Reliability of Concrete Masonry Unit Walls Subjected to Explosive Loads

This study discuses the development of a procedure that can be used to assess the reliability of concrete masonry unit infill walls subjected to personnel-delivered blast loads. Consideration is given to maintain reasonable computational effort for both the structural analysis and reliability models. Blast load and wall resistance models are developed based on experimental and analytical data, and resistance is evaluated with a large strain, large displacement transient dynamic finite element analysis. A sensitivity analysis is conducted to identify significant random variables and a reliability analysis conducted with a feasible level of computational effort. Reliability indices are estimated for two wall types and three design blast load levels in terms of wall failure as well as occupant injury, over various load frequency-of-occurrence times

Load Truncation Approach for Development of Live Load Factors for Bridge Rating

Various local governments have developed state-specific vehicular live load factors for bridge rating. However, a significant computational demand is often associated with such an effort. This is due to the large size of the weigh-in-motion (WIM) databases frequently used in the procedure. In this study, a method is proposed that can significantly reduce the computational cost of the analysis, while still maintaining reasonable accuracy. The proposed approach develops approximate live load random variable statistics by truncating the WIM database based on gross vehicle weight, then a complete reliability analysis is conducted to develop new live load factors that meet AASHTO-specified rating standards. Two WIM databases, one based on typically legal vehicles and another based on unusually heavy vehicles, are considered for evaluation. Results of the proposed approach are compared to an exact assessment as well as to a simplified method suggested by AASHTO. It was found that the proposed approach may provide very large reductions in computational cost with minimal loss of accuracy, whereas significant inaccuracies were found with the existing simplified approach

Development of Traffic Live Load Models for Bridge Superstructure Rating with RBDO and Best Selection Approach

Reliability-based design optimization (RBDO) is frequently used to determine optimal structural geometry and material characteristics that can best meet performance goals while considering uncertainties. In this study, the effectiveness of RBDO to develop a rating load model for a set of bridge structures is explored, as well as the use of an alternate Best Selection procedure that requires substantially less computational effort. The specific problem investigated is the development of a vehicular load model for use in bridge rating, where the objective of the optimization is to minimize the variation in reliability index across different girder types and bridge geometries. Moment and shear limit states are considered, where girder resistance and load random variables are included in the reliability analysis. It was found that the proposed Best Selection approach could be used to develop rating model as nearly as effective as an ideal RBDO solution but with significantly less computational effort. Both approaches significantly reduced the range and coefficient of variation of reliability index among the bridge cases considered

Load Path Uncertainty in a Wood Structure and the Effect on Structural Reliability

The roof truss bearing points of a light-framed wood house were instrumented with load cells. It was found that under dead load alone, symmetric and theoretically identical truss reactions have significant variation. A similar degree of reaction discrepancy was found under the application of uplift pressures caused by hurricane winds. Analysis revealed that the majority of this discrepancy is caused by inherent uncertainties in load path. Although uncertainties in load magnitude and material resistance are accounted for in design by use of appropriate load and resistance factors, load path is generally taken to be deterministic. In this study, load path uncertainty in a test structure is statistically quantified and the effect on the reliability of wood structural members is investigated. Although large uncertainties in reactions were present, it was found that the resulting influence on reliability was modest, with decreases in component reliability index ranging from 5-15%

Evaluation of Alternative Implementation Methods of Failure Sampling Approach for Structural Reliability Analysis

In this paper, several alternative approaches are used to implement the failure sampling method for structural reliability analysis and are evaluated for effectiveness. Although no theoretical limitation exists as to the types of problems that failure sampling can solve, the method is most competitive for problems that cannot be accurately solved with reliability index-based approaches and for which simulation is needed. These problems tend to have non-smooth limit state boundaries or are otherwise highly nonlinear. Results from numerical integration and three extrapolation approaches using the generalized lambda distribution, Johnson\u27s distribution, and generalized extreme value distribution are compared. A variety of benchmark limit state functions were considered for evaluation where the number of random variables, degree of non-linearity, and level of variance were varied. In addition, special limit state functions as well as two complex engineering problems requiring nonlinear finite element analysis for limit state function evaluation were considered. It was found that best results can be obtained when failure sampling is implemented with an extrapolation technique using Johnson\u27s distribution, rather than with numerical integration or the generalized lambda distribution as originally proposed with the method

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 the 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 study, 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 AASHTO LRFD and ACI-318 strength requirements and target reliability levels. 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 to 0.64 for tension-controlled sections, which indicates a potential increase in allowed strength over flexural members using non-ductile bars

Reliability-based Design Optimization of Concrete Flexural Members Reinforced with Ductile FRP Bars

In recent years, ductile hybrid FRP (DHFRP) bars have been developed for use as tensile reinforcement. However, initial material costs regain high, and it is difficult to simultaneously meet strength, stiffness, ductility, and reliability demands. In this study, a reliability-based design optimization (RBDO) is conducted to determine minimum cost DHFRP bar configurations while enforcing essential constraints. Applications for bridge decks and building beams are considered, with 2, 3, and 4-material bars. It was found that optimal bar configuration has little variation for the different applications, and that overall optimized bar cost decreased as the number of bar materials increased

Reliability Estimation of Complex Numerical Problems Using Modified Conditional Expectation Method

A simulation-based structural reliability analysis method is presented. It is intended as an alternate approach to estimate reliability for problems for which most-probable point of failure methods fail and when computational resources are limited. The proposed method combines conditional expectation and estimating the PDF or CDF of a selected portion of the limit state. In the proposed approach, complex limit state functions are simplified to two random variable problems. The success of the simplification depends on the quality of the CDF estimate. Results indicate that the method may provide accurate and efficient solutions for some difficult reliability problems

Initial Assessment of Liquefied Scrap Tire Concrete

A new approach to incorporate scrap tire material into concrete was investigated, where two reclaimed waste tire components, carbon black and fuel oil, were used to replace a portion of water. The effect of “liquid tire” content to water ratios from 5-40% on an otherwise typical concrete mix were assessed, where compressive and flexural strength, flexural toughness, modulus of elasticity, and several fresh concrete properties were determined. Results were compared to typically expected results of traditional shredded tire mixes with equivalent tire content. It was found that the liquid tire mixes experienced significantly less losses of compressive strength and workability than associated with shredded rubber mixes; an increase in flexural strength over a traditional concrete mix; and a significant decrease in stiffness over traditional as well as shredded tire mixes

Analysis of Alternative Ductile Fiber-reinforced Polymer Reinforcing Bar Concepts

Steel-reinforced concrete structural components are often associated with significant maintenance costs as a result of reinforcement corrosion. To mitigate this problem, fiber-reinforced polymer (FRP) bars have been used in place of traditional steel reinforcement for some applications. The non-ductile response of typical FRP bars is a concern, however. To overcome this problem, hybrid ductile FRP (HDFRP) bars have been developed for use in concrete flexural members with resulting ductility indices similar to sections reinforced with steel. In this study, five different HDFRP bar concepts are analyzed and compared in terms of ductility, stiffness, and relative cost. Of primary interest is the effect that the number of materials used in bar construction has on performance. Reinforced concrete beam and bridge deck applications are considered for analysis. It was found that all HDFRP-reinforced flexural members considered could meet code-specified strength and ductility requirements for steel-reinforced sections, although service load deflections were approximately twice that of steel-reinforced sections of the same depth. In general, ductility increased, and overall material cost decreased, as the bar material layers increased from 2 to 4. The 4-material continuous fiber bar approach was found to be most promising, with high ductility as well as relatively low cost