On stability of the Hamiltonian index under contractions and closures

The hamiltonian index of a graph $G$ is the smallest integer $k$ such that the $k$-th iterated line graph of $G$ is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an $A_G(F)$-contractible subgraph $F$ of a graph $G$ nor the closure operation performed on $G$ (if $G$ is claw-free) affects the value of the hamiltonian index of a graph $G$

Iron-Based shape memory alloy for strengthening of 113-Year bridge

This study focuses on the large-scale application of a Fe-Mn-Si shape memory alloy (Fe-SMA) for strengthening a historic roadway bridge in Petrov nad Desnou (113-years), Czech Republic. To the best of the authors’ knowledge, this is the first application of an iron-based SMA (Fe-SMA) for prestressed strengthening of a bridge. In this study, the shape memory effect (SME) of the Fe-SMA was used for the prestressed strengthening of bridge girders. A mechanical anchorage system was developed to apply multiple Fe-SMA strips to the steel girders of the bridge subjected to daily passengers and heavy trucks. The SME of the Fe-SMA was activated by heating to approximately 260 ◦C using ceramic heating pads. The test results showed that the recovery stress of the Fe-SMA strips resulted in a compressive stress of approximately –33 MPa in the lower flange of the bridge girder. This compressive stress significantly increased the yield and fatigue capacity of the strengthened girder. Before and after the strengthening, the bridge was loaded with a 45-ton crane to assess the efficiency and performance of the system. Laboratory experiments were performed to optimize the mechanical anchors and examine the feasibility of the proposed strengthening method prior to application to the bridge. Finally, long-term monitoring of the prestressed Fe-SMA plates after installation on the bridge was conducted. The results showed that the main loss of the prestressing force caused by relaxation occurred within the first 30 days after activation and was approximately 20% of the original prestress.The authors are grateful to the Ministry of Culture of the Czech Republic for funding the research work within the framework of the Program of Applied Research and Development of the National and Cultural Identity (NAKI-II) project: Methods for achieving sustainability of industrial heritage steel bridges, ID: DG18P02OVV033. The authors also thank the re-fer AG Company for providing materials used for this study

Uncertainties in Characteristic Strengths of Historic Steels Using Non-Destructive Techniques

The use of various non- or minor-destructive tests (NDTs) is often preferred to reduce the cost of structural surveys of historic structures made of cast and wrought irons or old carbon steels. This contribution thus explores the measurement errors associated with common NDT techniques and quantifies uncertainties in characteristic strength estimates based on NDTs only. It appears that a unity mean and coefficient of variation of 12% might be adopted for the measurement uncertainty of the methods under study (Brinell, Leeb, Poldi, Vickers, Rockwell). On average, the true characteristic ultimate strength is by ~15% larger than that based on many NDTs. This represents the expected gain when the characteristic value is estimated from five DTs instead of a large number of NDTs. In practice detailed reliability assessments should always be based on resul

On 1-Hamilton-connected claw-free graphs

A graph G is k-Hamilton-connected (k-hamiltonian) if G−X is Hamilton-connected (hamiltonian) for every set X ⊂ V (G) with |X| = k. In the paper, we prove that (i) every 5-connected claw-free graph with minimum degree at least 6 is 1-Hamilton-connected, (ii) every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with minimum degree at least 6 is 3-hamiltonian

Hierarchical Modelling of Uncertainty in NDT Tests of Historic Steel Bridges

Sustainable development can be supported by extending the service lives of existing road and railway bridges. Preservation and upgrade should be based on improved surveys, monitoring, reliability assessment, and strengthening methods. In the case of metallic materials, hardness methods (NDT) calibrated by a few tensile tests (DT) were shown to be associated with reasonable measurement uncertainty. This contribution discusses the current practice in assessment based on NDT results and introduces the hierarchical modelling of the measurement uncertainty in hardness tests. Preliminary results suggest that the variability of ultimate strength can hardly be estimated on the basis of NDTs only. It seems that the systematic component of measurement uncertainty has a lower coefficient of variation (3%) than the random component (8%); the variability of the latter may thus often exceed the variability of the ultimate strength of a homogeneous material.Ostrav

A Dirac theorem for trestles *

Abstract A k-subtrestle in a graph G is a 2-connected subgraph of G of maximum degree at most k. We prove a lower bound on the order of a largest ksubtrestle of G, in terms of k and the minimum degree of G. A corollary of our result is that every 2-connected graph with n vertices and minimum degree at least 2n/(k + 2) contains a spanning k-subtrestle. This corollary is an extension of Dirac's Theorem