Christopher D. Eamon

Effect of secondary elements on bridge structural system reliability considering moment capacity

Secondary elements such as barriers, sidewalks, and diaphragms may increase the load carrying capacity of girder bridges. This in turn affects reliability. The objective of this study is to evaluate the potential benefit of secondary elements on the system reliability of girder bridges, if these elements are designed with the structural system to participate resisting vehicular live loads. Simple span, two lane structures are considered, with composite steel girders supporting a reinforced concrete deck. For structural analysis, a finite element procedure is developed that combines a grillage model of the bridge deck with solid elements for edge-stiffening effects. Random variables considered are composite girder, barrier, and sidewalk flexural strengths (each in turn composed of many random variables), load magnitude (dead load and truck traffic live load), and live load position. System resistance parameters are estimated with a point integration method. System resistance is evaluated in terms of maximum load carried at ultimate capacity. It was found that the interaction of typical secondary element combinations has a varying effect on system reliability, depending on element stiffness, bridge span, and girder spacing.

Life-Cycle Cost Analysis of Alternative Reinforcement Materials for Bridge Superstructures Considering Cost and Maintenance Uncertainties

A life-cycle cost analysis (LCCA) was conducted on prestressed concrete bridge superstructures using carbon fiber reinforced polymer (CFRP) bars and strands. Traditional reinforcement materials of uncoated steel with cathodic protection and epoxy-coated steel were also considered for comparison. A series of deterministic LCCAs were first conducted to identify a range of expected cost outcomes for different bridge spans and traffic volumes. Then, a probabilistic LCCA was conducted on selected structures that included activity timing and cost random variables. It was found that although more expensive initially, the use of CFRP reinforcement has the potential to achieve significant reductions in life-cycle cost, having a 95% probability to be the least expensive alternative beginning at year 23–77 after initial construction, depending on the bridge case considered. In terms of life-cycle cost, the most effective use of CFRP reinforcement was found to be for an AASHTO beam bridge in a high traffic volume area.

Reliability Analysis of RC Beams Exposed to Fire

AbstractA procedure for conducting reliability analysis of RC beams subjected to a fire load is presented. This involves identifying relevant load combinations, specifying critical load and resistance random variables, and establishing a high-temperature performance model for beam capacity. Based on the procedure, an initial reliability analysis is conducted using currently available data. Significant load random variables are taken to be dead load, sustained live load, and fire temperature. Resistance is in terms of moment capacity, with random variables taken as steel yield strength, concrete compressive strength, placement of reinforcement, beam width, and thermal diffusivity. A semiempirical model is used to estimate beam moment capacity as a function of fire exposure time, which is calibrated to experimental data available in the literature. The effect of various beam parameters was considered, including cover, beam width, aggregate type, compressive strength, dead to live load ratio, reinforcement r...

Shape and Sizing Optimisation of Automotive Structures With Deterministic and Probabilistic Design Constraints

This paper presents the results of a study on the combined shape and sizing optimisation of automotive structures while examining the effects of different design constraints and associated uncertainties on reliability and efficiency of the optimum designs. Nonlinear transient dynamic finite element analysis is used for full- and offset-frontal crash simulations of a full vehicle model. Surrogate models are developed for the intrusion distance and peak acceleration responses at different vehicle locations based on the material and geometric characteristics of the rail component. The obtained solutions provide insight on the effect of uncertainties in optimum design of automotive structures.

Fiber-reinforced polymer composites

This chapter introduces the basic elements of fiber-reinforced polymer (FRP). It starts by presenting a brief review of the three constituents of FRP—fiber, matrix, and interface. It then discusses several important debonding issues, which are critical to the success of FRP strengthening, since the composite action of the FRP sheets can only be guaranteed when there is a solid bond between the concrete substrate and FRP. Finally, a full discussion of various durability issues of FRP is included.

Load Height and Moment Factors for Doubly Symmetric Wide Flange Beams

AbstractAn analytical procedure is used to study the effects of moment gradient and load height on the elastic stability of wide flange steel beams. Lateral torsional buckling is the limit state considered. Solutions are developed for a series of general moment functions which are produced by continuous load types with possible end moments. For each load type, an equivalent uniform moment factor is developed. Additionally, a load height factor is developed to modify the equivalent uniform moment factor for these load types where loading is applied above the shear center. Solutions are processed numerically using a Taylor series polynomial approximation. Results are presented in terms of an equivalent uniform moment factor and a load height factor. Comparison with national code procedures for moment factor show discrepancies that are conservative in some circumstances by up to 51% and unconservative in others by up to 8%. The largest discrepancies occur under the effect of reverse curvature bending and loa...

Life-cycle cost analysis of carbon fiber-reinforced polymer reinforced concrete bridges

This paper presents a life-cycle cost analysis of prestressed concrete highway bridges using carbon fiber-reinforced polymer (CFRP) reinforcement bars and strands. Side-by-side box beam and AASHTO beam bridge structures were considered over several span lengths and traffic volumes. The results show that despite the higher initial construction cost of CFRP reinforced bridges, they can be cost-effective when compared to traditional steel-reinforced bridges. The most cost-efficient design was found to be a medium-span CFRP reinforced AASHTO beam bridge located in a high-traffic area. A probabilistic analysis revealed that there is greater than a 95% probability that the CFRP reinforced bridge will become the least expensive option between 20 and 40 years of service, depending on traffic volume and bridge geometry. The break-even year between CFRP and steel reinforcement is typically at the time of the first major repair activity on the steel-reinforced concrete bridge.

Reliability Estimation using Dimension Reduction and Extended Generalized Lambda Distribution

This paper proposes an analytical approach for reliability analysis of structures with moderate to low level reliabilities (e.g., not larger than 0.99). In this approach, the primary statistical moments of a multi-dimensional performance function are estimated using the univariate dimension-reduction (DR) methodology based on additive decomposition of the performance function. Thus, complicated equations involving the evaluation of multidimensional integrals are transformed into simplified formulae requiring the solutions of multiple uni-dimensional integrals. The estimated statistical moments are then used to evaluate the unknown parameters associated with the extended generalized lambda distribution (EGLD). By minimizing the error between the moments of EGLD and those of the performance function as predicted by DR, the probability distribution of the performance function is estimated, and then the probability of failure is calculated. To evaluate the accuracy and efficiency of the proposed DR+EGLD approach, five example problems involving nonlinear limit state functions with low to moderate sets of random variables are examined. With direct Monte Carlo simulation and the first-order reliability method (FORM) as benchmark approaches, the effectiveness of the proposed approach is evaluated.

Resistance Factors for Ductile FRP-Reinforced Concrete Flexural Members

To prevent damage caused by corroding reinforcement, fiber-reinforced polymer (FRP) reinforcing bars have been used in place of steel in a relatively small but increasing number of structures in civil infrastructure. A concern with the use of traditional FRP bars, however, is the resulting lack of ductility. This problem has been overcome with the development of a new generation of composite reinforcement, ductile hybrid FRP (DHFRP) bars. However, standards that address the design of DHFRP bars are unavailable, and appropriate resistance factors for the use of DHFRP reinforcement are unknown. In this paper, a reliability analysis is conducted on tension-controlled concrete flexural members reinforced with DHFRP with the intent to estimate potential strength-reduction factors. Flexural members considered include a selection of representative bridge decks and building beams designed to meet strength requirements and target reliability levels dictated by relevant engineering standards. Nominal moment capacity is calculated from standard analytical models and is taken as first DHFRP material failure. Statistical parameters for load and resistance random variables in the reliability model are consistent with previous code calibration efforts. The resulting resistance factors ranged from 0.61-0.64 for tension-controlled sections, which indicates a potential increase in allowed strength with respect to flexural members using nonductile bars.

Design Live-Load Factor Calibration for Michigan Highway Bridges

AbstractIn this study, a reliability-based calibration of live-load factors for bridge design specific to the state of Michigan was conducted. Two years of high-frequency weigh-in-motion (WIM) data from 20 representative statewide sites were analyzed, and load effects were generated for bridge spans from 6 to 122 m (20 to 400 ft), considering simple and continuous moments and shears, and single-lane and two-lane effects. Seventy-five-year statistics for maximum live load were then estimated with probabilistic projection. Bridge girders considered for the calibration included composite steel, prestressed concrete, side-by-side and spread box beams, and special long-span structural members. In some cases, it was found that Michigan load effects were greater than those previously assumed, often requiring higher load factors than those in current use. Moreover, significant variation in the required load factor was found, potentially resulting in significant inconsistencies in reliability if a single load fact...