Modeling of Disc Spring Self-Centering Energy Dissipation Braces from Inactive State to Design Limit State

This paper presents a solution for the problem concerning the behaviour of a steel lattice girder subjected to dynamic load pulses. The theory of shakedown is used in the analysis. It is assumed that such loads cause a non-elastic response which includes dissipation of energy causing deformations and residual forces developed in the structural members of the girder. At a certain intensity of these forces, the girder can react to subsequent load pulses without further dissipation of energy, behaving in the elastic region after shakedown. This condition is referred to as adaptation of the structure to assumed cyclic loading. Elastic shakedown limit is determined through a direct analysis of the girder's dynamic behaviour, i.e. by checking if energy dissipation decreases with loading cycles. This gives the number of load applications after which no further increase of the energy dissipation is observed. The existing permanent deformations persist and residual forces remain in the same state. The analysis takes into account the possibility that compressed members can buckle which may result in non-elastic, longitudinal and transverse vibrations of these members. Non-linear geometry of members is taken into account. Then a perfectly elastic-viscoplastic model of the material is used. The main goal is to determine the state of the non-elastic movements of the girder joints and the residual internal forces developed in the girder members after each load application. The values obtained in this way serve as the basis for describing the next loading cycle. It is possible to use the approach presented in the paper to evaluate the effects of accidental loads. Then it is checked whether a small number of repetitions of accidental load would result in exceeding the serviceability limit state criteria of the maximum permanent deformation or displacement and/or strain amplitudes. If so, the magnitude of accidental load is greater than the elastic shakedown limit. Some examples are given to illustrate the application of the theory of shakedown.

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Predicting Resistance of Spherical-Type LNG Carrier Structures to Ship Collisions

Marine Technology and SNAME News ◽

10.5957/mt1.2002.39.2.86 ◽

2002 ◽

Vol 39 (02) ◽

pp. 86-94

Author(s):

Jeom Kee Paik ◽

Ick Hung Choe ◽

Silvia Rivas

Keyword(s):

Energy Dissipation ◽

Kinetic Energy ◽

Limit State ◽

Load Condition ◽

Steel Structures ◽

Initial Kinetic Energy ◽

Ultimate Limit State ◽

Assessment Procedure ◽

Limit States ◽

Spherical Type

The modern design of steel structures uses limit states classified into four types, namely, serviceability limit state, ultimate limit state, fatigue limit state and accidental limit state. The aim of this paper is to propose and illustrate a procedure to assess the capability of a spherical-type LNG carrier of 135 000 m3 to resist ship collisions. An assessment procedure based on the energy dissipation capability relating to structural crashworthiness can, in this case, be applied to protect spherical LNG cargo tanks from fracture in minor or moderate collision accidents as shown in the paper. In the procedures developed, while the loss of kinetic energy during the collision accident is approximately estimated by applying the momentum equilibrium of the two implicated ships, a series of relatively sophisticated numerical computations is under- taken to simulate the structural crashworthiness of the object ship in the full load condition at standstill, varying the loading conditions and types of the striking ship, when the LNG carrier side structure is considered to be struck by the bow of either a VLCC or another LNG carrier. Based on the computed results, the collision resistance indices (CRI), which in the present study are defined as a function of the ratio of the structural energy dissipation capability to the initial kinetic energy loss, are calculated for the object ship for various collision scenarios. Some important insights useful for preventing collision damage of the spherical LNG cargo tanks of the ship are also discussed.

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Ultimate vs. serviceability limit state in designing bridge energy dissipation devices

Earthquake Engineering Frontiers in the New Millennium ◽

10.1201/9780203758984-42 ◽

2017 ◽

pp. 293-297 ◽

Cited By ~ 1

Author(s):

F. Casciati ◽

L. Faravelli ◽

M. Battaini

Keyword(s):

Energy Dissipation ◽

Limit State ◽

Serviceability Limit State ◽

Energy Dissipation Devices

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Energy dissipation across the front of shock wave in rheological materials filled with second phase inclusions

Journal de Physique IV (Proceedings) ◽

10.1051/jp4:2006134135 ◽

2006 ◽

Vol 134 ◽

pp. 883-887

Author(s):

Jian-kang Chen ◽

Jue Zhu

Keyword(s):

Shock Wave ◽

Energy Dissipation ◽

Second Phase

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Flexural design of precast, prestressed ultra-high-performance concrete members

PCI Journal ◽

10.15554/pcij65.6-02 ◽

2020 ◽

Vol 65 (6) ◽

pp. 35-61

Author(s):

Chungwook Sim ◽

Maher Tadros ◽

David Gee ◽

Micheal Asaad

Keyword(s):

Prestressed Concrete ◽

High Performance ◽

High Performance Concrete ◽

Limit State ◽

Design Guidelines ◽

Design Tool ◽

Supplementary Cementitious Materials ◽

Ultra High Performance Concrete ◽

Concrete Members ◽

Cylinder Strength

Ultra-high-performance concrete (UHPC) is a special concrete mixture with outstanding mechanical and durability characteristics. It is a mixture of portland cement, supplementary cementitious materials, sand, and high-strength, high-aspect-ratio microfibers. In this paper, the authors propose flexural design guidelines for precast, prestressed concrete members made with concrete mixtures developed by precasters to meet minimum specific characteristics qualifying it to be called PCI-UHPC. Minimum specified cylinder strength is 10 ksi (69 MPa) at prestress release and 18 ksi (124 MPa) at the time the member is placed in service, typically 28 days. Minimum flexural cracking and tensile strengths of 1.5 and 2 ksi (10 and 14 MPa), respectively, according to ASTM C1609 testing specifications are required. In addition, strain-hardening and ductility requirements are specified. Tensile properties are shown to be more important for structural optimization than cylinder strength. Both building and bridge products are considered because the paper is focused on capacity rather than demand. Both service limit state and strength limit state are covered. When the contribution of fibers to capacity should be included and when they may be ignored is shown. It is further shown that the traditional equivalent rectangular stress block in compression can still be used to produce satisfactory results in prestressed concrete members. A spreadsheet workbook is offered online as a design tool. It is valid for multilayers of concrete of different strengths, rows of reinforcing bars of different grades, and prestressing strands. It produces moment-curvature diagrams and flexural capacity at ultimate strain. A fully worked-out example of a 250 ft (76.2 m) span decked I-beam of optimized shape is given.

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The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.1.05 ◽

2020 ◽

pp. 60-73

Author(s):

Yu V Nemirovskii ◽

S V Tikhonov

Keyword(s):

General Solution ◽

Least Squares ◽

Nonlinear Differential Equations ◽

Limit State ◽

Algebraic Equations ◽

Method Of Least Squares ◽

Elasticity Limit ◽

Limit Values ◽

Symbolic Calculations ◽

Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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