Thesis (Professional Degree)--University of Missouri, School of Mines and Metallurgy, 1938. / The entire thesis text is included in file. Typescript. Title from title screen of thesis/dissertation PDF file (viewed April 27, 2010) Includes bibliographical references (p. 28).

This thesis presents a method which facilitates rapid determination of the cable tension in suspension bridges. A set of tables and curves is included for use in the application of the method. The method is valid for suspension bridges with stiffening girders or trusses either hinged at the supports or continuous. A modified superposition method is discussed and the use of influence lines for cable tension in non-linear suspension bridges is demonstrated. A derivation of the suspension bridge equations is included and various refinements in the theory are discussed. A computer program to analyse suspension bridges was written as an aid in the research and for the purpose of testing the manual method proposed. A description of the program is included along with Its Fortran listing. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Master of Science

Master of Science

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

Suspension bridges possess a number of advantages, allowing overlapping average and large spans. The basic disadvantage of suspension bridges can be considered their increased deformability, particularly under the action of non-symmetrical and local loads. Deformability depends, in general, on the kinematical character of displacements of a flexible suspension cable. Required rigidity of suspension bridges is achieved, by increasing the height, and consequently the weight of a stiffening girder, by diagonal suspenders or two-cable or combined prestressed systems. Reduction of kinematical displacements of the main cable can also be achieved by a reduction of the sag-to-span ratio, but the smaller the sag of a cable, the greater are the cable thrust forces and the required cross-sectional areas of the cables. One of the ways of suspension systems stabilization is giving certain bending stiffness to the suspension cables. Such structural solution with success is used in suspension roofs. With the aim to increase the stability of suspension bridges the author proposes to use the finite bending stiffness cables. The cables can be made of standard steel profiles or have composite sections. Conventionally, they are called as “rigid cables”. To verify this solution, the investigation on behavior of suspension bridges with rigid cables under loading has to be undertaken.

Suspension bridges possess a number of advantages, allowing overlapping average and large spans. The basic disadvantage of suspension bridges can be considered their increased deformability, particularly under the action of non-symmetrical and local loads. Deformability depends, in general, on the kinematical character of displacements of a flexible suspension cable. Required rigidity of suspension bridges is achieved, by increasing the height, and consequently the weight of a stiffening girder, by diagonal suspenders or two-cable or combined prestressed systems. Reduction of kinematical displacements of the main cable can also be achieved by a reduction of the sag-to-span ratio, but the smaller the sag of a cable, the greater are the cable thrust forces and the required cross-sectional areas of the cables. One of the ways of suspension systems stabilization is giving certain bending stiffness to the suspension cables. Such structural solution with success is used in suspension roofs. With the aim to increase the stability of suspension bridges the author proposes to use the finite bending stiffness cables. The cables can be made of standard steel profiles or have composite sections. Conventionally, they are called as “rigid cables”. To verify this solution, the investigation on behavior of suspension bridges with rigid cables under loading has to be undertaken.

The reliability of the main cable of a suspension bridge is crucial to the reliability of the entire bridge. Throughout the life of a suspension bridge, its main cables are subject to corrosion due to various factors, and the deterioration of strength is a slowly evolving and dynamic process. The goal of this research is to find the pattern of how the strength of steel wires inside a suspension bridge cable changes with time. Two methodologies are proposed based on the analysis of five data sets which were collected by testing pristine wires, artificially corroded wires, and wires taken from three suspension bridges: Severn Bridge, Forth Road Bridge and Williamsburg Bridge. The first methodology is to model wire strength as a random process in space whose marginal probability distribution and power spectral density evolve with time. Both the marginal distribution and the power spectral density are parameterized with time-dependent parameters. This enables the use of Monte Carlo methods to estimate the failure probability of wires at any given time. An often encountered problem -- the incompatibility between the non-Gaussian marginal probability distribution and prescribed power spectral density -- which arises when simulating non-Gaussian random processes using translational field theory, is also studied. It is shown by copula theory that the selected marginal distribution imposes restrictions on the selection of power spectral density function. The second methodology is to model the deterioration rate of wire strength as a stochastic process in time, under Ito's stochastic calculus framework. The deterioration rate process is identified as a mean-reversion stochastic process taking non-negative values. It is proposed that the actual deterioration of wire strength depends on the deterioration rate, and may also depend on the state of the wire strength itself. The probability distribution of wire strength at any given time can be obtained by integrating the deterioration rate process. The model parameters are calibrated from the available data sets by matching moments or minimizing differences between probability distributions.

Fire resistance design and analysis is an under-studied and under-codified area of bridge engineering. With the lessening of conservatism in bridge design, the aging or our bridge infrastructure, and the increase in the ground transport of highly-flammable and -combustible materials, it is essential that the bridge engineering community better understand and incorporate methods for modeling the effects of fire on bridges. Typical fire resistance analysis looks at the response of individual structural components. Analysis for the component of a bridge is nowhere more important than for that of the main cables of suspension bridges. As such, we will survey and introduce the necessary analysis techniques to provide the bridge engineering community with the knowledge and tools to understand fire modeling and both rapidly and accurately assess their effects on suspension bridge main cables. The work of this dissertation is twofold. In the first portion, we address proper fire modeling techniques for bridge conditions and apply them in a sequential thermal-mechanical analysis of a three-dimensional model main cable with thermally-dependent material and mechanical properties. Although fire modeling has been addressed in a variety of scenarios, including extensive studies for building design and analysis as well as tunnel design and analysis, the types of fires, fire geometries, and air conditions associated with bridge fires vary drastically. Our work identifies the time to failure for our particular main cable example and subsequently compares both the temperature and strain distributions for temperature-dependent and temperature-independent models. Although the three-dimensional analysis is complete, we hope to emulate and expand on the work done in the building fire engineering community and bring to the literature methods to produce significant two-dimensional temperature distributions for when a main cable component is either partially or fully-exposed to fire. As such, the main fire modeling analyses mentioned in the previous paragraph lay the groundwork for our pursuit of closed-form analytical solutions necessary to rapidly and accurately assess the time-dependent temperature distribution within a cable cross-section exposed to fire. These solutions are formed with different approaches depending on the fire scenario in question. They include a separation of variables (eigenfunction) approach, sinusoidal transforms, Laplace transforms, Green's function solutions, and a semi-analytical hybrid method. We validate each of the approaches numerically using three different fire models.

Accurately determining the current state of a suspension bridge’s main cables is a critical component to reliably assessing the safety of the bridge. The primary cause for the deterioration of cable strength with time is universally recognized to be the corrosion of high strength steel wires, which together comprise the main cable. Hidden from view by the cable wrapping, this corrosion often goes undetected for years and is typically only discovered during costly and intrusive inspections. Furthermore, current inspection methods provide an incomplete picture of the variation in wire condition across the cable cross section. As a result, cable strength estimation techniques that rely solely on inspection data introduce a considerable degree of uncertainty. Finally, a method has not been developed for estimating the continuing decline in cable strength due to ongoing corrosion. A recent direction in research attempts to address the shortcomings of current inspection methodologies and the intent of this thesis is to further build upon these findings. In these recent studies, environmental conditions inside main cables are monitored to obtain information regarding the corrosive nature of the cable’s internal environment. The first goal of this thesis is to further this research direction by introducing a corrosion rate model for bridge wires that relates the monitored environmental parameters within a cable to the corrosion rate of bridge wires. Initially, temperature, relative humidity, pH, and Cl- concentration have been identified as the most relevant variables for predicting the corrosion rate of a bridge wire. By applying machine learning methods to a corrosion dataset in conjunction with these monitored environmental inputs, a long term corrosion rate model for bridge wires has been developed that is capable of capturing variability associated with these environmental parameters. This long term corrosion rate model is then applied to establish a methodology that will allow bridge owners and engineers to estimate the remaining strength of a main cable at any point in time. This is accomplished through the use of continually monitored environmental parameters which are input into the corrosion rate model. Incorporating the long term corrosion rate model developed in this thesis with current strength estimation techniques, the methodology presented in this thesis for the estimation of the remaining strength of suspension bridge cables may be readily adapted to other bridges and can be used to complement the current best practices for bridge inspection.