution. Results indicate a significant influence of considering nonlinear rotational behavior on column bending moments. These findings provide crucial insights for enhancing seismic design strategies for base‐isolated buildings.

Nonlinear seismic analysis of perforated steel plate shear walls using a macro-model

Steel plate shear wall (SPSW) with regularly spaced circular perforations has recently been developed. While the current edition of AISC 341-16 and CSA S16-14 have adopted perforated SPSW (P-SPSW) in their design standards, no simple numerical model is currently available for analyzing this SPSW system. A reliable macro-model is developed for regularly spaced circular perforations. The proposed macro-model is validated against available experimental results. Performance of three multi-storey (4-, 7-, and 10-storey) perforated SPSWs designed according to CSA S16-14 and NBCC 2015 is further investigated through conducting a series of time history analyses using a suite of 44 ground motions developed for western Canada. When compared with seismic analysis results of solid SPSWs, it is observed that the median shear envelopes for P-SPSWs are slightly less than that for solid ones. Also, in comparison to solid SPSW archetypes, the contribution of boundary columns in resisting the storey shear is found higher than the infill plate in most of the stories in P-SPSW archetypes. Finally, a sensitivity assessment is performed to evaluate the effect of perforation diameter on different responses of P-SPSWs, such as peak column axial forces, peak column bending moments, and maximum interstorey drift. It is observed that with an increase in the hole diameter, column axial force demand decreases, while the bending moment remains almost the same. Also, since adding perforations to the infill plate reduces the stiffness and strength of the P-SPSW system, the interstorey drift ratio is increased in comparison to solid SPSW.

Proposal and validation of a design procedure for concentrically braced frames in the chevron configuration

AbstractIn the recent past, several research studies have highlighted that the prescriptions reported in codes for the design of structures with concentric braces in the chevron configuration are often not effective in preventing yielding or buckling of non‐dissipative members and in ensuring collapse mechanisms characterised by uniform damage of braces. To investigate the reasons of these deficiencies, in this paper the seismic response of concentrically braced structures designed according to procedures reported in the literature and in the European seismic code is first examined. Then, a new design procedure is proposed, in which the innovative aspects are mainly related to the estimation of the bending moments in columns and to the formulation of requirements on the stiffness of braced beams and columns. The impact of the proposed procedure on the structural costs is computed on a large number of buildings characterised by different occupancy types and geometric properties. The seismic performance of these structures is evaluated by incremental nonlinear dynamic analysis and discussed at the achievement of the significant damage and near‐collapse limit states.

Some issues regarding the models of the mass and damping matrices in nonlinear seismic analysis of moment resisting steel frames

Software users concerning seismic analysis of buildings usually use the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes are commonly used to calculate C. In addition, it is commonly believed that damping forces are small so there are no significant errors if the Rayleigh model is used. The evaluation of the accuracy of these practices for the case of steel buildings constitutes the main objective of this research. To this aim the seismic responses of three models, representing steel buildings of low-, mid- and high-rise are considered. If ML is used, shears and bending moments in columns are underestimated by up to 31% and 65%, respectively. If the first two modes are used, shears, drifts, and bending moments in beams are underestimated by up to 27%, 50%, and 55%, respectively, while for axial loads and bending moments in columns the underestimation can be up to 78%. Similarly, damping forces and damping moments are underestimated by up to 350% and 325%, respectively. Damping moments represent a considerable fraction (0.47) of plastic moments in beams. If KO is used in C, axial loads in columns are underestimated by up to 80%. The results of this study give rise to state that the consistent mass matrix should be used in the structural modelling of the structural system under consideration. Similarly, first mode and one superior, and the tangent stiffness matrix should be used to formulate the Rayleigh damping matrix.

Investigating the seismic isolation effect of the cushioned pile raft foundation in soft clay through dynamic centrifuge tests

Cushioned pile-raft foundation (Cushioned-PR) is a new type of foundation for sea-crossing bridges in deep water (more than 50 m in depth). Cushioned-PR is able to tolerate a certain amount of slide that occurs between the raft and the piles under strong earthquakes. This characteristic could reduce the seismic motion transmitted to the superstructure to maintain the integrity of the bridge. Thus, Cushioned-PR has become popular for bridges under the threat of strong earthquakes. However, the dynamic responses of the Cushioned-PR under various earthquake intensities in soft clay have not been thoroughly understood. It is essential to better evaluate the isolation effect of Cushioned-PR to improve the design. In this study, the non-linear behavior of Cushioned-PR and the isolation effect of its interposed layer are evaluated using centrifuge tests. A series of dynamic centrifuge tests are performed with a 3 × 3 pile group foundation embedded in soft clay under different earthquake motions. Both the cushioned pile raft foundation system (Cushioned-PR) and the connected pile raft foundation system (Connected-PR) are tested in the centrifuge tests. Acceleration and residual displacement of the super-structure, and bending moment of columns and piles, are monitored during the experiments. The results show that the interposed layer in Cushioned-PR has a significant impact on the bending moment and residual displacement of the pile-raft system. Based on the observation from this study, the maximum bending moment of the column in the Cushioned-PR is around 28%–54% of the values from the Connected-PR. On the other side, the maximum horizontal displacement of Cushioned-PR is about 2–10 times larger than that of the Connected-PR. The results show that Cushioned-PR can effectively reduce the seismic excitation transmitted to the super-structure if the seismic intensity is high. However, the benefit of Cushioned-PR is marginal under low-intensity earthquakes.

3D Numerical Analyses of Column-Supported Embankments: Failure Heights, Failure Modes, and Deformations

Design of column-supported embankments (CSE) requires the evaluation of global stability using the conventional limit equilibrium method (LEM). Yet, for CSEs using unreinforced concrete columns and load transferring geogrids, the failure mechanisms and corresponding soil-structure interactions are not well understood. There is increasing evidence pointing to large bending moments in columns and failure of columns in flexure, as opposed to a failure by shear as assumed in limit equilibrium analyses. In response to these design uncertainties, the failure height, failure mode, and deformations of eight column-supported embankment scenarios were investigated using three-dimensional (3D) numerical analyses. For the same embankment scenarios at failure height, factors of safety (FS) were then calculated using the two-dimensional (2D) LEM for investigating its applicability in evaluating global stability of CSEs. The 3D numerical analyses examined CSE stability for the limiting conditions at undrained end-of-construction and after long-term dissipation of excess pore water pressures. The numerical model included representations of flexural tensile failure in the concrete columns and tensile failure in the geosynthetic reinforcement. Scenarios consisted of a base case with typical concrete column design, five single-parameter variations using base case conditions, and two multiparameter variations using base case conditions. The undrained condition was the most critical, and two failure modes were found: (1) multisurface shearing in the embankment coupled with bending failure of columns and near-circular shear failure in the clay, and (2) multisurface shearing in the embankment coupled with bending failure of columns and shearing in the upper portion of the soft foundation clay. Both failure modes were accompanied by a rupture of the geosynthetic when included in the load transfer platform. Soil-column interactions were complex, and many columns failed in bending at lower embankment heights than those that produced collapse. The factors of safety calculated using the LEM were overstated. This is because the LEM assumes failure by shear, which has limited applicability for examining the complex mechanisms by which CSEs fail. The practical implication is that the LEM should not be used for evaluating global stability of this system type and, by extension, other system types in which soil-structure interactions result in failures controlled by mechanisms other than shear.

Comparative Study on Seismic Response of Pile Group Foundation in Coral Sand and Fujian Sand

The physical and mechanical properties of coral sand are quite different from those of common terrestrial sands due to the special marine biogenesis. Shaking table tests of three-story structures with nine-pile foundation in coral sand and Fujian sand were carried out in order to study the dynamic response characteristics of pile-soil-structure system in coral sand under earthquake. The influence of shaking intensity on the dynamic response of the system was taken into consideration. The results indicated that the peak value of the excess pore pressure ratio of coral sand was smaller than that of Fujian sand under two kinds of shaking intensities; moreover, the development speed of excess pore pressure ratio of coral sand was smaller than that of Fujian sand. The liquefaction of coral sand was more difficult than Fujian sand under the same relative density and similar grain-size distribution. The horizontal displacement, settlement, column bending moment, and pile bending moment of coral sand were smaller than those of Fujian sand, respectively. The magnification effect of column bending moment of buildings in coral sand was less than that in Fujian sand with increasing shaking intensity. This study can provide some supports for the seismic design of coral reef projects.

Influence of the stiffness of beam-column connections on the structural analysis of reinforced concrete buildings

Abstract Conventional structural analysis of buildings in reinforced concrete is performed considering beam-column connections as rigid. However, experimental results prove the existence of relative rotations in beam-column connections of reinforced concrete structures, showing the partial transfer of bending moment. In this study the influence of the stiffness of beam-column connections on the global stability and in the column bending moments of buildings in reinforced concrete was investigated. A building was designed with rigid connections and deformable connections to identify the importance of considering the influence of the stiffness of the beam-column connections in the overall stability of monolithic and in the redistribution efforts in reinforced concrete structures. In order to determine the stiffness rotation of deformable connections, two analytical models available in literature were used, and a comparison between the results obtained by each analytical model was also performed. Based on the results, it is concluded that neglecting the influence of the stiffness of the beam-column connections on the analysis of monolithic reinforced concrete structures may result in different solutions compared to the real behavior of the structure. The stiffness values obtained with the analytical models usually differ from the condition of rigid connections, suggesting an adjustment on the standard consideration of rigid connections adopted by the computer programs of structural calculation.

Analysis and Design of Two-Tiered Steel Braced Frames under In-Plane Seismic Demand

AbstractA seismic design strategy, which is intended to be implemented within the framework of the U.S. seismic design provisions for steel structures, is presented for single-story steel concentrically braced frames that are divided into two tiers. In this method, the columns are designed to resist the axial loads acting in combination with the in-plane flexural demand resulting from uneven distribution of brace inelastic deformations over the frame height. This design procedure, which establishes enhanced requirements beyond the 2010 edition of the U.S. seismic design provisions, prevents concentration of deformation in one tier and causes frame nonlinear deformation to be distributed between the tiers. The column bending moments depend on the story shear resistance that develops in each tier when the bracing members are at buckling and in the postbuckling range. The method also aims to control tier drifts to protect the bracing members from excessive inelastic demand, which could cause brace fracture. ...

Assessment and Code Considerations for the Combined Effect of Seismic Base Isolation and Viscoelastic Dampers

To propose an initial formulation for the passive control section of the Turkish Earthquake Code, the impact of base isolation and viscoelastic dampers on a four-storey reinforced concrete (RC) frame building was considered under various one-dimensional quake excitations. Both statically equivalent seismic load methods (comparing Turkish Earthquake code with Uniform Building Code) and linear time history analyses were applied to the RC building based on a portion of the 1999 Kocaeli Earthquake ground motion record (modified to possess predominant spectral periods of sec and sec representing hard and soft soil conditions, resp.). Effective peak ground acceleration was set to 0.40 g. Time history variations of upper column dis-placements and bending moments were compared, as well as storey drift ratios. Reductions of the fixed-base case column bending moments were obtained of up to 73% under base isolation, up to 25% with viscoelastic dampers, and up to 83% (with a unified response reduction factor) when both devices were both present.

EFFECTS OF RANDOMLY DISTRIBUTED INFILL ON COLUMNS OF REINFORCED CONCRETE FRAMES WITH SOFT GROUND STOREY

Reinforced concrete (RC) frames with an open ground floor and various infill distributions have been analyzed for seismic loadings by the finite element method. The infills have been modeled by diagonal struts. Focus is placed on the effects of infill distribution on various structural responses, including (i) the lateral deflection, (ii) the column axial forces, (iii) the column bending moments, (iv) the base shear, and (v) the natural period of the frame. The equivalent static force method (ESFM) and response spectrum method (RSM) for linear structures have been applied, and the results obtained have been compared. It was found that the structural responses do not change appreciably by the ESFM analysis for random infill distributions, while they increase noticeably in the RSM analysis. This manifests the inadequacy of using the ESFM for general purposes, for which modifications were proposed in this paper for the design of RC columns. As the natural period of the RC frame converges with the code equations only for higher amounts of infill, it is necessary to incorporate the amount and distribution of infill in the dynamic analysis of RC frames.

A closed-form analysis of perimeter member behavior in a steel building frame subject to fire

This paper outlines a closed-form methodology that can be used to predict the increase in demand experienced by the perimeter columns that are part of a fire-exposed steel building frame. The two-dimensional elevation-view subassembly considered for this study includes a two-storey length of the perimeter column and the floor beam framing into the column in the direction perpendicular to the building’s exterior. When heated, this beam will expand and induce bending moment and lateral deflection in the column as well as increased axial force in the beam itself. Our proposed approach has two primary components: (1) a material model that approximates nonlinearity and considers temperature effects, and (2) a mechanical model that represents the perimeter column and beam interaction. These models are used to develop a simplified closed-form solution for beam axial force and perimeter column bending moment that may be used as part of a performance-based design for fire exposure. The simplified model solutions are compared to the results of a more complex and detailed multi-story finite element analysis model. A comparison of these results shows that the simplified model results give good estimations of structural behavior.

ACCURACY OF EVALUATION OF COLUMN BENDING MOMENT BASED ON SHAKE TABLE TESTS

ACCURACY OF EVALUATION OF COLUMN BENDING MOMENT BASED ON SHAKE TABLE TESTS

DYNAMIC BEHAVIOUR OF REINFORCED CONCRETE FRAMES DESIGNED WITH DIRECT DISPLACEMENT-BASED DESIGN

The Direct Displacement-based Design methodology is applied to six reinforced concrete tube-frame structures and tested using inelastic time-history analyses. Using the established design method inter-storey drifts are found to exceed assumed drift limits, and a series of changes to the design displacement profiles and lateral force distribution are proposed to improve agreement. These changes are then applied to the six frames and further time-history analyses carried out at different earthquake intensities. The inter-storey drift behaviour is found to be significantly improved, with code-based drift limits consistently satisfied. Finally a revised form of the Modified Modal Superposition is proposed to account for higher-mode amplification of column shear forces, while a simple intensity-dependent scaling factor to be applied in the capacity design process is developed for column bending moments. The suggested equations are applied to the frame designs, and found to be in acceptable agreement with time history results at a range of earthquake intensities.

Effect of Column Stiffness on Braced Frame Seismic Behavior

Steel concentrically braced frames are generally designed to resist lateral force by means of truss action. Design considerations for columns in these frames are therefore governed by the column axial force while column bending moment demands are generally ignored. However, if the columns cannot carry moments, then dynamic inelastic time-history analyses show that a soft-story mechanism is likely to occur causing large concentrated deformations in only one story. Such large concentrations of damage are not generally seen in real frames since columns are generally continuous and they possess some flexural stiffness and strength. This paper develops relationships for column stiffness and drift concentration within a frame based on pushover and dynamic analyses. It is shown that continuous seismic and gravity columns in a structure significantly decrease the possibility of large drift concentrations. An assessment method and example to determine the required column stiffness necessary to limit the concentration of story drift is provided.

An experimental study of the fire performance of non-sway loaded concrete-filled steel tubular column assemblies with extended end plate connections

This paper presents the results of an experimental study of the behaviour of concrete filled steel tubular column assemblies using extended end plate connections. The objectives of this study are to investigate the effects of rotational restraint on column bending moments and column effective lengths. Two series of column assemblies have been fire tested at the University of Manchester’s fire testing laboratory. In each test, a hot-finished rectangular steel tube of grade S275 and dimension of either RHS 200×100×5mm or RHS 200×100×12.5mm, filled with nominally C30 concrete, was connected to a pair of steel beams at one end using extended end plate connections. Each series of tests consist of four combinations of two levels of total axial load in the column, with either equal or unequal loads on the connected beams. Design calculations are performed by using a finite element heat transfer computer program (ABAQUS) in combination with the ambient temperature design method for composite columns in Eurocode 4 Part 1.1, but with modified composite cross-sectional capacities at elevated temperatures. Due to different thicknesses of the steel tubes, the two series of fire tests show different behaviour. For tests using the thinner tube, local buckling was observed. From the results of design calculations, it is found that the position of local buckling of the steel tube has direct influence on the effective length of a concrete filled column. The effective length of a concrete filled column with a pin end may be taken as the distance from the largest local buckle of the steel tube to the pin end. For tests using the thicker tube, no local buckling was observed. The results of design calculations suggest that the effective length of these columns can be determined according to the method in Eurocode 4 Part 1.2. For these test columns, this means that the column effective length should be taken as 0.7 times the column height. The design column bending moment may be taken as the unbalanced beam load acting eccentrically from the column centreline.

An experimental study of non-sway loaded and rotationally restrained steel column assemblies under fire conditions: analysis of test results and design calculations

Abstract This paper presents the results of an analysis of two series of experimental studies of non-sway loaded and rotationally restrained steel column assemblies under fire conditions. Although there have been a number of theoretical studies of restrained column behaviour in fire, the main objective of this study is to fill an important gap in experimental results. A separate paper has described the objectives of these experiments, their set up, instrumentation, an assessment of the testing system and a brief summary of test results. This paper gives results of a detailed analysis of the tests. The main focuses of this paper are variations in bending moment and effective lengths of the test columns. The main variables of these fire experiments are the level of axial load in a column, the initial column bending moment and the type of connection. It has been observed that bending moments in a rotationally restrained column change in a complicated manner under fire conditions. However, for fire resistant design, from comparisons between column failure temperatures of different tests and between recorded column failure temperatures and those calculated using BS 5950 Part 8 and Eurocode 3 Part 1.2, the initial bending moment and type of connection have negligible influences. In particular the following conclusions may be drawn: • The column failure temperature was mainly dependent on the axial load in a column and was not affected by the level of initially applied bending moment and also was not affected by the type of beam to column connection. • Using both BS 5950 Part 8 and Eurocode 3 Part 1.2 to calculate column failure temperatures or failure loads, better agreements between test and calculated results are reached when column bending moments are ignored and the column effective length ratio is taken as 0.7.

The effects of structural continuity on the fire resistance of concrete filled columns in non-sway frames

This paper presents the results of a series of theoretical studies on the effects of structural continuity on the fire resistance of composite columns of concrete filled steel tubes. In particular, these theoretical studies concern the changes in column effective lengths, axial loads and bending moments under fire conditions and the effects of these changes on column fire resistance. These studies are carried out to confirm (or otherwise) the recommendation on column effective length in Eurocode 4 Part 1.2 and to put forward additional suggestions on column axial loads and bending moments at the fire limit state. Finite element analysis is used to evaluate the non-uniform temperature distributions in composite cross-sections and to analyse the structural response at elevated temperatures. The results of these studies have validated the recommendation in Eurocode 4 Part 1.2 that the boundary conditions for continuous columns may be assumed to be built-in. They also suggest that at the fire limit state, additional axial loads in columns due to restrained thermal expansions are very small and that column bending moments become much lower than those at ambient temperature. For calculating its fire resistance, a column may be assumed to be under pure axial load equal to its ambient temperature value, the result of which may only slightly overestimate the exact column fire resistance.

木造軸組の柱の曲げモーメントに関する研究

The strain distribution is measured in column of two wood frame constructions subjected to a horizontal shear load by means of strain gauge method. One of construction specimens is a wood frame with a knee brace the other one is with a wall panel in a transom. The results are as follows: 1. The rupture strain of column is about 4000 x 10^<-6>. 2. As the joint between column and sill has some of moment resistance, the maximum bending moment of column is decreased. 3. The frame with a wall panel is more similar to a rigid frame construction than the frame with a knee brace. 4. The estimation method proposed in this paper is useful for predicting the maximum bending moment of column of these types of wood frame under a horizontal shear load.

Active vibration control of frame structures with smart structures using piezoelectric actuators (Vibration control by control of bending moments of columns)

A smart structure was tested for active vibration control of frame structures in which the bending moment of the columns was controlled by stack-type piezoelectric actuators integrated into the columns. Excitation tests were carried out for a model of a four-storey building 3.7 m in height and 2000 kg in total weight in which thirty-two piezoelectric actuators were used for bending moment control. The actuators were installed in two ways: in one case eight actuators were attached to each column of the first storey, and in the other case four actuators were attached to each column of the first and second storeys. Two control strategies, a model-matching method and the control theory, were examined for the smart structure. The tests showed that the smart structure could effectively reduce the responses of the building model, and all combinations of actuator installation method and the control strategy yielded almost the same performance.