Load And Resistance Factor Design Specifications Research Articles

History of Transition From Allowable Stress Design to Load and Resistance Factor Design and Beyond

The Standing Committee on Foundations for Bridges and Other Structures has supported the implementation of the load and resistance factors (LRFD) design philosophy into practice. The committee has contributed by hosting discussions on the advantages, issues, and impact of the implementation of the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) into foundation design and other related fields. The background and a historical overview of the development of LRFD in bridge foundation design are presented in this paper. Several National Cooperative Highway Research Program (NCHRP) projects have been of paramount importance on this matter. Milestone research projects are described, and a perspective on the future of the field is drawn. This document is intended to be a roadmap through the most useful material to understand reliability analysis and its application to geotechnical engineering. It is intended to be of interest to those engineers charged with performing reliability-based calibration in need of a starting point. The primary literature and steps followed to develop the current AASHTO LRFD specifications are highlighted. This paper aims to contribute to the understanding and future improvement of the LRFD specifications.

Modified slenderness limits for bending resistance of longitudinally stiffened plate girders

In this study, the slenderness limits for flanges and webs were examined to rationally evaluate the flange local buckling (FLB) strength of longitudinally stiffened I-girders. It is known that the bending resistance of a plate girder greatly increases when the web is longitudinally stiffened. This additional strength can be attributed to the fact that the stiffened web provides improved restraint to the rotation of the compression flanges as well as web bend-buckling strength. This study conducted a series of numerical analyses and it was found that the American Association of State Highway and Transportation Officials' (AASHTO's) load and resistance factor design (LRFD) requirements provide highly conservative estimates of the FLB strength of longitudinally stiffened plate girders, especially in noncompact sections. The reason is that the buckling coefficient and corresponding slenderness limit for a noncompact flange is determined based on the bending resistance of an unstiffened girder. Therefore, this study conducted a series of eigenvalue analyses in which the slenderness ratios of flanges and webs were considered. As a result, a buckling coefficient equation that reasonably reflects the interaction of the stiffened web and flange was derived. Based on the results of the analyses, this study proposed modified slenderness limits for the noncompact web and noncompact flange of a stiffened girder. It was verified that the bending resistance of longitudinally stiffened girders could be rationally estimated on the basis of the AASHTO LRFD specifications only by replacing the slenderness limits with the proposed formulas.

Verification of LRFD approach for piles in sand and mixed soils

The potential consequences of switching the design and construction of bridge foundations in sand and mixed soil profiles from an interim procedure based on Allowable Stress Design to the Load and Resistance Factor Design (LRFD) procedure were examined. Independent data of 451 production steel H-piles driven in sand and 173 production steel H-piles driven in mixed soil profile were used to evaluate the adequacy of the regionally calibrated LRFD procedure and investigate its economic implications. This study concludes that the regional LRFD procedure will increase the plan pile length by 25% for sand and 12% for mixed soil profile as opposed to 86% and 93%, respectively, if the American Association of State Highway and Transportation Officials (AASHTO) procedure had been implemented. Despite the additional cost incurred by switching to the regional LRFD procedure, it satisfies the target reliability index of 2.33 for a redundant pile group and the 1% probability of failure stipulated in the AASHTO LRFD Specifications. Alternatively, it can be stated that the currently used method has a reliability index of 1.7 for sand and 2.00 for mixed soil profile with approximately 30% and 10% more probability of failures, respectively. Although the research and findings presented in this paper are specific to a local area, these methods could be adopted globally to facilitate the implementation of the regional LRFD procedure in bridge foundations.

Live Load Distribution Factor at the Piers of Skewed Continuous Multicell Box Girder Bridges Subjected to Moving Loads

The multicell box girder bridge is a popular choice of designers because of its large torsional stiffness. The skewness at the support line of bridges has a significant influence on distribution of live loads. The current American bridge design code, AASHTO load and resistance factor design (LRFD), defines several correction factor expressions to account for the skew effect in bridges. In addition, the effect of skewness on reactions of continuous multicell box girder bridges is obtained by using the skew correction factor of shear or by the shear distribution factor of straight bridges, despite a significant disparity between the shear and reaction that is observed in skewed bridges. This study investigated the effect of skewness on the reactions and shear distribution factors for three continuous multicell box girder bridges. There was a significant difference between reactions at the piers and the shear distribution factors of skewed bridges. Thus, a statistical analysis was used to propose new equations for the skew correction factors and the external girder correction factor of shear and reaction to improve the accuracy of the AASHTO LRFD specifications.

Minimum Rail Height and Design Impact Load for Longitudinal Barriers that Meet Test Level 4 of Manual for Assessing Safety Hardware

In 2009, the Manual for Assessing Safety Hardware (MASH) was adopted as an updated replacement of NCHRP Report 350. Under MASH, the impact severity of Test Level 4 (TL-4) (Test 4–12) was increased by 56%. Test vehicle mass was increased from 17,640 to 22,050 lb. Impact speed was increased from 50 to 56 mph. Although this is a significant increase in the amount of lateral energy imparted to the barrier, the 54-kip design impact load currently suggested by the AASHTO load and resistance factor design (LRFD) bridge specifications has not been updated to meet MASH TL-4 requirements. Similarly, the AASHTO LRFD specifications require all TL-4 railings to have a minimum height of 32 in. However, because of the increase in test vehicle mass and impact velocity under MASH, the minimum height for TL-4 railings is expected to be greater than 32 in. This height was verified by a recent unsuccessful MASH Test 4–12 of a New Jersey profile rigid concrete barrier 32 in. tall. The research presented in this paper used finite element analysis and subsequent crash testing to determine the minimum rail height for MASH TL-4 impact conditions. The researchers also determined the appropriate lateral impact design load for use with AASHTO LRFD bridge specifications for the design of TL-4 bridge rails.

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.

Comparison of AASHTO LRFD and ASD specifications for structural design of cantilever abutments and retaining walls

The American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specification became the mandatory design specifications for United States highway structures in October 2007. This has introduced a number of changes in mandatory engineering design and analysis procedures. The differences between the allowable stress design (ASD) standard specifications and the LRFD specification are evaluated in this paper, as well as how they apply to earth retaining structure design. The effect of the new design standards on structural proportioning and cost were examined through several design examples. The difference between the LRFD specifications and the ASD standard specifications was insignificant for cantilever abutments and retaining walls 4.6 m and taller. However, an increase in footing length of about 30% and an increase in cost of approximately 10% of the cost of the retaining structures can result from designing shorter abutments and retaining walls using the LRFD specifications. While in some designs, these cost impacts to a structure can be significant, the AASHTO LRFD specifications provides a safe and reliable design method of paramount importance to engineers and the public.

Analytical and Experimental Investigation of Bridge Girder Shear Distribution Factors

Tests on twelve bridges (six along Interstate 55 and six along Interstate 70∕270 in Illinois) were performed to determine the validity of certain provisions for calculating bearing forces in the load and resistance factor design (LRFD) and the load factor design bridge specifications. The bridges were selected to be typical of Illinois interstate highway bridges and maintain a range of parameters to study. These bridges were instrumented on their beam webs with three strain gauge rosettes installed on each beam to measure shear stresses caused by loads. Static tests and slow moving 8 km/h (5mi/h) tests with a loaded truck in specified locations were performed. Dynamic tests at highway speeds were also completed. Finite-element models were developed and compared to the test results. The study shows that the LRFD specification procedures closely approximate the shear distribution factors determined by finite-element analysis and testing.

Unified Flexural Resistance Equations for Stability Design of Steel I-Section Members: Uniform Bending Tests

The 2004 AASHTO and 2005 AISC provisions for flexural design of steel I-section members have been revised in their entirety relative to previous specifications to simplify their logic, organization, and application, while also improving their accuracy and generality. This paper evaluates the lateral-torsional and flange local buckling (LTB and FLB) predictions from these and previous specifications versus uniform bending experimental test results. A total of 154 rolled and 123 welded I-section member LTB tests, and 11 rolled and 36 welded I-section member FLB tests are considered. Reliability indices are estimated for load and resistance factor design (LRFD) of buildings based on the test statistics combined with established statistics for material and fabrication bias factors and the ASCE 7 load model. The notional reliability for LTB is found to be reasonably constant and consistent with the targeted level in the first AISC LRFD specification of 1986. The unified equations, combined with a design-oriented procedure for calculation of elastic LTB K factors, are shown to capture the test results accurately throughout the inelastic and elastic LTB ranges, leading to substantial liberalization of the calculated resistances in certain cases. The mean resistances for inelastic LTB and FLB are captured accurately by a linear equation in the corresponding slenderness parameters. The reliability for FLB is found to be slightly higher than that for LTB.

Comparison of Standard Load and Load and Resistance Factor Bridge Design Specifications for Buried Concrete Structures

For the past 30 years, it has been common practice to use AASHTO standard design specifications for underground precast concrete structures. Today, the bridge engineering profession is making the transition from the standard AASHTO load factor design bridge specifications to the load and resistance factor design (LRFD) specifications. The FHWA has mandated that all culverts, retaining walls, and other standard structures designed after October 2010 be designed according to the AASHTO LRFD bridge design specifications for a project to receive federal funding. This paper compares related provisions from both specifications used in designing underground concrete structures, such as underground utility structures, drainage inlets, three-sided structures, and box culverts. Although many provisions of these two codes are the same, important differences could have a significant impact on the amount of reinforcement, member geometry, and cost to produce buried reinforced concrete structures. Many AASHTO LRFD code provisions that differ from the standard specifications include terminology, load factors, implementation of load modifiers, load combinations, multiple presence factors, design vehicle live loads, distribution of live load to slabs and earth fill, live load impact, and live load surcharge. This study demonstrates that greater reliability and a more uniform factor of safety are obtained when the LRFD specifications are used.

STABILITY EVALUATION OF STEEL CABLE-STAYED BRIDGES BY ELASTIC AND INELASTIC BUCKLING ANALYSES

The purpose of this paper is to compare the design equation of Allowable Stress Design (ASD) with that of Load and Resistance Factor Design (LRFD) concerning the member stability for the economic design of cable-stayed bridges. Both elastic and inelastic buckling analyses are carried out for the cable-stayed bridges with the effective buckling lengths of the key members calculated. The axial-flexural interaction equations prescribed in ASD and LRFD are used to check the stability of main members in cable-stayed bridges. Parametric studies are performed for the bridges with a center span of 300, 600, 900, and 1200 m of different girder depths. Peak values of the interaction equations are calculated at the intersection between the girder and towers. Since the peak values of the interaction equations by inelastic buckling analysis are less than those by elastic buckling analysis, a more economical design of the girder and towers can be achieved using the inelastic buckling analysis. In addition, the use of LRFD specifications can result in a more economical design by about 20% on average than the ASD specifications for steel cable-stayed bridges.

Guideline for Interpreting AASHTO Specifications to Design or Evaluate Buried Structures with Comprehensive Solution Methods

Design engineers and consultants are required to satisfy the criteria set forth in the AASHTO LRFD Bridge Design Specifications when designing buried culverts within the national transportation infrastructure. Adherence to the specifications is especially difficult when an engineer uses a comprehensive solution method such as a finite element program to predict the deformations and internal forces of the culvert-soil system. Part of the difficulty is in knowing how to apply factored loads as well as to determine their values. A more difficult problem is to assess whether the culvert is structurally safe according to the AASHTO LRFD specifications. Said another way, the design criteria and the corresponding factored capacities as written in the specifications are less than well defined. A succinct interpretation is presented of the AASHTO specification for load and resistance factor design (LRFD) for buried structures with regard to factored loads and design criteria. Tabularized values are provided for load factors and load modifiers to quantify dead loads, earth loads, and live loads, which are required for a LRFD analysis to produce the factored demands. Also presented are tabularized descriptions of the design criteria and the corresponding factored capacities, which are defined and quantified for corrugated metal, reinforced concrete, and plastic pipe materials. For some culverts, the design criteria have been generalized to provide sufficient information that is compatible with comprehensive analysis methods. Although intended especially for design engineers who use comprehensive analysis tools, the information presented is also useful and educational for engineers who use the simplified design solutions in the AASHTO LRFD specifications.

The 2005 American steel structures design code

The American Institute of Steel Construction was founded in 1921 and issued the first US structural steel design code in 1923. 1 1 The steel design code in the US is officially called the Specification for Structural Steel Buildings. In this paper the words specification and code are used interchangeably, meaning the same thing. It was 10 pages long and based on the principles of allowable stress design (ASD). The ASD code was subsequently published in various editions, through the ninth in 1989. No substantive changes have been made to this document since the eighth edition (1978). Limit state design, or Load and Resistance Factor Design (LRFD) as it is called in the United States, was officially introduced by the first (1986) edition of the LRFD Specification. It was based on extensive research and development carried out over 15 years. This code has since been revised twice; the current version is the third edition (1999). The presence of two design codes has created difficulties for US designers and industry. The AISC Committee on Specifications therefore undertook to develop a single, unified structural steel design code, which has just been approved (April 13, 2005). The paper describes the key concepts of the new code, including the use of nominal strength criteria in combination with appropriate measures of reliability. Among many other developments, significant additions have been made in the requirements for stability and bracing design for framing systems, including novel methods using inelastic criteria.

Reliability-Based Code Calibration for Design of Wood Members Using Load and Resistance Factor Design

The procedures underlying the load and resistance factor design (LRFD) format for engineered wood construction combine elements of reliability analysis with the experience gained from decades of successful use of allowable stress design procedures. However, the judgments applied in much of the early development or LRFD hinged directly on the load factors and underlying load distribution assumptions in the 1993 version of the ASCE 7 load standard. Since that time, load factors in ASCE 7 have changed several times and additional information is available regarding load distributions. Assumptions regarding resistance statistics also have evolved during the past decade. For example, early reliability analyses were based on resistance distributions derived from individual data sets. Unfortunately, this approach is confounded by often significant differences that occur between data sets. This approach also neglects the self-calibrating nature of engineered wood product specifications. This paper examines the range of computed reliability indices that result from updating the assumed load statistics and assumed resistance statistics. Several load cases involving dead, live, snow, and wind load are examined. The reference structural configuration is a simple flexural member. The results show that the range of computed reliability indices is most significantly influenced by regional variations in load statistics. While these results also show slight differences in computed reliability indices from one engineered wood product to another, these differences are not judged to be significant. The results of this study will not only assist the Structural Engineering Institute Design of Engineered Wood Construction Standards Committee in their upcoming revision of ASCE 16, but can also serve as a template for other material standards committees (steel, concrete) as they update their LRFD specifications to reflect evolutionary changes in ASCE 7.

The New Hathaway Bridge, Panama City, Florida: Segmental Concrete Bridge Project Designed Under AASHTO Load and Resistance Factor Design Specifications

The new Hathaway Bridge in Panama City, Florida, is a design-build bridge replacement project that consists of replacing an existing structure with two side-by-side precast segmental box girder bridges. The project was designed by the Orlando office of HNTB Corporation and constructed by Granite Construction Company. Each new bridge has seven 330-ft (100.6-m) spans, 265-ft (80.8-m) transition spans, and 200-ft (61-m) end spans. The load and resistance factor design (LRFD) specification used for the design was the AASHTO LRFD specification (1998 with interims through 2000). The LRFD design is compared with the AASHTO specification requirements (16th edition) as well as the requirements of the Guide Specifications for Design and Construction of Segmental Concrete Bridges (2nd edition). Studies during design showed that, for this bridge, the transverse and longitudinal bending requirements under the LRFD specification were similar to what would have been expected under previous specifications using HS20 load...

Simplified Live Load Distribution Factor Equations for Bridge Design

Live load distribution factors have been used in bridge design for decades as a simple method with which to estimate live load effects. Live load distribution is important for the design of new bridges as well as for the evaluation of existing bridges. AASHTO's Standard Specifications for Highway Bridges and the AASHTO LRFD Bridge Design Specifications contain the most common methods in use for computing live load distribution factors. The load and resistance factor design (LRFD) equations were developed under NCHRP Project 12-26 and reflect the wide variation in modern bridge design. The limited ranges of applicability and complexity have been viewed as weaknesses of these equations since their adoption into the LRFD specifications. When bridges fall outside these ranges, the specifications mandate that a refined analysis be used. The design community would welcome a simple and reliable procedure for live load distribution. Research was done to develop simplified live load distribution factor equations f...

Live Load Distribution Widths for Reinforced Concrete Box Sections

AASHTO introduced the AASHTO LRFD Bridge Design Specifications in 1994. These load and resistance factor design (LRFD) specifications included new provisions for distributing live loads to reinforced concrete bridge decks that also apply to the design of reinforced concrete box sections with depths of fill less than 2 ft. Designs according to the LRFD specifications can be much more conservative than designs according to the AASHTO Standard Specifications for Highway Bridges and are inconsistent at a span of 15 ft. A finite element study sponsored by the Pennsylvania Department of Transportation investigated these issues and determined appropriate live load distributions for box sections subjected to live loads; the results are presented. The computer models were three dimensional for analysis of the distribution of live load effects along the length (flow direction). Box section models had spans of 8 ft, 16 ft, and 24 ft, and all had an 8-ft rise. The models had different slab and wall thicknesses, diffe...

Methodologies for Evaluation of Effective Slab Width

A composite section is made up of a steel girder and concrete slab connected by shear connectors. The shear lag phenomenon usually takes place in such a section and results in underestimation of stresses and strains at the web-to-flange intersections of the girder. With the introduction of the concept of effective slab width, the actual width can be replaced by an appropriate reduced slab width. The classical effective slab width definition does not take into account the strain variation through the slab thickness. More sophisticated definitions are introduced and used with finite element analyses. The method of finite element modeling is discussed, and the model is successfully verified with experimental results. Parametric study is conducted to investigate the effective slab width for both positive and negative moment sections. The effective slab width is computed and compared with the current AASHTO load and resistance factor design (LRFD) specifications. The results demonstrate that full width can be used as the effective slab width in the design and analysis in most cases for the design and analysis of both positive and negative moment sections. The current AASHTO LRFD specifications are found to be conservative for configurations with widely spaced girders, especially in negative moment sections.

Load Combination Factors for Extreme Events

The AASHTO load and resistance factor design (LRFD) specifications were developed with the use of a reliability-based calibration that covered the basic combination of dead load plus live load. The other load combinations were obtained from previous generations of specifications and the experience of bridge engineers and thus may not be consistent with the reliability methodology of the LRFD specifications. Work done as part of a recent NCHRP project to study in a systematic way the reliability of bridges under the combined effects of extreme load events and to develop a rational set of load combination factors consistent with the LRFD philosophy is described. The load events considered include live loads, seismic loads, wind loads, ship collision loads, and short-term scour. The analysis considered structural safety as well as foundation safety, and member safety was compared with system safety. The study recommended revisions to the AASHTO LRFD load combination factors and also calibrated new factors for combinations of events that include the presence of short-term scour. The calibration took into account previous experience with so-called safe bridge structures to provide acceptable and consistent levels of reliability.

Methodologies for Evaluation of Effective Slab Width

A composite section is made up of a steel girder and concrete slab connected by shear connectors. The shear lag phenomenon usually takes place in such a section and results in underestimation of stresses and strains at the web-to-flange intersections of the girder. With the introduction of the concept of effective slab width, the actual width can be replaced by an appropriate reduced slab width. The classical effective slab width definition does not take into account the strain variation through the slab thickness. More sophisticated definitions are introduced and used with finite element analyses. The method of finite element modeling is discussed, and the model is successfully verified with experimental results. Parametric study is conducted to investigate the effective slab width for both positive and negative moment sections. The effective slab width is computed and compared with the current AASHTO load and resistance factor design (LRFD) specifications. The results demonstrate that full width can be used as the effective slab width in the design and analysis in most cases for the design and analysis of both positive and negative moment sections. The current AASHTO LRFD specifications are found to be conservative for configurations with widely spaced girders, especially in negative moment sections.