Load And Resistance Factor Design Research Articles

Load and resistance factor design of fiber reinforced polymer composite bridge deck

The majority of our bridges were constructed with conventional civil engineering materials of steel and concrete in a typical slab on girder or truss construction. Reinforced concrete bridge decks have approximately 40% life of the steel girders that support these structures. In order to support the use of alternative materials to replace deteriorating concrete decks, this paper outlines the Load and Resistance Factor Design (LRFD) of Fiber Reinforced Polymer composite (FRP) panel highway bridge deck. The deck would be of a sandwich construction where 152.4mm×152.4mm×9.5mm square pultruded glass FRP (GFRP) tubes are joined and sandwiched between two 9.5mm GFRP plates. The deck would be designed by Allowable Stress Design (ASD) and LRFD to support AASHTO design truckload HL-93. There are currently no US standards and specifications for the design of FRP pultruded shapes including a deck panel therefore international codes and references related to FRP profiles will be examined and AASHTO-LRFD specifications will be used as the basis for the final design. Overall, years of research and laboratory and field tests have proven FRP decks to be a viable alternative to conventional concrete deck. Therefore, conceptualizing the design of FRP bridge decks using basic structural analysis and mechanics would increase awareness and engineering confidence in the use of this innovative material.

TUBULAR STRENGTH COMPARISON OF OFFSHORE JACKET STRUCTURES UNDER API RP2A AND ISO 19902

Offshore jacket platforms in Malaysia are designed using API RP2A Working Stress Design (WSD) code. WSD code has proved its effectiveness and has been in use for long time, but it needs to be changed into Load and Resistance Factor Design (LRFD) based code which is being followed by all building code agencies. In WSD, design safety factor is provided only on resistance side and is based on judgement and experience. In place of WSD, Limit State Design or LRFD has proved to be more rational as it is based on probabilistic models. The reliability of jacket platforms is maintained in API RP2A LRFD by setting target safety factor the same as that provided in WSD designs, which means structures designed as per LRFD code will have the same reliability as API RP2A WSD (which has already provided safe structures and the best available practice for design). When adopting LRFD methodology, the appropriate load and resistance factors can be optimised through the process of calibration. Knowledge of the strength equations in the different codes and the similarities and differences between them is useful for the calibration. The first step in the calibration process is the determination of reliability of structural tubular members of the jacket designed as per existing practice of WSD and LRFD code. Here in this research, API RP2A WSD code and International Standard Organization (ISO 19902) (LRFD based code) are taken into consideration for the reliability analysis. In this paper, the relevant strength equations of three codes are identified and compared and the similarities and differences are determined for tubular members which are the main part of jacket structures.

Resistance factor calculations for LRFD of axially loaded driven piles in sands

This paper presents the development of Load and Resistance Factor Design (LRFD) of axially-loaded driven piles in sands. The resistance factors of base and shaft resistances were calculated separately to account for their different uncertainty levels. The ratios of dead-to-live load and ultimate base resistance to limit shaft resistance change the uncertainty levels of total load and total pile capacity, respectively; thus, those ratios should be reflected in the calculation of base and shaft resistance factors. For the development of LRFD for axially-loaded driven piles in sands, the ultimate limit state for an axially-loaded driven pile was established based on the Imperial College Pile (ICP) design method; the uncertainties of loads and resistance were accessed; reliability analyses were performed using the First-order Reliability Method (FORM); and finally, reasonable resistance factors of base and shaft resistances were calculated based on the results of reliability analyses for different target reliability index levels. The load factors used for the calculation of resistance factors are the ones proposed by AASHTO and ASCE/SEI 7-05. From the results of extensible reliability analyses using FORM, the resistance factors for base and shaft resistances were found to be highly dependent on the ratios of the dead-to-live load and the ultimate base resistance to the limit shaft resistance. Resistance factors are proposed for different combinations of these ratios within their possible ranges.

국내 통계자료를 이용한 설계기준의 하중저항계수 검증

2007년 개정된 콘크리트구조설계기준에서 제시하고 있는 강도설계법의 하중 조합은 ACI 318-05 기준의 하중저항계수설계법(LRFD)을 참고하여 작성된 것이다. LRFD는 하중계수와 저항계수의 조합으로 이루어져 있고, 이 계수들의 선정은 대상 파괴 모드에 대하여 미리 규정된 파괴 확률 또는 신뢰도 지수의 수준에 부합하여야한다. 이 때 하중계수 및 저항계수의 결정은 대상 구조물의 지역적 및 시대적 특성을 반영할 수 있는 통계 자료에 기초한 구조 신뢰성 이론에 따라 이루어져야 한다. 그러나 현재 우리나라의 설계기준은 통계자료의 많은 부분을 외국의 연구 결과에 의존 하고 있는 실정이다. 이를 개선하기 위하여 이 연구에서는 지금까지 국내에서 연구된 자료에 기초하여 현행 콘크리트 구조설계기준의 안전 수준을 분석하고 이에 따른 합리적인 목표 신뢰도 지수를 결정하였으며, 이를 바탕으로 국내 현실에 적합한 저항계수(강도감소계수)를 제안하였다. 이 연구의 결과는 향후 우리나라의 고유한 저항계수 및 하중계수를 개정할 때 유용한 자료로 활용될 수 있을 것으로 기대된다.

Load and Resistance Factors for External Stability Checks of Mechanically Stabilized Earth Walls

The use of load and resistance factor design (LRFD) to design geotechnical components of transportation infrastructure in the United States is now mandated by the Federal Highway Administration (FHWA). The advantages of LRFD over working stress design (WSD) may lead to its gradual adoption in geotechnical design even in the absence of any mandates. If load and resistance factors are based on reliability analysis, a mechanically stabilized earth (MSE) wall may be designed to a target reliability index (or a target probability of failure). Load and resistance factor design of MSE walls must consider multiple ultimate limit states, associated with both external and internal stabilities. This paper develops factors for use for the two ultimate limit states, sliding and overturning, used in design that are related to the external stability of MSE walls. Equations that closely reproduce the ultimate limit states with as little uncertainty as possible are proposed. The uncertainties of the parameters and the transformations for ultimate limit state equations are assessed using data from an extensive literature review. The first-order reliability method (FORM) is then used to produce resistance factor values for each limit state for different levels of target reliability index.

A quantile-based approach for calibrating reliability-based partial factors

This paper proposes a quantile-based approach for calibrating reliability-based partial factors that is based on an equivalence principle between the design quantiles for the random variables and the target reliability. The potential advantage is to allow a single design quantile to maintain a more uniform reliability over a wider range of design parameters. The proposed approach does not require the capacity to be lumped as a single lognormal random variable in the Load and Resistance Factor Design (LRFD) format nor does it require tedious segment by segment optimization of the resistance factors in the Multiple Resistance Factor Design (MRFD) format. The applicability, usefulness, and limitation of the proposed approach are illustrated using three examples. The results show that the proposed approach is able to maintain a uniform reliability over a wider range of design parameters with a single design quantile, which cannot be easily attained by other calibration methods such as the First-Order Reliability Method.

Statistical Distribution of Bridge Resistance Using Updated Material Parameters

Resistance (load-carrying capacity) of a bridge girder is a random variable and can be determined by considering the uncertainty in material, fabrication, and professional/analysis properties. Previous calibrations of load and resistance factor design (LRFD) determined the distribution of bridge resistance on the basis of data from more than 30 years ago. This study uses the latest Material properties available in, the literature to update the resistance distribution. The statistical distribution of the resistance was determined through Monte Carlo simulation. The results of the analysis show an increase in bias and a decrease in the coefficient of variation (COV) for all types of bridges in comparison with those used in previous calibration studies. The changes in bias and COV are the result of higher bias and lower COV in material properties owing to better quality control in concrete and steel manufacturing. Steel and concrete bridges saw the greatest change in resistance distribution. Prestressed bridges saw little change because the material properties of prestressing steel, which is the most sensitive parameter in the prestressed bridges, did not change significantly since the previous calibration study. With these resistance distributions, it is expected that the calibration of the load factor in the AASHTO specification will lead to a lower live load factor, thereby possibly reducing the material cost of the bridge. In addition, the ratio of actual to required (design) resistances of representative bridges in Missouri was determined. The analysis showed that almost all representative bridges had a capacity-to-demand ratio greater than 1 according to current AASHTO standards.

Load and resistance factor design (LRFD) calibration for steel grid reinforced soil walls

This paper reports the results of load and resistance factor design (LRFD) calibration for pullout and yield limit states for steel grid reinforced soil walls owing to soil self-weight loading plus permanent uniform surcharge. The calibration method uses bias statistics to account for prediction accuracy of the underlying deterministic models for reinforcement load, pullout capacity and yield strength of the steel grids, and random variability in input parameters. A new revised pullout design model is proposed to improve pullout resistance prediction accuracy and to remove hidden dependency with calculated pullout resistance values. Load and resistance factors are proposed that give a uniform probability of failure of 1% for both pullout and yield limit states. The approach adopted in this paper has application to a wide variety of other reinforced soil wall technologies.

Reliability-based load and resistance factors for soil-nail walls

Existing soil nailing design methodologies are essentially based on limit equilibrium principles that together with a lumped factor of safety or a set of partial factors on the material parameters and loads account for uncertainties in design input parameter values. Recent trends in the development of design procedures for earth retaining structures are towards load and resistance factor design (LRFD). In the present study, a methodology for the use of LRFD in the context of soil-nail walls is proposed and a procedure to determine reliability-based load and resistance factors is illustrated for important strength limit states with reference to a 10 m high soil-nail wall. The need for separate partial factors for each limit state is highlighted, and the proposed factors are compared with those existing in the literature.

현행설계법 및 하중저항계수설계법에 의한 완전 조립식 교량 하부구조의 설계결과 비교

The design comparison and nonlinear analysis of totally prefabricated bridge substructure systems are performed. The prefabricated bridge substructures are designed by the methods of present design and load and resistance factor design (LRFD). For the design, the current Korea Highway Bridge Code (KHBD), with DB-24 and DL-24 live loads, is used. This study evaluates the present design method of KHBD (2005) and AASHTO-LRFD (2007) for totally prefabricated bridge substructure systems. A computer program, named RCAHEST (Reinforced Concrete Analysis in Higher Evaluation System Technology), for the analysis of reinforced concrete structures, was used.

LRFD Resistance Factors for Design of Driven H-Piles in Layered Soils

The load and resistance factor design (LRFD) of piles embedded in layered soils that are commonly classified as sand, clay, and mixed soil sites is investigated using static analysis methods at the strength limit state. Unlike the current practice, the main emphasis of this study is to use a more clearly defined, less ambiguous classification for the sites based on the percentage of soil types present along the pile embedment length. Two different site classifications and the corresponding LRFD resistance factors are recommended for different static methods, used during the pile design stage, in accordance with the AASHTO-LRFD calibration framework. For this purpose, a total of 90 high-quality static load tests data obtained from steel H-piles were used, including 10 load tests conducted recently on heavily instrumented steel H-piles. The new group of data facilitated verification of the proposed methods, which were first developed based on the 80 load test data and then updated based on the entire 90 pile tests. In addition to a locally developed static method known as the Bluebook approach, several commonly adopted static analysis approaches, as well as combinations of methods, have been examined with due consideration to soil variation along the pile length. The investigation found that (1) the Bluebook method consistently provided higher resistance and efficiency factors, (2) using a 70% rule is an appropriate means to define the soil type at the site while maintaining simplicity in the design approach, and (3) utilizing a more refined site classification based on the percentage of cohesive versus cohesionless soils existing along the pile embedded length further enhanced the LRFD approach for pile foundations.

Capacity reduction and fire load factors for LRFD of steel columns exposed to fire

Capacity reduction and fire load factors corresponding to the load and resistance factor design (LRFD) format are developed for steel columns exposed to fire. A sample deterministic framework to determine fire and steel temperatures and the capacity of steel columns is adopted for this analysis to structure the methodology. A specific number of parameters that affect the structural response, including the fire load, ratio of floor area to the total area of the fire compartment, opening factor, thermal absorptivity of compartment boundaries, thickness, density and thermal conductivity of insulation, dead load, and live load are taken as random variables. Mechanical and sectional properties of steel (e.g., yield strength, cross-sectional area, etc.), are also considered to be random variables. The effect of active fire protection systems (e.g., sprinklers, smoke and heat detectors, fire brigade, etc.), in reducing the probability of occurrence of a severe fire is included. Given the choice of framework and based on detailed reliability analyses, it is shown that the capacity reduction and fire load factors should vary depending on the presence of active fire protection systems in a building.

Analysis of installation damage tests for LRFD calibration of reinforced soil structures

North American design codes are now committed to the development of load and resistance factor design (LRFD) for reinforced soil structures including internal stability limit states. Reliability-based analysis is required to carry out these calibrations. A framework for LRFD calibration has been proposed by the writers that requires bias statistics for load and resistance terms for each limit state function. In this paper the formulation of the limit state for reinforcement tensile rupture is developed and the component strength-reduction bias statistics identified. The paper describes how to compute bias statistics from project-specific installation damage trials for use in reliability-based design for the reinforcement rupture limit state or using data from multiple sources for LRFD calibration. A database of results from field installation damage trials on 103 different geosynthetic products was collected from 20 different sources. A total of 799 and 2248 in-air tensile test results were reviewed for undamaged and damaged geosynthetic specimens, respectively. This database is used to compute installation damage bias statistics for six different categories of geosynthetic and four categories of backfill soils classified according to the D 50 particle size. A practical outcome is that for analysis purposes, bias statistics can be grouped into two ranges for each geosynthetic type based on D 50 of the soil greater than or less than 19 mm. The paper shows how bias statistics together with load and resistance factors for the geosynthetic rupture limit state function recommended by AASHTO (2010) can be used to calculate probability of failure using Monte Carlo simulation and demonstrates the sensitivity of probability of failure to magnitude of installation damage bias statistics. The installation damage data is valuable for future LRFD calibration to select resistance factors for use in design codes for the geosynthetic rupture limit state in reinforced soil structures.

Evaluation of FRP Posttensioned Slab Bridge Strips Using AASHTO-LRFD Bridge Design Specifications

Deterioration of concrete structures caused by corrosion of steel reinforcement requires large capital investments in order to repair or replace existing structures which may or may not be nearing the end of their expected service lives. Fiber-reinforced polymer (FRP) reinforcement has emerged as a viable alternative to conventional reinforcement with lower life cycle costs. Serviceability typically governs the design of FRP structures because of the inherent low stiffness of FRP materials. As a result, concrete members tend to exhibit high deflections, large crack widths, and a reduction in shear capacity compared to similar steel-reinforced members. This study focuses on glass fiber–reinforced polymer (GFRP) reinforced slab strips cast with self-consolidating concrete (SCC) and posttensioned with carbon fiber–reinforced polymer (CFRP) tendons to improve the serviceability, shear capacity, and deformability of slab bridges. The flexural performance of five FRP slabs and one steel-reinforced control slab are compared to the design provisions of the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications.

Hydrologic Uncertainty in Prediction of Bridge Scour

Load and resistance factor design (LRFD) incorporates state-of-the-art analysis and design methodologies with load and resistance factors that are based on the known variability of applied loads and material properties. These load and resistance factors are calibrated from actual bridge statistics to ensure a uniform level of reliability. LRFD allows a bridge designer to focus on a design objective or limit state; doing so can lead to a similar probability of failure in each component of the bridge. Bridges designed with the LRFD specifications should have relatively uniform reliability levels; such uniformity should ensure superior serviceability and long-term maintainability. Bridge hydraulics engineers should have the option of and ability to perform scour calculations that incorporate similar probabilistic methods. With this objective in mind, NCHRP Project 24–34 was initiated in April 2010 to develop a risk–reliability-based methodology that was based on risk and reliability and that could be used in calculating bridge pier, abutment, and contraction scour at waterway crossings so that scour estimates could be linked to a probability. The developed probabilistic procedures will be consistent with LRFD approaches used by structural and geotechnical engineers. This paper discusses sources of uncertainty in hydrologic estimates as those sources relate to bridge scour computations and summarizes a conceptual approach to the problem.

Load and Resistance Factor Design Calibration for Bridge Pile Foundations

In response to the documented advantage of the load and resistance factor design (LRFD) approach over the working stress design approach, FHWA issued a policy memorandum on June 28, 2000, requiring all new bridges initiated after October 1, 2007, to be designed according to the LRFD approach. This paper presents current design and construction practices for bridge pile foundations that were established through a survey of Iowa county engineers as well as consulting firms that design piles for the county offices. Conducted during the second and third quarters of 2008 as part of an ongoing research study centered on the LRFD approach for pile foundations in Iowa, this study highlights the benefits associated with a thorough description of regional deep foundation design and construction practices on successive LRFD resistance factor calibrations. The specific topics targeted in the study were current foundation practice; the extent of timber pile usage; pile analysis and design; and pile drivability, pile design verification, and quality control. Since this is the first study to have been conducted at the county jurisdictional level on the topic of pile foundation design after the FHWA mandate, the current status of the implementation of the LRFD approach for bridge foundation design was examined. The responses obtained from 44 Iowa county engineers and eight consulting firms revealed that (a) regional variation in pile foundation practice cannot be captured via a state-level investigation, inhibiting the performance of effective regional LRFD calibrations, and (b) the degree of implementation of the LRFD approach at the county level is about 84%.

Reliability-Based Design of Mechanically Stabilized Earth

Current design specifications for mechanically stabilized earth reinforcements incorporate metal-loss models to consider the loss from the corrosion of the metallic reinforcements, but these models have limited application with respect to reinforcement type and fill conditions. Results discussed in this paper broaden the recommendations for metal-loss modeling and describe effects of fill quality and reinforcement type on performance and service life. The variation in metal loss is considered within the context of reliability-based design, through the load and resistance factor design (LRFD) approach adopted in current AASHTO bridge design specifications. Under this approach, several variables that affect resistance, including metal loss, are considered, with a single parameter that controls the reliability of the design. Thus, new resistance factors are presented from the analysis of a newly expanded performance database, in terms of different reinforcement types and fill materials. The results from an example problem are presented to demonstrate the application of LRFD and the newly derived resistance factors that consider metal type, reinforcement type, design methods, and the design impacts of different electrochemical properties of reinforced fill.

Load and resistance factor design (LRFD) approach for the reliability-based seismic design of bridge abutments

The paper presents a study on the application of a load and resistance factor design (LRFD) approach to reliability based seismic design of bridge abutments. The failure criteria for defining the performance functions are overturning failure about the toe point, eccentricity failure of the resultant force, sliding failure along the base and bearing capacity instability. Using a pseudo-static limit equilibrium method, analysis is conducted to evaluate the stability of bridge abutments subjected to earthquake loads. The first-order reliability method (FORM) is used to estimate the probability of failure in four modes of failure. Load and resistance factors needed to maintain stability against four modes of failure by targeting various component reliability indices (2.0–4.0) are obtained for various values of coefficients of variation (COV) of unit weights of concrete and backfill (γ w and γ), friction angle of backfill and foundation soil (φ and φ b ), cohesion of foundation soil (c), vertical load acting on abutment (V) and horizontal seismic acceleration coefficient (k h ). The results have been provided in a tabular form. A comparative study between LRFD and ASD is also presented with a design example at the end.

Reliability-based calibration of resistance factors for static bearing capacity of driven steel pipe piles

As part of a study to develop load and resistance factor design (LRFD) codes for foundation structures in South Korea, resistance factors for the static bearing capacity of driven steel pipe piles were calibrated in the framework of the reliability theory. A database of 52 static load test results was compiled, and the data from these load test piles were sorted into two cases: a standard penetration test (SPT) N-value at pile tip (i) less than 50 and (ii) equal to or more than 50. Reliability analyses and resistance factor calibration for the two static bearing capacity analysis methods adopted in the Korean Design standards for foundation structures were performed using the first-order reliability method (FORM) and the Monte Carlo simulation (MCS). Reliability indices and resistance factors computed by the MCS are statistically identical to those computed by FORM. Target reliability indices were selected as 2.0 and 2.33 for the group pile case and 2.5 for the single pile case. The resistance factors recommended from this study are specific for the pile foundation design and construction practice and the subsurface conditions in South Korea.

Load and Resistance Factor Design (LRFD) of Nuclear Straight Pipes for Loads That Cause Primary Stress

Class 2 and 3 nuclear piping is designed according to the allowable stress design (ASD) method used in the ASME Boiler and Pressure Vessel (B&PV) code, Sec. III, Division 1, NC and ND-3600 according to which safety factors applied to the strength of steel (resistance) provide acceptable safety margins for the piping design. This paper describes the development of design equations according to the load and resistance factor design (LRFD) method for loads that cause primary stress such as sustained weight, internal pressure, and earthquake for different levels of piping operation. The LRFD method differs from the ASD since multiple factors, applied separately to each load and the strength of steel, provide safety margins that correspond to a known and acceptable probability of failure for the piping. Load combinations are provided, statistical properties for the variables under consideration are presented and the partial safety factors are moreover illustrated for different values of the target reliability index.