Charts for Preliminary Selection of NU Girder Sections Based On Kansas Department of Transportation LRFD Design Guidelines for Prestressed Concrete Beams

The Kansas Department of Transportation, which currently uses a series of standard prestressed concrete beam sections referred to as K-girders for prestressed beam bridge projects, is considering a switch to use of NU I-girder sections. The NU I-Girder sections are attractive for their efficiency, but Kansas engineers are not accustomed to their use. The aim of this analytical study was to develop an Excel-based tool that can be used to produce charts that engineers can use for preliminary selection of NU I-girder section sizes and strand numbers. The calculations described herein are in compliance with KDOT Bridge Design Specifications

Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

It is of high interest, in the context of Adiabatic Quantum Computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.Comment: 7 pages, 5 figures; corrected reference

Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions

Proposed Revisions to the Strength-Reduction Factor for Axially Loaded Members

Modifications correct anomalies for nonprestressed reinforced concrete members subjected to flexure and axial load

Synthesis of Rating Methodologies for Concrete Bridges without Plans

In response to Federal Highway Administration requirements, many states are confronted with assigning load ratings to large numbers of concrete bridges that do not have plans. The AASHTO Manual for Bridge Evaluation does not specify which methodologies should be used to establish load ratings for concrete bridges without plans, nor does it clearly state how extensive the evaluation of such structures should be. To inform engineers responsible for load rating structures without plans, this report highlights available non-destructive evaluation methods that are able, to varying extents, to locate and determine the size of concrete reinforcing bars. It also provides a survey of current and emergent methodologies for establishing load ratings for concrete bridges without plans. Finally, to characterize the state-of-the-practice, results are reported from a survey distributed to state bridge engineers. There are large differences among states in terms of the specificity of established procedures and overall methodologies employed to assign load ratings to the more than 25,000 bridges without plans located in the 24 states that responded to the survey. Recommendations for approaching this problem in a rational and cost-effective manner are made after considering both published evidence and ease of implementation across large inventories of structures

Load Rating Reinforced Concrete Bridges without Plans: State-of-the-Practice

In response to Federal Highway Administration requirements, several states are in the process of ensuring all bridges within their inventories are load rated. A challenging aspect of this effort is load rating reinforced concrete bridges that have no structural plans when there are thousands of such structures within a state inventory. To inform these efforts, the literature was reviewed to identify existing methodologies and a survey was distributed to engineers at state departments of transportation throughout the United States to understand how practicing engineers approach this problem. The survey responses show there are numerous bridges in the U.S. without plans; over 25000 bridges without plans are located in the 18 states that provided responses. Concrete structures comprise 70% of such bridges. To load rate concrete bridges without plans, most responding states report primarily using engineering judgement, which may include reference to performance under existing traffic, era-specific design traffic loads, assumed material properties and reinforcement quantities, or data collected using load tests or non-destructive evaluation. Several methodologies are described and advantages/limitations of each are discussed

Entanglement in a first order quantum phase transition

The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is obtained at zero field. The spectrum is computed for a large number of spins and allows one to study the ground state entanglement properties which displays a jump of its concurrence at the critical point.Comment: 4 pages, 3 EPS figure

A Review of Research on Shear Strength Decay in Members under Load Reversals

In the design of reinforced concrete earthquake-resisting frame members, it is critical that shear distress be limited in order to ensure acceptable deformation capacity and reduce damage. Accordingly, several ACI Building Code1 provisions for beams and columns of frames categorized as “special moment frames” are aimed at minimizing shear distress. Pertinent requirements include using a capacity design approach to calculate demand, neglecting any contribution of the concrete to nominal shear strength in beams, and limiting hoop spacing to one-fourth of the effective (beams) or overall (columns) member depth. These provisions are largely based on findings from early research aimed at understanding the behavior of frame members subjected to cycles of load reversals. The aim of this paper is to review relevant research on the behavior of frame members under earthquake-type demands, beginning with the first tests of flexural members subjected to fully reversed loads and ending with the 1983 ACI Building Code2, as it was the first ACI Code edition to incorporate several provisions aimed at minimizing shear strength decay. This paper describes the basis for pertinent ACI Building Code provisions (other code or design documents were not included in this review), emphasizes the importance of low shear stress demands, and highlights reinforcement detailing options that have been shown to improve member behavior. This review should therefore be of interest to students and structural engineers, particularly those learning or involved in earthquake-resistant design of reinforced concrete structures