Load And Resistance Factor Design Approach Research Articles

Structural reliability assessment of steel bridges using OSIM visual inspection data and Bayesian updating

Structural reliability theories are used in the calibration of load and resistance factor design (LRFD) in the Canadian Highway Bridge Design Code (CHBDC). The LRFD approach contains certain assumptions about uncertainties in the load and capacity estimation that prevent it from fully exploiting the information gathered during visual inspections. This paper presents a reliability-based framework for analyzing the visual inspection data obtained according to the Ontario structure inspection manual (OSIM). Existing deterioration models are adapted. The Bayesian interference is utilized to estimate the updated structural properties according to the prior information from the bridge maintenance and deterioration models and the new information collected from visual inspections. The criteria set by the CHBDC are used to analyze components and systems reliability. The value of the proposed framework for bridge evaluation and optimizing maintenance is demonstrated through the full implementation of a case-study bridge in the Canadian Province of NB.

Calibration of resistance factors for design of shallow foundations against sliding

The design of shallow foundations typically proceeds by using the load and resistance factor design (LRFD) methodology to avoid various limit states with some probability. This paper looks at the sliding limit state of shallow foundations, and the sliding resistance factors required for the LRFD approach are estimated using reliability analyses of surface strip foundations. Cohesive and frictional soils are separately studied under wind loading conditions. Monte Carlo simulations are used to estimate the sliding failure probability of foundation designs on cohesive soils, and an analytical method is developed for frictional soils. The results indicate the existence of a “worst case” correlation length for cohesive soils, and the sliding resistance factor required to achieve target maximum lifetime failure probabilities is around 0.4–0.65 for moderate soil variability. For frictional soils, the required sliding resistance factor is about 0.5–0.85 for ν ϕ′ = 0.15. Overall, the sliding resistance factors recommended here agree well with the resistance factors of ϕ gu = 0.6 for cohesive soils and ϕ gu = 0.8 for frictional soils stipulated by geotechnical LRFD code provisions in Canada. The analyses can be used to estimate the reliability of current designs and can also aid the calibration of geotechnical design codes.

Calibration of resistance factors for gravity retaining walls

ABSTRACT Geotechnical design codes have been migrating from the traditional allowable stress design towards load and resistance factor design (LRFD). In this paper, calibration of the geotechnical resistance factors for sliding and overturning limit states of gravity retaining walls is performed using a reliability-based method. For each limit state, the LRFD approach is applied to design the gravity retaining wall, and its probability of failure is estimated using the Random Finite Element Method (RFEM). An example gravity retaining wall is analyzed using the described methodology, and the results suggest that for a given resistance factor the sliding failure probability is greater than the overturning failure probability, and a positive correlation between the soil effective internal frictional angle and unit weight random fields significantly reduces the failure probability. For reasonable ranges of the target maximum lifetime failure probability, the required resistance factor for the sliding limit state is close to that for the overturning limit state. In addition, the sliding resistance factor given by the Canadian Highway Bridge Design Code seems slightly unconservative, while the recommended overturning resistance factor is slightly conservative. The current analysis can be used to guide the calibration of these geotechnical resistance factors used in design codes.

Load and resistance factor design versus reliability-based design of shallow foundations

ABSTRACT The load and resistance factor design (LRFD) approach employed in geotechnical design codes is often calibrated using the reliability-based design (RBD) method. However, the LRFD may not achieve the target safety level exactly. This paper makes comparisons between the LRFD and RBD by considering the ultimate and serviceability limit state design of strip foundations. The RBD is carried out via the Random Finite Element Method. It is found that the failure probability and the resulting foundation width for ULS obtained using the RBD increase with the soil spatial correlation length, gradually reaching a plateau. The comparison between the LRFD and RBD results for ULS suggests that the LRFD is conservative for low to medium soil variability, particularly at smaller correlation lengths. The reliability-based SLS design is less dependent on the soil correlation length, particularly for lower coefficients of variation of the soil elastic modulus. However, a resistance factor of 1.0 for SLS is unconservative, and resistance factors of 0.65, 0.7 and 0.8 are better aligned with the RBD when the target failure probabilities are 1×10−3, 1×10−2 and 1×10−1. The current study can be used to guide the design of shallow foundations and the calibration of the LRFD approach.

Calibration of resistance factor for design of pile foundations considering feasibility robustness

The resistance factor for pile foundations in load and resistance factor design (LRFD) is traditionally calibrated considering target reliability index (βT) and statistics of load and resistance bias factors. However, the resistance bias factor is hard to quantify statistically. Consequently, the design obtained using the calibrated resistance factor can still miss βT if the variation in resistance bias factor has been underestimated. In this paper, we propose a new resistance factor calibration approach to address this dilemma by considering “feasibility robustness” of design in the calibration process. Herein, the feasibility robustness is defined as a probability that the βT requirement can still be satisfied even in the presence of uncertainty or variation in the computed bearing capacity. For illustration, LRFD approach for pile foundations commonly used in Shanghai, China is examined. Emphasis is placed on re-calibration of resistance factors at various feasibility robustness levels, with due consideration of the variation in the resistance bias factor. A case study is presented to illustrate the use of the re-calibrated resistance factors. The results show that the feasibility robustness is gained at the expense of cost efficiency; in other words, the two objectives are conflicting. To aid in the design decision-making, an optimal feasibility robustness level and corresponding resistance factors are suggested in the absence of a designer’s preference.

R-LRFD: Load and resistance factor design considering robustness

LRFD (Load and Resistance Factor Design) is becoming a design method of choice in geotechnical practice, in lieu of the factor of safety (FS)-based design approach. However, even with LRFD, the need to reduce the variation in the predicted performance of a geotechnical system (or a geotechnical structure), referred to herein as the system response under applied loads, is still apparent. This paper presents a novel approach for applying existing LRFD codes, with explicit consideration of design robustness, safety, and cost efficiency. The recently developed reliability-based robust geotechnical design (RGD) approach is modified such that it can be integrated with the standard LRFD approach. This modified RGD approach is termed R-LRFD, which stands for Robust Load and Resistance Factor Design. In R-LRFD, the robustness of the system response against the variation in uncertain parameters is explicitly considered. Unlike the reliability-based design (RBD), the user is not required to conduct a full statistical characterization of uncertain parameters. With R-LRFD, the gain in the robustness, as reflected by the reduction in the sensitivity of the system response to the recognized but unquantified uncertainty of input parameters, is accompanied by an increase in cost. Thus, the concepts of Pareto front and knee point are introduced to aid in making an informed design decision. Further, a simplified procedure is developed to identify the most preferred design (knee point) in the design space, which is generally solved with multi-objective optimization algorithms. The effectiveness and significance of the proposed R-LRFD approach are demonstrated with two examples: one is the design of drilled shaft in sand (illustrated with a discrete design space) and the other is the design of drilled shaft in clay (illustrated with a continuous design space).

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.

“DESIGN OF REINFORCED SOIL WALLS BY LRFD APPROACH”

In this paper, the detail of Load and Resistance Factor Design (LRFD) approach which is based on reliability concept for the design of Reinforced Soil (RS) walls is presented. For conventional methods i.e Allowable Stress Design (ASD) Method, the factor of safety is applied only to resistance and loads are considered without variations. For LRFD method, factor of safeties are applied for both load and resistance. Due to availability of large statistical data and economy, this method is preferred. An attempt is made to solve one numerical example of geosynthetic RS walls due to soil selfweight plus permanent uniform surcharge using LRFD as well as other conventional methods (ASD) viz. FHWA, Modified Rankine, NCMA and B.S Code Methods and the results of the LRFD methods are compared with conventional design methods and concluding remarks are presented. The various equations are obtained based on various curves plotted by using ASD and LRFD approaches. From these equations it is clear that if FOS against tensile rupture is known for any RS wall having 7m height and same properties and environmental conditions as mentioned in current study then FOS against pullout failure and pullout capacity can be computed for these walls.

LRFD Calibration for Steel Strip Reinforced Soil Walls

The paper reports the results of load and resistance factor design (LRFD) calibration for pullout and yield limit states for steel strip reinforced soil walls under self-weight loading. An important feature of the calibration method is the use of bias statistics to account for prediction accuracy of the underlying deterministic models for reinforcement load, pullout capacity and yield strength of the steel strips, and random variability in input parameters. To improve the accuracy of reinforcement load predictions, small adjustments to current semiempirical American Association of State Highway and Transportation Officials (AASHTO) load design charts are proposed. Similarly, current empirical-based design charts found in AASHTO and Federal Highway Administration (FHWA) guidance documents for the estimation of the pullout resistance factor for smooth and ribbed steel strips are adjusted to improve the accuracy of pullout capacity predictions. The results of calibration lead to a load factor of 1.35 that is consistent with current practice and resistance factors that together give a consistent probability of failure of 1% for all three limit states considered. Furthermore, comparison with allowable stress design (ASD) past practice (AASHTO simplified method) shows that the operational factors of safety using a rigorous LRFD approach give the same or higher factors of safety and lower probabilities of failure. In this study, data for steel strip reinforced soil walls are used as an example to illustrate rigorous reliability theory-based LRFD calibration concepts. However, the general approach is applicable to other reinforced soil wall technologies and calibration outcomes can be updated as more data become available.

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.

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%.

LRFD Approach for FRP-Reinforced Thermoplastic Beams

Thermoplastic beams are currently being used primarily in marine and waterfront applications, and can be used in bridges and buildings. A summary is presented of an experimental and theoretical study of the flexural behavior of a commercially available thermoplastic beam known as Seatimber with simple supports and subjected to a gradually increasing midspan concentrated load. Theoretical predictions are based on a non-linear moment-curvature analysis coupled with a central finite-difference scheme. Simplified criteria for a load and resistance factor design (LRFD) approach is outlined and its use demonstrated through analysis and design examples.

LRFD Approach for FRP Channel Section Columns

Pultruded fiber-reinforced plastic (FRP) channel section columns can develop flexural, torsional, and flexural—torsional buckling modes when subjected to a gradually increasing axial load. In this study, the results of a theoretical and experimental investigation on a FRP channel section column are first presented. Buckling and squash load formulas for the problem are summarized and used for plotting column maximum load envelope. It is also found that the load-carrying capacity of channel section columns can be dramatically increased by `equalizing' the cross-sectional depth and width. Finally, based on the column formulas, a load and resistance factor design (LRFD) approach is outlined and its use demonstrated through practical analysis and design examples.

Stability of FRP Beams under Three-point Loading and LRFD Approach

This article presents the results of an experimental and theoretical study of I-section fiber-reinforced plastic (FRP) beams subjected to a gradually increasing midspan load. The load is applied about the beam major axis from the compression flange side through a point below the shear center. The boundary conditions are flexurally and torsionally pinned. A 4 2 1/4 in. 3 pultruded I-section is adopted for the study and beam span lengths of 108, 96, 84, and 72 in. are used. The flexural-torsional response of the FRP beams is studied experimentally up to the maximum loadcarrying capacity. The experimental peak loads are compared with those arrived at theoretically using an equilibrium approach and are found to be in good agreement. To obtain a design expression for estimating the beam buckling load, an elastic buckling moment expression from the load and resistance factor design (LRFD) specification of the American Institute of Steel Construction is first modified. Next, a LRFD approach for the beam is outlined and its use demonstrated through analysis and design examples.

Reliability-based load and resistance factor design for piping: an exploratory case study

This paper presents an exploratory case study on the application of Load and Resistance Factor Design (LRFD) approach to the Section III of ASME Boiler and Pressure Vessel code for piping design. The failure criterion for defining the performance function is considered as plastic instability. Presently used design equation is calibrated by evaluating the minimum reliability levels associated with it. If the target reliability in the LRFD approach is same as that evaluated for the presently used design equation, it is shown that the total safety factors for the two design equations are identical. It is observed that the load and resistance factors are not dependent upon the diameter to thickness ratio. A sensitivity analysis is also conducted to study the variations in the load and resistance factors due to changes in (a) coefficients of variation for pressure, moment, and ultimate stress, (b) ratio of mean design pressure to mean design moment, (c) distribution types used for characterizing the random variables, and (d) statistical correlation between random variables. It is observed that characterization of random variables by log-normal distribution is reasonable. Consideration of statistical correlation between the ultimate stress and section modulus gives higher values of the load factor for pressure but lower value for the moment than the corresponding values obtained by considering the variables to be uncorrelated. Since the effect of statistical correlation on the load and resistance factors is relatively insignificant for target reliability values of practical interest, the effect of correlated variables may be neglected.

Limit States and Factor of Safety in Design of an Anchored Sheet Pile Wall

Factors of safety in the traditional design of anchored sheet pile walls have been introduced in a variety of ways. Furthermore, empirical and semiempirical factors are used to modify the calculated depth of embedment, anchor rod force, and maximum bending moment in sheet piling. This leads to a range of designs within the traditional allowable stress design (ASD) approach. Even in the new ultimate limit states design (LSD) method, two approaches are available. One approach is to use load and resistance factor design (LRFD), and the other is to use partial safety factors on the material properties in combination with load factors. In view of the number of design alternatives available, a calibration study of LSD with ASD for an anchored bulkhead was performed. The practical problem of a steel sheet pile wall in a layered cohesionless soil and cohesionless soil overlying cohesive soil was analyzed. The depth of embedment, the anchor rod force, and the maximum bending moment in sheet piling were determined for a range of soil parameters by using LSD and ASD methods. The factors recommended in various codes, manuals, and handbooks were used to perform calibration studies. The results of the parametric study indicate that the load and resistance factors recommended in the LRFD approach must be reevaluated.

Load and resistance factor design (LRFD) approach for reinforced-plastic channel beam buckling

Pultruded fiber reinforced plastic (PFRP) structural sections are rapidly gaining impetus in civil engineering applications. Thin-walled open beams with channel, I-shaped, and other types of sections are of practical importance to designers. In this paper, a load and resistance factor design (LRFD) approach for lateraltorsional buckling is presented based on an experimental and theoretical study of the behavior of PFRP channel section beams under the influence of gradually increasing static loads. Some experimental results for combined bending and torsion are also presented. Single span members with unrestrained end warping are considered with concentrated vertical loads passing through (a) the shear center, (b) the geometric centroid, and (c) a location which is neither at the shear center nor at the centroid. A pair of concentrated loads are applied symmetrically about the beam midspan, through a system of loading plates and tie rods in order to allow an unrestrained deformation of the beam. The loads are increased gradually and the resulting midspan vertical, lateral, and torsional deflections are recorded. The loads are generated with hydraulic jacks and recorded by means of calibrated load cells. Strains are also recorded at key locations using electrical resistance gages. Relationships between the applied load and the resulting deflections and strains are plotted and compared for the three load cases. The magnitude and significance of the warping stresses in comparison to the flexural stresses are identified. For the case of shear center loading, the deflections are monitored for various clear spans of the beam. This information is then utilized to generate the relationship between the lateral torsional instability load versus the minor axis slenderness ratio. An approximate theoretical formula is also developed to predict the lateral-torsional buckling load as possible prelude to the evolution of a formal construction specification formula for use by design engineers. The predicted buckling loads found using the formula are in excellent agreement with the experimental results. A comparison of the results from the formula applied to the case of compression flange loading is also made to those using the current AISC-LRFD specification. Lastly, the use of a proposed LRFD approach is demonstrated by means of analysis and design examples. The effect of the applied load height on the buckling load capacity is explained using the buckling formula.