Inelastic Torsion Research Articles

Verification of seismic enforced-displacement pushover procedure on torsionally flexible, asymmetric, multi-storey r/c buildings

A recently proposed direct Displacement-based procedure of nonlinear static (pushover) analysis on multi-storey reinforced concrete (r/c) buildings is verified here against the results of Nonlinear Response History Analysis. An asymmetric, regular in elevation, torsionally flexible, multi-storey r/c building designed according to Eurocode EN 1998 is investigated. Taking fully into account the inelastic torsion and the higher mode effects, as well as the P-Delta effects, the proposed procedure applies a pattern of seismic floor enforced-displacements along on the “Capable Near Collapse Principal Axes of the building”, aiming at Near Collapse state.  The envelope of the results of sixteen final non-linear static analyses on the investigated building shows that the main aspects of the spatial seismic action effects can be safely captured by the proposed procedure, especially regarding the inelastic interstorey drift ratios, as well as the plastic mechanism of the building.

A Comparative Shaking Table Study on Inelastic Torsion and Torsional Performance of Conventional Thermal Power Plant Main Building and Thermal Power Plant Main Building with the Buckling-Restrained Braces

A Comparative Shaking Table Study on Inelastic Torsion and Torsional Performance of Conventional Thermal Power Plant Main Building and Thermal Power Plant Main Building with the Buckling-Restrained Braces

Shake table tests of seven-story reinforced concrete structures with torsional irregularities: Test program and datasets

The shake table tests presented in this article aims to explore seismic displacement demands for existing reinforced concrete buildings resulting from inelastic torsion associated with different sources of irregularities. Two half-scale seven-story reinforced concrete structures were subjected to unidirectional earthquake excitations on the shake table at the National Center for Research on Earthquake Engineering (NCREE) Tainan laboratory. The specimens reflected structural weaknesses of buildings which collapsed during the Meinong earthquake in Taiwan. This data paper presents an overview of the project as well as the organization of obtained test datasets. The data are available for public use under the Designsafe-CI project “Shake table tests of seven-story reinforced concrete structures with torsional irregularities.”

Effect of steel braces buckling on inelastic torsion and design prevention of steel braced concrete frame structure

The influence of steel brace buckling on inelastic torsion of steel braced concrete frame structure is studied. On the background of a project, the shaking table test results of two structural models with ordinary steel brace (BRC) and buckling-restrained brace (BRB) are compared, and the inelastic torsion and sudden increase caused by steel brace buckling is confirmed. Finite element analysis models with BRC, BRB and floor load eccentricity are established, in which the restoring force model of steel brace considered the asymmetry of tensile and compressive bearing capacity, and the concrete beam and column members considered M3 and PMM hinge respectively to study the process and characteristics of the influence of BRC buckling on the nonlinear torsion of the structure. The mechanism of inelastic torsion of steel braced concrete frame structure (F-BRC) induced by BRC buckling is studied, and the principle that the dynamic BRC buckling makes the structure acquire inertial force as well as inertial torsion moment is found out. It is more reasonable to explain the inelastic torsional process and the mechanical characteristics of the structure by this principle than by the theory of strength eccentricity and stiffness eccentricity. Finally, based on the principle, six numerical examples with different brace schemes under the excitation of eight earthquake waves are calculated, and the changing rules of the torsional moment are studied. Some design limitation suggestions are put forward.

A Phenomenological Study on Inelastic Torsion Caused By Nonlinear Behavior Changes during Earthquake Excitations

Torsion of many symmetric structures, which were designed based on the seismic codes, is due to their asymmetricity induced during inelastic behavior. Although the structure was designed symmetrically assuming elastic based criteria, different factors such as material inconsistency in structure, construction details discrepancy and construction errors may result in asymmetric behavior in inelastic deformation range. So far, these considerations have been rarely contemplated in previous published investigations and should be studied regarding the importance of irregularity in increase of seismic demand of structures in the inelastic range. In this paper, as the first step, the asymmetry and irregularity in plan due to non-similar inelastic characteristics with respect to axis passing through center of gravity as well as the effect and importance of each irregularity factors are studied by changing the excitation properties applying to one-storey one-bay steel structures. This simplified structure is chosen due to studying and illustrating the absolute effect of this kind of irregularity in which higher mode effect is eliminated. The results show that the behavior of a structure with inelastic asymmetry is completely different from the structure with elastic asymmetry. As for inelastic asymmetry structure, although the translational and rotational oscillations before yielding were uncouple, these DOFs after yielding become coupled until reaching the terminal rotation point (rotation reaches a constant value) and then become uncoupled, i.e., again oscillated symmetrically. This behavior is different from the structures with elastic asymmetricity, in which the translational and rotational movements being coupled during all the excitation time. This effect has not been recognized in previews studies on inelastic behavior of initially elastic symmetry buildings. The study of these behaviors aids the designer to choose the appropriate rehabilitation method for a vulnerable irregular structure.

Torsion Profiling of Proteins Using Magnetic Particles

We report a method to profile the torsional spring properties of proteins as a function of the angle of rotation. The torque is applied by superparamagnetic particles and has been calibrated while taking account of the magnetization dynamics of the particles. We record and compare the torsional profiles of single Protein G-Immunoglobulin G (IgG) and IgG-IgG complexes, sandwiched between a substrate and a superparamagnetic particle, for torques in the range between 0.5 × 103 and 5 × 103 pN·nm. Both molecular systems show torsional stiffening for increasing rotation angle, but the elastic and inelastic torsion stiffnesses are remarkably different. We interpret the results in terms of the structural properties of the molecules. The torsion profiling technique opens new dimensions for research on biomolecular characterization and for research on bio-nanomechanical structure-function relationships.

Secondary torsional moment deformation effect in inelastic nonuniform torsion of bars of doubly symmetric cross section by BEM

In this paper a boundary element method is developed for the inelastic nonuniform torsional problem of simply or multiply connected prismatic bars of arbitrarily shaped doubly symmetric cross section, taking into account the secondary torsional moment deformation effect. The bar is subjected to arbitrarily distributed or concentrated torsional loading along its length, while its edges are subjected to the most general torsional boundary conditions. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed plasticity model exploiting three dimensional material constitutive laws and numerical integration over the cross sections. An incremental–iterative solution strategy is adopted to resolve the elastic and plastic part of stress resultants along with an efficient iterative process to integrate the inelastic rate equations. The one dimensional primary angle of twist per unit length, a two dimensional secondary warping function and a scalar torsional shear correction factor are employed to account for the secondary torsional moment deformation effect. The latter is computed employing an energy approach under elastic conditions. Three boundary value problems with respect to (i) the primary warping function, (ii) the secondary warping one and (iii) the total angle of twist coupled with its primary part per unit length are formulated and numerically solved employing the boundary element method. Domain discretization is required only for the third problem, while shear locking is avoided through the developed numerical technique. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy.

Inelastic nonuniform torsion of bars of doubly symmetric cross section by BEM

In this paper a boundary element method is developed for the inelastic nonuniform torsional problem of simply or multiply connected cylindrical bars of arbitrarily shaped doubly symmetric cross section taking into account the effect of warping shear stresses. The bar is subjected to arbitrarily distributed or concentrated torsional loading along its length, while its edges are subjected to the most general torsional boundary conditions. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed plasticity model exploiting three dimensional material constitutive laws and numerical integration over the cross sections. An incremental – iterative solution strategy is adopted to restore global equilibrium along with an efficient iterative process to integrate the inelastic rate equations. Three boundary value problems with respect to the variable along the bar axis angle of twist, to the primary and to the secondary warping functions are formulated and solved employing the boundary element method. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy.

Effect of axial restraint in composite bars under nonlinear inelastic uniform torsion by BEM

In this paper, the effect of axial restraint in the elastic–plastic uniform torsion analysis of cylindrical bars taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The bar is axially elastically supported at the centroids of its end cross sections, treating the cases of free axial boundary conditions (vanishing axial force), restrained axial shortening or given axial force as special ones. The cross section of the bar is an arbitrary doubly symmetric composite one, consisting of materials in contact, each of which can surround a finite number of inclusions, while the case of a homogeneous cross section is treated as a special one. The stress–strain relationships for the materials are assumed to be elastic–plastic-strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometrically nonlinear term, often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross section is evaluated directly employing the primary warping function of the cross section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals. The significant increase of the torsional rigidity of the bar and the arising axial force due to the axial restraint are concluded.

Nonlinear inelastic uniform torsion of composite bars by BEM

In this paper the elastic–plastic uniform torsion analysis of composite cylindrical bars of arbitrary cross-section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationships for the materials are assumed to be elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/elastic moment ratio in uniform inelastic torsion is demonstrated.

Nonlinear inelastic uniform torsion of bars by BEM

In this paper the elastic–plastic uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationship for the material is assumed to be elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/elastic moment ratio in uniform inelastic torsion is demonstrated. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals.

The Role of Inelastic Torsion in the Determination of Residual Deformations

Recent developments in performance-based seismic design and assessment approaches have emphasized the importance of properly assessing and limiting the residual (permanent) deformations typically sustained by a structure after a seismic event, even when designed according to current code provisions. The performance-based design framework for residual deformations, previously developed by the authors for 2-D regular structures, is further extended to the behavior of 3-D irregular (asymmetric in-plan) buildings. The seismic response of a set of single-story systems, comprising of seismic resisting frames, and modeled to represent alternative materials (concrete or steel), is investigated under uni-directional earthquake loading excitations. Different layouts in plan, leading to either torsionally unrestrained or restrained systems, are considered. The influence of varying torsional restraint is investigated to define how residual diaphragm rotations and center-of-mass displacements are affected by changing levels of stiffness and strength, or mass eccentricity. From these findings additions to the previously proposed estimation procedure are made, with a specific example used to validate the suggested changes. Finally, a general example is developed based on currently available methods of evaluating maximum torsion response. It is suggested that such approaches are likely to be insufficient as they do not explicitly define how seismic-resisting elements are influenced by inelastic torsional response.

Inelastic torsion of multistorey buildings under earthquake excitations

The inelastic earthquake response of eccentric, multistorey, frame-type, reinforced concrete buildings is investigated using three- and five-storey models, subjected to a set of 10, two-component, semi-artificial motions, generated to match the design spectrum. Buildings designed according to the EC8 as well as the UBC-97 code were included in the investigation. It is found that contrary to what the simplified one-storey, typical, shear-beam models predict, the so-called ‘flexible’ side frames exhibit higher ductility demands than the ‘stiff’ side frames. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. This investigation constitutes one of the first attempts to study the problem of inelastic torsion by means of realistic, multistorey inelastic building models. Additional studies with similar or even more refined idealizations will certainly be required to arrive at definite results and recommendations for possible code revisions. Copyright © 2005 John Wiley & Sons, Ltd.

Inelastic Torsion for Preliminary Seismic Design

Because of torsion, the demanded strength and interstory drift at certain parts of the structure increase above those required by just translational deformation. These effects differ for elastic and inelastic behavior, tending to be larger when inelastic behavior involves a torsional mechanism of the structure. A clear contradiction exists in the present consideration of torsion effects during the design process because torsion effects are elastically considered, while most of the seismic code design methodology is based on the safety level earthquake (EQ). This paper shows that for a special class of buildings, the reduction in the building strength resulting from inelastic torsion can be obtained using the classical theorems of plastic analysis. By analyzing an auxiliary structure, a simplified formula for the reduction in strength due to inelastic torsion is obtained. Using this simplified formula, guidelines to control inelastic torsion during preliminary seismic design are offered.

Inelastic Torsion of Steel I-Beams

A large twist rotation model for the nonlinear inelastic analysis of the nonuniform torsion of I-section beams is presented in this paper. A finite-element procedure has been developed based on the model. The nonlinear equilibrium equations of beams in nonuniform torsion including the effect of the large twist rotation have been derived. The elastic-plastic behavior of beams in nonuniform torsion is studied using the finite-element procedure and the results are compared with tests. It is found that I-section beams have much larger torsional capacities than can be predicted by linear plastic collapse analysis, and that torsional failure occurs not by the formation of a mechanism but by the tensile rupture of the flanges. A method is proposed for calculating the full plastic nonuniform torque for practical design purposes.

Inelastic Bending and Torsion of Steel I‐Beams

The inelastic combined bending and torsion of I‐section beams is investigated in this paper using the finite‐element method. The elastic‐plastic load‐deformation relationships of beams under combined bending and torsion are determined by taking into account the effects of large deformations, material inelasticity, and initial conditions of residual stresses and geometric imperfections. The interactions between in‐plane bending, flexural‐torsional buckling, and torsion are studied. The effects of secondary bending actions about the minor axis caused by torsional rotations are important for the interaction between bending (with flexural‐torsional buckling) and destabilizing torsion. Interaction equations for the design of I‐section beams against combined bending and free torsion, and against combined flexural‐torsional buckling and destabilizing torsion, are proposed. It is found that a commonly quoted circular interaction equation for combined bending and torsion does not always provide a true lower bound for I‐section beams.

On large-strain inelastic torsion of glassy polymers

Large-strain elastic-viscoplastic torsion of circular tubes and solid bars of glassy polymers is investigated under fixed-end as well as free-end conditions. The analysis employs a large inelastic deformation model for glassy polymers that incorporates a recently proposed constitutive law for the so-called orientational hardening, which is identified to play a key role in the description of the deformation-induced anisotropy in glassy polymers. The solution of the problem is obtained numerically by means of simple, special purpose finite elements. Results are presented in terms of predicted torque vs twist curves for all cases. Furthermore, we present axial force vs twist curves for fixed-end torsion or elongation vs twist curves for free-end torsion, both phenomena being associated with anisotropic hardening. In some cases, the predicted stress distributions are also given. The differences between free-end and fixed-end torsion are emphasized. Numerical results predicted by the model are compared with experimental results for polycarbonate found in the literature.

Inelastic torsion and strain recovery of metallic glasses

Heating-induced strain recovery of metallic glasses Ni 60Nb 40, Fe 81B 14Si 5 and Co 87Nb 5Zr 8 inelastically predeformed by torsion at various temperatures is investigated. It is determined that strain recovery measurements are a fine indicator of deformation mode. Inhomogeneous deformation results in formation of long-range internal stress fields and always leads to partial strain recovery on heating. Homogeneous deformation is accompanied by formation of local internal microstresses which are the reason of complete strain recovery. The transition from inhomogeneous to homogeneous deformation mode is determined mainly not by homologous testing temperature but by preliminary heat treatment.

Inelastic uniform torsion of steel members

This paper develops a mitre model for the shear strain distribution in steel members under uniform torsion. The mitre model provides reasonable approximations for the shear stress distributions, except near re-entrant corners, and accurate predictions of the fully plastic uniform torque. The elastic torque-twist relationship is predicted with high accuracy, and the inelastic relationship with reasonable accuracy. The mitre model uses a simple approximation to the shear strain distribution caused by uniform torsion. It can be expected to provide a relatively simple method of predicting the inelastic behaviour of steel members when uniform torsion acts in combination with axial force and bending moment.

Inelastic nonuniform torsion of steel I-beams

Abstract This paper presents a finite element model for analysing the elastic-plastic nonuniform torsion behaviour of thin-walled steel I-beams. The model uses Vlasov's warping strain model to represent warping torsion, and a mitre model for uniform torsion. The mitre model allows the representation at the tips of flanges of the transverse uniform torsion shear stresses. For elastic-plastic analysis, the incremental theory of plasticity is adopted, employing the Prandtl-Reuss flow rule and the von Mises yield criterion. The material state determination algorithm and the variable arc-length method are also employed to improve the accuracy and reliability of the solutions. The numerical integration over the cross-section is carried out by dividing it into a number of triangular areas and then applying the no-bias area-coordinate Gaussian numerical integration scheme. The numerical examples provided show that good agreement is obtained with predictions of other models of inelastic nonuniform torsion and the experimental results by using the present finite element model. It is also concluded that the present model can predict more realistic results at higher rotations than other models which ignore the transverse uniform torsion shear stresses.