DSpace-CRIS at TU Wienhttps://repositum.tuwien.atThe reposiTUm digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 03 Aug 2021 07:30:33 GMT2021-08-03T07:30:33Z50101The buckling sphere: A symbiosis of mechanics and geometryhttp://hdl.handle.net/20.500.12708/724Title: The buckling sphere: A symbiosis of mechanics and geometry
Authors: Mang, Herbert A.; Pavlicek, Stefan; Jia, Xin
Abstract: The basis of this work is a novel symbiosis of mechanics of solids and spherical geometry to quantify and illustrate the variation of the “non-membrane” percentage of the strain energy in the prebuckling region of linear elastic beams, arches, plates and shells, and structures assembled of such one-dimensional and two-dimensional members. The zenith angle of an arbitrary point of a specific curve on an octant of the unit sphere, called buckling sphere, is related to this energy percentage. For the limiting case of buckling from a membrane stress state this curve degenerates to a point, characterized by zero values of both spherical coordinates. For all other stress states the azimuth angle increases with the proportionally increasing load. Its magnitude at the stability limit correlates with a global quantity that depends on both the “non-membrane” deformations and the stiffness of the structure at incipient buckling. The azimuth angle is computed with the help of the so-called consistently linearized eigenproblem, which is solved by means of the Finite Element Method. This eigenvalue problem is the basis for a hypothesis for the “non-membrane” percentage of the strain energy. In the theoretical part of the paper, the concept of the buckling sphere is presented. The subsequent numerical investigation consists of four examples, referring to buckling from a membrane stress state, a pure bending stress state, and a general stress state. The practical motive for this research is the intention to investigate the influence of “non-membrane” action just before buckling on the initial postbuckling behavior of elastic structures.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7242016-01-01T00:00:00ZAssessment of solutions from the consistently linearized eigenproblem by means of finite difference approximationshttp://hdl.handle.net/20.500.12708/725Title: Assessment of solutions from the consistently linearized eigenproblem by means of finite difference approximations
Authors: Jia, Xin; Mang, Herbert A.
Abstract: The consistently linearized eigenproblem (CLE) plays an important role in stability analysis of structures. Solution of the CLE requires computation of the tangent stiffness matrix and of its first derivative with respect to a dimensionless load parameter λ, denoted as . In this paper, three approaches of computation of are discussed. They are based on (a) an analytical expression for the derivative of the element tangent stiffness matrix , (b) a load-based finite difference approximation (LBFDA), and (c) a displacement-based finite difference approximation (DBFDA). The convergence rate, the accuracy, and the computing time of the LBFDA and the DBFDA are compared, using the analytical solution as the benchmark result. The numerical investigation consists of the analysis of a circular arch subjected to a vertical point load at the vertex, and of a thrust-line arch under a uniformly distributed load. The main conclusion drawn from this work is that the DBFDA is superior to the LBFDA.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7252015-01-01T00:00:00ZThe influence of interfacial joints on the structural behavior of segmental tunnel rings subjected to ground pressurehttp://hdl.handle.net/20.500.12708/719Title: The influence of interfacial joints on the structural behavior of segmental tunnel rings subjected to ground pressure
Authors: Zhang, Jiao-Long; Schlappal, Thomas; Yuan, Yong; Mang, Herbert A.; Pichler, Bernhard
Abstract: The local behavior of segment-to-segment interfaces has a significant influence on the overall structural behavior of segmental tunnel rings subjected to ground pressure. This is quantified by means of structural simulations, combining analytical solutions of the linear theory of slender circular arches with time-dependent and nonlinear interface models for unreinforced and bolted interfaces. The time-dependent behavior results from creep of concrete and the nonlinear behavior from interfacial separation, crushing of concrete, and yielding of steel. Structural sensitivity analyses are performed with respect to the coefficient of lateral ground pressure. The influence of creep of concrete at unreinforced interfaces on the overall structural behavior is demonstrated, based on the interface models by Gladwell and Janßen. Furthermore, the elastic limits and the bearing capacities of segmental tunnel rings are quantified both for unreinforced and bolted interfaces. The corresponding interface law is based on the Bernoulli-Euler hypothesis and on linear-elastic and ideal-plastic behavior of both concrete and steel. In order to underline the reliability of the computed bearing capacities, a bearing-capacity test on a real-scale segmental tunnel ring is re-analyzed. It is concluded that (i) creep of concrete at the interfaces results in an increase of the structural displacements, while the distributions of the inner forces remain practically the same, (ii) interfacial bolts improve the serviceability of segmental tunnel rings, because they ensure the position stability of the lining, and (iii) the bearing capacity of segmental tunnel rings subjected to ground pressure can be estimated reliably, based on the combination of realistic interface models and analytical solutions of the linear theory of slender circular arches.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7192019-01-01T00:00:00ZServiceability Limits of Reinforced Concrete Hingeshttp://hdl.handle.net/20.500.12708/855Title: Serviceability Limits of Reinforced Concrete Hinges
Authors: Schlappal, Thomas; Kalliauer, Johannes; Vill, Markus; Gmainer, Susanne; Mang, Herbert A.; Eberhardsteiner, Josef; Pichler, Bernhard
Abstract: Concrete hinges are monolithic necks in reinforced concrete structures. The serviceability limit states addressed herein refer to the open question how to limit tolerable relative rotations as a function of the compressive normal force transmitted across the neck. Analytical formulae are derived in the framework of the Bernoulli-Euler hypothesis and of Hooke’s law. The usefulness of corresponding dimensionless design diagrams is assessed based on experimental data taken from the literature and on new results from structural testing of reinforced concrete hinges. This way, it is shown that the proposed mechanical model is suitable for describing serviceability limit states. Corresponding design recommendations are elaborated and exemplarily applied to verification of serviceability limit states of the reinforced concrete hinges of a recently built integral bridge. Because the reinforcement is explicitly accounted for, the tolerable relative rotations are larger than those according to the guidelines of Leonhardt and Reimann. Bending-induced tensile macrocracking beyond one half of the smallest cross-section of the neck is acceptable, because the tensile forces carried by the reinforcement ensure the required position stability of the hinges.
Description: The final publication is available via <a href="https://doi.org/10.1016/j.engstruct.2019.109861" target="_blank">https://doi.org/10.1016/j.engstruct.2019.109861</a>.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/20.500.12708/8552020-01-01T00:00:00ZTorsional warping eigenmodes of FGM beams with longitudinally varying material propertieshttp://hdl.handle.net/20.500.12708/762Title: Torsional warping eigenmodes of FGM beams with longitudinally varying material properties
Authors: Murin, Justin; Aminbaghai, Mehdi; Hrabovsky, Juraj; Balduzzi, Giuseppe; Dorn, Michael; Mang, Herbert A.
Description: The final publication is available via <a href="https://doi.org/10.1016/j.engstruct.2018.08.048" target="_blank">https://doi.org/10.1016/j.engstruct.2018.08.048</a>.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7622018-01-01T00:00:00ZSecond-order torsional warping theory considering the secondary torsion-moment deformation-effecthttp://hdl.handle.net/20.500.12708/766Title: Second-order torsional warping theory considering the secondary torsion-moment deformation-effect
Authors: Aminbaghai, Mehdi; Murin, Justin; Balduzzi, Giuseppe; Hrabovsky, Juraj; Hochreiner, Georg; Mang, Herbert A.
Abstract: In this paper, the influence of the variable axial force and of the Secondary Torsion-Moment Deformation-Effect (STMDE) on the deformations of beams due to torsional warping is investigated. The investigation is based on the second-order torsional warping theory of doubly symmetric beams with thin-walled open or closed cross-sections. The effect of the axial force on the torsional stiffness of thinwalled beams is considered according to the second-order torsional warping theory. The solutions of the underlying differential equations are used for setting up the relations, needed for application of the transfer matrix method. They are derived, considering both static and dynamic action. This enables stablishing the local element matrix of the twisted beam in the framework of the Finite Element Method (FEM). The numerical investigation comprises static and modal analyses of thinwalled beams with I cross-sections and rectangular hollow cross-sections. The results are compared with results obtained by the FEM, using solid and beam elements available in standard software.
Description: The final publication is available via <a href="https://doi.org/10.1016/j.engstruct.2017.06.023" target="_blank">https://doi.org/10.1016/j.engstruct.2017.06.023</a>.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7662017-01-01T00:00:00ZMathematical conditions for and physical meaning of a maximum of the determinant of K_T in the prebuckling regimehttp://hdl.handle.net/20.500.12708/726Title: Mathematical conditions for and physical meaning of a maximum of the determinant of K_T in the prebuckling regime
Authors: Mang, Herbert A.; Jia, Xin
Abstract: It is shown that the determinant of the tangent stiffness matrix has a maximum in the prebuckling regime if and only if the determinant of a specific linear combination of the first and the third derivative of this matrix with respect to a dimensionless load factor vanishes. The mathematical tool for this proof is the so-called consistently linearized eigenproblem in the frame of the Finite Element Method. The physical meaning of the mentioned maximum is the one of a minimum of the percentage bending energy of the total strain energy. The paper provides mathematical and physical background knowledge on numerical results that were obtained 35 years ago.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7262013-01-01T00:00:00ZHigh-dynamic compressive and tensile strength of specimens made of cementitious materialshttp://hdl.handle.net/20.500.12708/775Title: High-dynamic compressive and tensile strength of specimens made of cementitious materials
Authors: Binder, Eva; Reihsner, Roland; Yuan, Yong; Mang, Herbert A.; Pichler, Bernhard L.A.
Abstract: The strength of specimens made of cementitious materials increases with increasing loading rate. Herein, the<br />model of Fischer et al. (CCR 58, 2014, 186–200) is revisited in the context of high-dynamic compression and<br />extended to high-dynamic tension. The model is based on the assumptions (i) that cracking will start if the quasistatic<br />material strength is reached, and (ii) that the high-dynamic strength gain refers to the increase of the stress<br />during the failure process of the tested specimen. The model explains the behavior of cylindrical specimens made<br />of dry cement paste, mortar, and concrete, subjected to high-dynamic compression. It also elucidates the performance<br />of cylindrical specimens made of dry mortar and concrete, subjected to high-dynamic tension. It is<br />concluded that the high-dynamic strength gain is a structural effect and that structures will be damaged if the<br />dynamic stress exceeds the quasi-static strength, no matter how fast the stress is increased and how short the<br />stress pulse lasts.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7752020-01-01T00:00:00ZA hybrid analysis method for displacement-monitored segmented circular tunnel ringshttp://hdl.handle.net/20.500.12708/723Title: A hybrid analysis method for displacement-monitored segmented circular tunnel rings
Authors: Zhang, Jiao-Long; Vida, Christoffer; Yuan, Yong; Hellmich, Christian; Mang, Herbert A.; Pichler, Bernhard
Abstract: Segmented tunnel rings exhibit load-induced interfacial dislocations. In order to facilitate structural analysis, a hybrid method is developed and applied to a real-scale test of a segmented tunnel ring. Point loads, imposed on the tested ring, and measured interfacial discontinuities serve as input for the analysis. Moreover, the method accounts for the structural behavior of the individual segments by means of newly derived transfer relations. They represent analytical solutions of the first-order theory of slender circular arches, exhibiting constant cross-sectional properties. The tool for the development of this basically well-known theory is the principle of virtual power. Its involvement is motivated by the possibility of a mechanically consistent derivation of relations, some of which have been used for a long time without analyzing their scientific background. The validity and the usefulness of the transfer relations follow from a comparison of newly derived solutions with (i) alternative analytical solutions, (ii) Finite Element solutions, and (iii) experimental data. The computational efficiency and the usefulness of the developed hybrid method are demonstrated by structural analysis of a segmented tunnel ring. It provides valuable insight into the load-carrying behavior of the tested structure without the need to describe the nontrivial behavior of segment-to-segment interfaces.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7232017-01-01T00:00:00ZDisplacement-based finite difference approximations of derivatives of the tangent stiffness matrix with respect to the load parameterhttp://hdl.handle.net/20.500.12708/154Title: Displacement-based finite difference approximations of derivatives of the tangent stiffness matrix with respect to the load parameter
Authors: Jia, Xin; Mang, Herbert A.
Abstract: The vehicle to investigate to which extent energy‐based categorization of buckling can be linked up with spherical geometry is the so‐called consistently linearized eigenproblem. This investigation requires computation of the first and the second derivative of the tangent stiffness matrix equation image with respect to a dimensionless load parameter λ in the frame of the Finite Element Method (FEM). A finite‐difference approximation of the first derivative of equation image , redefined as a directional derivative, has proved to meet the requirements of computational efficiency and sufficient accuracy. It represents a displacement‐based finite‐difference approximation, abbreviated as DBFDA. The present work is devoted to the computation of a DBFDA of the second derivative of ˜ KT with respect to λ. For the special case of a two‐dimensional co‐rotational beam element, an analytical solution of this derivative is presented. A circular arch, subjected to a vertical point load on its apex, serves as an example for numerically assessing the usefulness of the computed DBFDAs of the first and the second derivative of equation image with respect to λ.
Description: This is the peer reviewed version of the following article: Jia, X. and Mang, H. A. (2014), Displacement-based finite difference approximations of derivatives of the tangent stiffness matrix with respect to the load parameter. Proc. Appl. Math. Mech., 14: 195–196, which has been published in final form at <a href="https://doi.org/10.1002/pamm.201410085">https://doi.org/10.1002/pamm.201410085</a>. <br />This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/20.500.12708/1542014-01-01T00:00:00Z