Torsional Provisions Research Articles

New definition for torsional irregularity based on floors rotations of reinforced concrete buildings

Earthquake investigations confirm that un-symmetric buildings suffer more damage than their symmetric counterparts. Torsional vibrations due to irregularity are one of the main factors which cause damage to buildings. Seismic codes include provisions to consider the torsional vibrations in the design of structures. However, the design of the stiff side elements may be unconservative. In this study, a total of 15 Dual system buildings were analyzed using nonlinear dynamic analysis to propose a new definition for torsional irregularity considering the effects of plan asymmetry on the earthquake response of mid-rise dual system buildings. Based on the analysis results, two new equations were derived using nonlinear regression analysis to check the torsional irregularity and the torsional amplification. Afterward, the proposed torsional irregularity provisions were compared with the torsional irregularity provisions of Europe code (EC-8), Japanese code & ASCE 7-16 code, and the results indicate that the torsional irregularity provisions of all the codes are unconservative. The current investigation proposes new equations to be used in the existing codes for torsional irregularity design considerations to improve the accuracy of the current codes' torsional irregularity provisions.

Locating optimum torsion axis in asymmetric buildings subjected to seismic excitation

Seismic torsional effects in buildings are attributed to the distance between the centres of mass of the floor slabs and the centres of rigidity of the building. Various procedures have been developed to locate these points, but their scattering over the height of the structure makes their use very difficult in implementing the code torsional provisions. As an alternative, the concept of the optimum torsion axis has been introduced: a vertical axis through which application of lateral in-plane forces would cause minimum torsional response. A convenient method is presented for the determination of this axis by means of the discrete-element approach (stiffness method) and its accuracy is demonstrated in common building structures with mass and stiffness irregularities.

Effects of Coupling between Lateral and Torsional Motions in Seismic Response of Buildings

The goal of the present paper is to study the adequacyof torsional provisions in the international buildings code (IBC)for irregular building taken into account effect of the angles ofseismic attacks. The responses of the frame-shear-wall twelvestory asymmetric building under earthquake loading by usingequivalent lateral force procedure and dynamic responsespectrum analysis have been studied intensively in this presentresearch paper. This study performs static and dynamicresponse analyses of building models under earthquake groundmotions compatible with the design response spectrum definedin the international buildings code. The dynamic responsespectrum was scaled according to the code static base shear. Thestatic and dynamic base shear with different angles of seismicattacks has been calculated. The scaling factors, angles ofseismic attacks, accidental storey torsions, storey shear,dynamic and static base shear have been evaluated here. Thetorsional moment at different storey levels for dynamic analysishas been estimated and compared with the static values.

Reinforced Concrete Beams with and without FRP Web Reinforcement under Pure Torsion

AbstractBecause of a lack of research on torsion, the Canadian design codes and AASHTO design specifications do not provide torsion provisions for the design of concrete bridge members reinforced with fiber-reinforced polymer (FRP) bars and stirrups. This paper reports on eight full-scale RC beams tested under pure torsional loading. The beams measured 4,000 mm long, 250 mm wide, and 600 mm deep. The test variables were the type and ratio of torsional reinforcement. Sand-coated glass-FRP (GFRP) and carbon-FRP (CFRP) bars and stirrups were used. The test beams included three beams totally reinforced with GFRP, three beams totally reinforced with CFRP, and two control beams reinforced with conventional steel. One beam for each of the three types was built without stirrups to determine the concrete contribution to torsional resistance. The test results indicate that all specimens failed as a result of diagonal torsional cracking. The test results were analyzed and compared with the corresponding predicted va...

Evaluating the new CAN/CSA-S806-12 torsion provisions for concrete beams with FRP reinforcements

Recently, the Canadian Standards Association proposed the first and only torsion design provisions for the case of beams with fiber reinforced polymer (FRP) reinforcements within the Canadian standard “Design and construction of building structures with fiber-reinforced polymers” (CAN/CSA-S806-12). The evaluation of the shear provisions of this code has shown more accurate and consistent shear predictions compared with other codes. The purpose of this study is to evaluate the torsion provisions of the CAN/CSA-S806-12. Such evaluation is performed considering the available experimental database from four different studies examining over 20 concrete beams with FRP or mixed (i.e. FRP and steel) reinforcements, tested under torsion. The cracking and ultimate torque as well as the failure mode predicted using the CAN/CSA-S806-12 were compared with the experimentally observed ones. The CAN/CSA-S806-12 was found to be overly conservative. Thus, modifications were proposed to the current CAN/CSA-S806-12, which were found to provide slightly better results.

Comparison of wind tunnel measurements with NBCC 2010 wind-induced torsion provisions for low- and medium-rise buildings

The aim of this study is to assess wind-induced torsional loads on low- and medium-rise buildings determined in accordance with the National Building Code of Canada (NBCC 2010). Two building models with the same horizontal dimensions but different gabled-roof angles (0° and 45°) were tested at different full-scale equivalent eave heights (6, 12, 20, 30, 40, 50, and 60 m) in open terrain exposure for several wind directions (every 15°). Wind-induced measured pressures were numerically integrated over all building surfaces and results were obtained for along-wind force, across-wind force, and torsional moment. Torsion load case (i.e., maximum torsion and corresponding shear) and shear load case (i.e., maximum shear and corresponding torsion) were evaluated to reflect the maximum actual wind load effects in the two horizontal directions (i.e., transverse and longitudinal). The evaluated torsion and shear load cases were also compared with the current torsion- and shear-related provisions in the NBCC 2010. The results demonstrated significant discrepancies between NBCC 2010 and the wind tunnel measurements regarding the evaluation of torsional wind loads on low- and medium-rise buildings. Finally, shear and torsion load cases were suggested for evaluating wind loads in the design of low- and medium-rise rectangular buildings.

Importance of seismic design accidental torsion requirements for building collapse capacity

SUMMARYSeismic ground motions induce torsional responses in buildings that can be difficult to predict. To compensate for this, most modern building codes require the consideration of accidental torsion when computing design earthquake forces. This study evaluates the influence of ASCE/SEI 7 accidental torsion seismic design requirements on the performance of 230 archetypical buildings that are designed with and without accidental torsion design provisions, taking building collapse capacity as the performance metric. The test case archetypes include a broad range of heights, gravity load levels, and plan configurations. Results show that the ASCE/SEI 7 accidental torsion provisions lead to significant changes in collapse capacity for buildings that are very torsionally flexible or asymmetric. However, only inconsequential changes in collapse capacity are observed in the buildings that are both torsionally stiff and regular in plan. Therefore, the study concludes that accidental torsion provisions are not necessary for seismic design of buildings without excessive torsional flexibility or asymmetry. Copyright © 2013 John Wiley & Sons, Ltd.

Equivalent lateral force method for buildings with setback: adequacy in elastic range

Static torsional provisions employing equivalent lateral force method (ELF) require that the earthquake-induced lateral force at each story be applied at a distance equal to design eccentricity (<TEX>$e_d$</TEX>) from a reference resistance centre of the corresponding story. Such code torsional provisions, albeit not explicitly stated, are generally believed to be applicable to the regularly asymmetric buildings. Examined herein is the applicability of such code-torsional provisions to buildings with set-back using rigid as well as flexible diaphragm model. Response of a number of set-back systems computed through ELF with static torsional provisions is compared to that by response spectrum based procedure. Influence of infill wall with a range of opening is also investigated. Results of comprehensive parametric studies suggest that the ELF may, with rational engineering judgment, be used for practical purposes taking some care of the surroundings of the setback for stiff systems in particular.

Seismic performance of torsionally stiff and flexible multi-story concentrically steel braced buildings

SUMMARY It is expected that application of torsion provisions in typical seismic codes shows different levels of efficiency for torsionally stiff and flexible buildings. This paper studies difference in performances of a range of code designed torsionally stiff and flexible five-story building models. The models are classified in eight configurations to cover common range of buildings designed with the seismic provisions of Iranian Standard 2800 as a typical seismic design code. Seismic nonlinear dynamic time history behavior of eight building models subjected to seven horizontal bi-directional design spectra compatible ground motions is investigated. These models cover a wide band of very torsionally stiff to very flexible buildings. Response parameters are element ductility demand and building story drift ratio. These criteria are appropriate indices for structural and nonstructural damages, respectively. The results indicate that the present linear static procedure of building codes such as the Iranian Standard 2800 is not generally adequate for structures with very low torsional stiffness. Copyright © 2012 John Wiley & Sons, Ltd.

Wind-induced torsional loads on low buildings

Wind-induced instantaneous pressures on low building envelopes continuously vary in temporal and spatial dimensions and this may lead to significant torsional moments on the building's lateral load resisting system. Studies on wind-induced torsional loads on low buildings are very limited. Wind-induced torsion provisions in the American Society of Civil Engineers Standard (ASCE/SEI 7-10, 2010), the National Building Code of Canada (NBCC, 2010), and the European Code (EN 1991-1-4, 2005) were reviewed and compared for three gabled-roof (18.4°) low buildings. Significant discrepancies were found among the provisions of these wind standards in evaluating torsional wind loads on low buildings. In addition, wind-induced torsional loads on low buildings have been measured in a boundary layer wind tunnel. Three low buildings, with the same plan dimensions but different gabled-roof angles (0°, 18.4°, 45°) and two different heights (i.e. full, and half eave building height) were tested in simulated open and urban terrain exposures for different wind directions (from 0° to 180° every 15°). The experimental results were compared with current wind-induced torsional load provisions. It was found that NBCC (2010) underestimates the torsional moments on low buildings significantly.

The use of Modal Rigidity Center for Assessing Code Provisions in Asymmetric Buildings

This study investigates the adequacy of the equivalent pseudo-static analysis to predict the dynamic response of eccentric, medium height buildings, in the case that the axis of masses coincides with the vertical axis (m-CR axis) passing through the modal center of rigidity. The aim of the paper is to examine whether the coincidence of the axis of masses and the m-CR axis in asymmetric structural configurations, reveals uncoupled systems, which can be analyzed by a planar lateral loading with no consideration of any torsional effects. The concept of the modal center of rigidity (m-CR) has been demonstrated by the author in earlier papers and this study presents the results of dynamic analyses of uniform mixed-bent-type multistory buildings with simple eccentricity, ranging from torsionally stiff to torsionally flexible systems, and compares these data with those of static analyses under a planar lateral loading passing through the m-CR axis. It is shown that the results (shear and moment envelops developed at the edge resisting elements) of the dynamic analyses are in close agreement with the static results obtained under a lateral force determined on the grounds of the acceleration response spectrum and having the shape of the first mode displacements of the symmetrical counterpart structure. This response is similar to that of single story systems, when there is a coincidence of the centers of mass and stiffness and no torsional oscillations are developed under a translatory ground motion. Therefore, as in one-story eccentric structures the center of stiffness is used as a reference point for implementing the code torsional provisions, in the same way, in multi-story buildings, the m-CR axis can be used as reference axis for implementing the same code provisions.

Seismic nonlinear static new method of spatial asymmetric multi‐storey reinforced concrete buildings

SUMMARYIn order to obtain the seismic demands of spatial asymmetric multi‐storey reinforced concrete (r/c) buildings, a new seismic nonlinear static (pushover) procedure that uses inelastic response acceleration spectra is presented in this paper. The latter makes use of the optimum equivalent nonlinear single degree of freedom system, which is used to represent the general spatial asymmetric multi‐storey r/c building. For each asymmetric multi‐storey building, a total of 12 suitable nonlinear static analyses are needed according to the new proposed procedure, whereas at least 96 suitable nonlinear dynamic analyses are required in the case of nonlinear response history analysis (NLRHA), respectively. In addition, the present paper provides answers to a series of further questions with reference to the spatial action of the two horizontal seismic components in the static nonlinear (pushover) analyses, as well as to the documented calculation of the available behaviour factor of the asymmetric multi‐storey r/c building. According to the paper, this new proposed seismic nonlinear static procedure is a natural extension of the documented equivalent seismic static linear (simplified spectral) method that is recommended by the established contemporary seismic codes, with reference to torsional provisions. Finally, through a restricted parametric analysis carried out in this paper, a relevant numerical example of a two‐storey r/c building is presented for illustration purposes, where the seismic demand floor inelastic displacements are compared with the respective displacements obtained by the NLRHA. Consequently, the new proposed seismic nonlinear static procedure, which uses inelastic response acceleration spectra, can reliably evaluate the extreme values of floor inelastic displacements (on the flexible and stiff side of the building), as is shown by the above comparisons. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Modal rigidity center: it's use for assessing elastic torsion in asymmetric buildings

The vertical axis through the modal center of rigidity (m-CR) is used for interpreting the code torsional provisions in the design of eccentric multi-story building structures. The concept of m-CR has been demonstrated by the author in an earlier paper and the particular feature of this point is that when the vertical line of the centers of mass at the floor levels is passing through m-CR, minimum base torsion is developed. For this reason the aforesaid axis is used as reference axis for implementing the code provisions required by the equivalent static analysis. The study examines uniform mixed-bent-type multistory buildings with simple eccentricity, ranging from torsionally stiff to torsionally flexible systems. Using the results of a dynamic response spectrum analysis as a basis for comparisons, it is shown that the results of the code static design are on the safe side in torsionally stiff buildings, but unable to predict the required strength of bents on the stiff side of systems with a predominantly torsional response. Suggestions are made for improving the code provisions in such cases.

Practical calculation of the torsional stiffness radius of multistorey tall buildings

AbstractThe present paper refers to the definition of the torsional stiffness radii of multistorey tall buildings using both the continuous and the discrete model of the structure. The magnitude of the torsional stiffness radius of a building is the most important structural characteristic in order to explain the torsional behaviour of a building during an earthquake as it directly affects the building's torsional flexibility. The importance of the torsional flexibility of buildings is recognized by contemporary Seismic Codes that propose a grid of torsional provisions in order to avoid soft‐storey operation due to floor torsional vibrations around a vertical axis. However, contrary to single‐storey buildings, the torsional stiffness radius of multistorey buildings is not defined directly because both the translational and torsional stiffness of these buildings are expressed in matrix form. In the present paper, this weakness has been overcome using the continuous model of the structure, from which the torsional stiffness radius of a general monosymmetric multistorey tall system arises via a closed mathematical equation. The discrete model of the structure has numerically verified this closed mathematical equation. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Effect of Overstrength on the Seismic Behaviour of Multi-Storey Regularly Asymmetric Buildings

In past years, seismic response of asymmetric structures has been frequently analysed by means of single-storey models, because of their simplicity and low computational cost. However, it is widely believed that use of more realistic multi-storey models is needed in order to investigate effects of some system characteristics (such as overstrength, higher modes of vibration, etc.) that make behaviour of multi-storey schemes different from that of single-storey systems. This paper examines effects of the overstrength in element cross-sections on the seismic behaviour of multi-storey asymmetric buildings. It is shown that in actual buildings this characteristic, which is sometimes very variable both in plan and along the height of the building, may lead to distributions of ductility demands different from those expected according to the results from single-storey models. Consequently, torsional provisions, which aim at reducing ductility demands of single-storey asymmetric systems to those of the corresponding torsionally balanced systems, should be re-checked in light of the behaviour of realistic multi-storey buildings.

Analysis of Coupled Lateral-Torsional-Pounding Responses of One-Storey Asymmetric Adjacent Structures Subjected to Bi-Directional Ground Motions Part I: Uniform Ground Motion Input

This paper presents results of a parametric study of seismic induced lateral-torsional-pounding responses of an asymmetric and a symmetric one-storey system subjected to bi-directional ground motion. The properties of the symmetric model are fixed, while the vibration frequency and eccentricity of the asymmetric model vary in the numerical computation. 20 sets of bi-directional horizontal earthquake ground motion time histories are numerically simulated for the analysis. All the simulated motions are compatible individually with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5g. Ensemble mean peak responses of the two systems to the 20 sets ground motions are estimated. Both linear elastic and nonlinear inelastic behaviours are studied. Effects of torsional stiffness, structural vibration frequency, eccentricities, and initial gap between two structures are investigated. Numerical results are presented in dimensionless form and compared with the code torsional provisions. In this paper, the input ground motion time histories at all the structural supports are assumed to be uniform. An accompany paper of this study is devoted to discuss the effect of the spatially varying ground motion on coupled lateral-torsional-pounding responses of the adjacent structures (Hao and Gong 2005).

A Design-Oriented Approach to Strength Distribution in Single-Story Asymmetric Systems with Elements Having Strength-Dependent Stiffness

Recent studies have pointed out that the stiffness and strength of many lateral force-resisting elements (LFRE) are dependent parameters. This paper examines the implication of this finding in the distribution of design strength among LFRE. It is shown here that in order to minimize torsional response, one should use a strength/stiffness distribution combination that leads to the location of the center of strength, CV, and the center of stiffness, CR, on opposite sides of the center of mass, CM. A design-oriented strength-allocation procedure to arrive at such strength and stiffness distributions is presented. Its effectiveness in minimizing torsional response is demonstrated through comparison of seismic performance of structures having strength allocated on the basis of the proposed procedure with those following current UBC and EC8 torsional provisions.

Seismic Analysis of Asymmetric Buildings with Flexible Floor Diaphragms

Even though a rigid floor diaphragm is a good assumption for seismic analysis of most buildings, several building configurations may exhibit significant flexibility in floor diaphragm. However, the issue of static seismic analysis of such buildings for torsional provisions of codes has not been addressed in the literature. Besides, the concept of center of rigidity needs to be formulated for buildings with flexible floor diaphragms. In this paper, the definition of center of rigidity for rigid floor diaphragm buildings has been extended to unsymmetrical buildings with flexible floors. A superposition-based analysis procedure is proposed to implement code-specified torsional provisions for buildings with flexible floor diaphragms. The procedure suggested considers amplification of static eccentricity as well as accidental eccentricity. The proposed approach is applicable to orthogonal as well as nonorthogonal unsymmetrical buildings and accounts for all possible definitions of center of rigidity.

Design for Torsion and Shear in Prestressed Concrete Flexural Members

This paper presents a unified method for the torsion and shear design of prestressed and non-prestressed concrete flexural members, and provides an alternative method to the provisions of the ACI Building Code. The method applies to rectangular, box and flanged sections such as L-beams. The approach depends on subdividing the given section into component rectangles. Equations are given for the shear and torsion web reinforcement of beams as well as expressions for the minimum reinforcement and required amount of longitudinal steel. The design method is illustrated with a fully worked numerical example of a spandrel beam. The shear and torsion provisions in the Sixth Edition of the PCI Design Handbook are based on the principles outlined in this paper, which will also be referenced in ACI 318-05. The design method has been shown to be reliable, accurate and easy to use.

Evaluation of dynamic eccentricity by considering soil–structure interaction: a proposal for seismic design codes

A stochastic approach is adopted for the linear analysis of three-dimensional dynamic soil–structure interaction of asymmetric buildings in the time domain to evaluate the dynamic eccentricity of torsional provisions in seismic building codes. The asymmetric system is idealized as a single-storey building resting on different soil conditions. The soil beneath the superstructure is modeled as linear elastic solid elements, and the effect of the surrounded unbounded soil is considered by imposing viscous boundary elements along the sides of soil block. The contact surface between foundation mat and solid elements of soil is discretized by linear plane interface elements with zero thickness. The interface element is further developed to accommodate the proper compatibility between rigid foundation and soil. However, the method can be adapted to include the effects of soil non-linearity and slip as well as the separation of the foundation mat on the response of asymmetric systems. The response of soil–structure interaction of torsionally coupled system under an ensemble of artificial non-stationary earthquake records has been reviewed to verify the dynamic eccentricity of torsional provisions in seismic building codes. The dynamic eccentricity obtained from this study is compare to the dynamic eccentricity of Uniform Building Code (UBC, 97) and Eurocode (EC-8, 94). By taking into consideration the role of the important structural parameters and the soil–structure interaction effects, a simple equation for the design eccentricity is proposed.