Resistance Factor Design Research Articles

Optimal Design of Semirigid Connection Steel Frame with Steel Plate Shear Walls Using Dolphin Echolocation Algorithm

Steel frame with steel plate shear walls (SPSWs) is used to resist lateral loads caused by wind and earthquakes in high-rise buildings. In this load-resisting system, the cost and performance are more efficient than in the moment frame system. Behaviors of beam-to-column connections are assumed to be pinned or fixed to simplify the calculation in the past few decades. However, studies have stated that such a simulation fails to reveal the response of beam-to-column connections. In this paper, a newly developed metaheuristic optimization algorithm—the dolphin echolocation algorithm (DE)—based on foraging prey using echolocation in dolphins is applied as the present study optimizer. Two different two-dimensional semirigid connection steel frames with SPSWs are optimized to obtain the minimum cost of semirigid connection steel frame with steel plate shear walls with constraints to element stresses and story drift ratio according to the American Institute of Steel Construction (AISC) Load and Resistance Factor Design (LFRD). SPSW is modeled as a brace with equivalent lateral stiffness, while the P−△ effects are considered in the steel frame. Semirigid connections are used to reveal the actual responses of beam-to-column connections. The results demonstrate the proposed method’s effectiveness for optimizing semirigid connection steel frames with SPSWs and the interaction between semirigid connections and the SPSWs.

Analysis and stiffeners' design of a steel bridge girder

Plate girders are designed to carry massive loads over large spans. Flanges resist moment and web resists shear forces. Shear strength of steel girders having slender webs is much less than the yielding shear capacity. It is mainly due to the buckling of the web prior to reaching the yield strength of the material. Webs are generally reinforced with transverse stiffeners to increase their buckling strength. Stiffened webs resist shear also after buckling, which is called as post buckling strength. Tension field theories explain the formation of the post buckling strength and predict the stiffened web’s ultimate shear strength. Most design code provisions are set on tension field theories. There exists plenty of tension field theories proposed until today. This paper covers the design shear strength check and design flexural strength check and the stiffeners’ design of a steel girder specimen which was designed intentionally to fail in shear buckling. Analysis and stiffeners’ design were performed according to the provisions for load and resistance factor design (LRFD) in the ANSI/American Institute of Steel Construction (AISC) 360-16 - Specification for Structural Steel Buildings.

Estimating live-bed local scour around bridge piers in cohesionless sediments: applicability and bias of selected models

To design the foundation system of waterway bridges, Load and Resistance Factor Design guidelines suggest use of deterministic scour depth prediction models. Understanding the inherent bias of deterministic scour depth prediction models will advance the development of reliability index-based foundation design regime. Four bridge scour depth prediction models were assessed in terms of two statistical parameters, termed herein mean absolute percentage error (MAPE), and conservatism, percentage of cases the predicted scour depth exceeded the measured scour depth. Live-bed laboratory and field scour depth databases were used in analyses to quantify model scatter by comparatively assessing the computed scour depth versus measured data. For live-bed laboratory data, values of MAPE ranged from 23.5% to 59.8%, whereas conservatism ranged from 28.4% to 97.8%. For live-bed field data, conservatism varied from 93.3% to 95.1%, while MAPE ranged from 205.6% to 319%. Statistical models were applied to ascertain the biasness of the four deterministic models. Accuracy and conservatism of a given model were consequently adjusted through proposed modification factors. The proposed approach allows for the selection of a suitable modification factor to satisfy a target probability of deceedance or a target conservatism.

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.

Reliability-based load and resistance factor design model for energy piles

Energy piles have been popular globally with functions of both pile foundation and ground source heat pumps. Although several researches have been devoted to the probabilistic design and assessment of energy piles, the corresponding procedures are too complicated for engineers. As a simple variant of the reliability-based design method, the load and resistance factor design (LRFD) approach for the geotechnical design of energy piles is presented in this study. Firstly, the load-transfer model for energy piles is developed to investigate the effect of cyclic thermal loading on the pile settlement. Then, the LRFD procedures based on first-order reliability method and target reliability method are implemented into two different constrained nonlinear optimization problems, respectively. The proposed LRFD model for energy piles is demonstrated through an example pile and a series of parametric analyses.

Context-Dependent Parameter Sensitivities in Rock Slope Stability

Context-dependent sensitivities of parameters and reliability-based design (RBD) of rock slopes are the subjects of this paper. The similarities and differences between the design points in RBD and those of partial factor design methods are discussed. It is demonstrated that partial factors provided by the design point of the first-order reliability method (FORM) can provide case-specific insights and guidance to partial factor design methods like Eurocode 7 (EC7) and the load and resistance factor design (LRFD). It is suggested that conducting RBD-via-FORM in tandem with partial factor designs is more illuminating and meaningful than calibration of partial factors of parameters which can be sensitive in one case but insensitive in another case. Three cases are analysed probabilistically with respect to plane sliding in rock slopes with one or more discontinuities. In the first two cases, different deterministic solution procedures are used for the single block and two-block mechanisms, for comparison with stereographic projection method and closed form equation, respectively, prior to extending the cases into RBD. The third case involves a failed slope in a limestone quarry, analysed using FORM in this paper, for comparison with Monte Carlo simulation.

Reliability analysis & performance-based code calibration for slabs/walls of protective structures subject to air blast loading

A multilevel performance-based design (PBD) framework is developed for panels of Protective structures subjected to air blast. These provisions improve the existing design approach of blast resistance structures for ultimate limit state. Present study develops probabilistic deflection-based capacity and demand models for three performance levels associated with four damage states occurring during an air blast. The chosen protective structures for current study are reinforced Normal Strength Concrete (NRC) and reinforced Ultra-High Strength Concrete (UHSC) panels. The probabilistic models are developed using Bayesian inference (Posterior Statistics). The database is generated through numerical experimental design using finite element (FE) based software, LS-DYNA. The influence of air blast on panel is validated on a panel and obtained results shows the trustworthiness of numerical model. Grounded on these models the fragility estimation is carried out and attained plots demonstrates the consistency. Using a reliability based approach, the Load and Resistance Factors for Design (LRFD) are developed associated with the proposed three performance levels. Hazard curves and total probability are estimated using established dataset from literature available. The estimated LRFD factors can be used for the design of NRC & UHSC panel of slab/walls of protective structure subjected to air blast.

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.

Resistance factors for reliability based-design of fiber reinforced concrete suspended slabs in flexure

Due to the inherent uncertainties in the properties of construction materials, fabrication processes, applied loads, and the approximate nature of analysis methods, modern design codes have adopted the Load and Resistance Factor Design format (LRFD) to design civil engineering structures. In this format, loads and resistance are factored to consider the random nature of design variables. For instance, the reinforced concrete suspended slabs design is covered by ACI 318 [(Committee 318, 2019) 11 code, which is currently based on the LRFD format. On the other hand, the design of fiber reinforced concrete suspended (FRC) slabs fall under ACI 544.4 [(Committee 544, 2018) 22, which is not based on LRFD; therefore, it warrants an appropriate resistance factor to be used in conjunction with the current ASCE 7 [(American Society of Civil Engineers, 2017) 33 load factors and load combinations. In this paper, a reliability-based design procedure is developed to calibrate the resistance factor for the flexural design of FRC slabs with and without conventional steel reinforcement. Statistical and probabilistic analyses of experimental data showed that the resistance model for the flexural design of hybrid FRC slabs obeys the lognormal distribution with a bias of 1.33 and a coefficient of variation of 0.24. But for FRC slabs without additional reinforcement, the bias factor and the coefficient of variation of the resistance model increase to 1.56 and 0.37, respectively. In the case of conventional reinforced concrete slabs, the current resistance factor is . In the case of FRC slabs, an additional resistance factor of shall be applied to account for the contribution of fibers. This factor consistently provides the minimum safety level (i.e., the reliability index is close to or larger than the target reliability). However, in the case of FRC slabs without conventional steel reinforcement, a resistance factor of 0.75 is recommended to consistently meet the target safety level. The effectiveness of fibers in hybrid reinforced concrete slabs is more pronounced (smaller reduction of compared to 25% for slabs with fibers alone), thus, supporting the synergetic effect between the two reinforcing materials.

LRFD Approach for Load Rating U.S. Army-Owned Bridges That Require Engineering Judgment

As part of their 2020 Biennial Inspection Program, the U.S. Army is conducting a load rating effort for its bridges located at military installations throughout the United States. To date, 201 structures at 26 army bases are being evaluated for both civilian and military vehicles. Seventy-two of these structures are reinforced concrete bridges with unknown reinforcement which must therefore be rated using engineering judgment. The American Association of State Highway and Transportation Officials’ (AASHTO) Manual for Bridge Evaluation provides guidance for these structures when the live loads are civilian vehicles. For army-owned bridges, however, an allowable military load classification must also be determined. A procedure called “correlation classification” is currently used to determine the proper military load classification for a particular bridge. The current procedure, however, is based on the allowable stress method. To allow the use of load resistance factor design (LRFD), a new correlation equation and methodology using LRFD principles was developed. The methodology, however, requires the load rater to incorporate knowledge about the bridge into the load rating process. For older bridges with lighter design vehicles, and low the average daily traffic bridges, the correlation concept was also used to determine if a posting was required for state legal and emergency vehicles. This exercise demonstrated that the current correlation equation can be successfully modified to incorporate LRFD principles and applied to determine the military load classification for reinforced concrete structures that require engineering judgment. The application of the new correlation equation is illustrated with two examples: a reinforced concrete beam bridge and a box culvert.

Chronology of Service Limit State Development for Geotechnical Elements Designed Using AASHTO Load and Resistance Factor Design

The purpose of this paper is to provide a chronology of the development of the Service Limit State design process for geotechnical elements that are designed using the reliability-based Load and Resistance Factor Design (LRFD) approach in the Bridge Design Specifications of AASHTO. This chronology will help future researchers to better understand the basis of decisions made by AASHTO, with input from the FHWA, and thus will serve as an important benchmark for future work.

A stochastic framework for the assessment of horizontally curved aluminium bridge decks on steel girders

A purpose-developed structural reliability assessment (SRA) framework for the evaluation of horizontally curved aluminium alloy bridge decks on steel I-girders of centre subtended angle, θ≤34.4 with precinct on the American association of state highway and transportation officials (AASHTO) load resistance factor design (LRFD) specification is presented. The finite element analysis (FEA) simulations were performed in the ABAQUS© CAE, whilst the probabilistic assessment model was developed using the first-order reliability method (FORM). Besides performing detailed design checks and a validation exercise, the developed SRA framework was used to examine the structural behaviour of the bridge assembly in the presence of stochastic design truck axle loads, structure’s self-weight, among other loads, whilst varying geometric properties. The most critical structural responses chosen at salient points obtained via FEA simulation is applied in deriving the limit state function (LSF), which is then substituted into the stochastic model within the purpose-developed iterative FORM algorithm to calculate the reliability index (RI), β of the structure. It is shown that the proprietary AlumadeckTM system conforms with the LRFD specification, which stipulates that the target value of RI is 3.5 for resistance factor (RF) of 1.0 (assuming 80% composite action compression flange). The result also reveals that the RI shows a strong dependence on the composite action between the deck and the girder for RF of 1.0 full composite action (considering the failure of the bottom flange), indicating the safety index is within acceptable limits. Furthermore, it is revealed that the minimum composite action for safety is 40%, corresponding to a safety index of 1.16. Hence, it can be inferred from the foregoing that the AlumadeckTM can withstand the stochastic axle load it is subjected to considering the HL-93 load design condition and satisfies all design criteria considered from a stochastic perspective based on the AASHTO LRFD guidelines, provided the minimum stiffner thickness tstiffner of 7mm is adopted (based on the FEA simulation results). A case study conducted herein established that the structural configuration selected (i.e. depth at 2.4m, flange thicknesses at 21mm, flange width at 50cm and web thickness at 16mm) demonstrates the structural safety and durability of the bridge system coupled using the AlumadeckTM.

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 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.

Reliability-Based Assessment of Concrete Decks Designed Using Approximate Method at the Strength I Limit State

The Approximate Method coupled with the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications (BDS) is applied for designing reinforced concrete bridge decks. Although the LRFD BDS has an intrinsic design return period of 75 years and a target reliability index of 3.5 at the Strength I Limit State, many concrete bridge decks exhibit much shorter service life. Besides the limitations of the crack control limit state at service, the inadequate nominal resistance at the Strength Limit State could contribute to the shortened service life. This paper presents a reliability-based assessment of the current concrete deck design provisions by utilizing actual truck load spectra collected from the national weigh-in-motion (WIM) data. Axle groups, including single axles, tandem axles, and tridem axles, were identified from the WIM data. The moment effects are obtained from influence surface analysis, formulating the live load statistics, particularly for the decks that are supported by girders. It was found that the current design load is not able to represent and envelop the actual traffic load. Additionally, the reliability indices are calculated for a series of reinforced concrete decks on account of both bending moment capacity and arching action moment capacity. The arching action was found to greatly enhance the reliability index for the positive moment region, providing satisfactory reliability indices. The negative moment region may or may not meet the target reliability index depending on the design criteria.

ALTERNATIF DESAIN STRUKTUR ATAS JEMBATAN RANGKA BAJA TIPE HALF THROUGH ARCH PADA JEMBATAN TRISULA BLITAR, JAWA TIMUR

The bridge is an important infrastructure in the transportation system, namely as a means of crossing the river, as well as connecting between cliffs. The bridge has various shapes, one of which is a curved bridge with cables. Arch bridge is suitable for trident bridge because it has a long span. Through this thesis, the author tries to plan an alternative building over an existing bridge with a curve type. Preliminary planning data includes the total length of the existing bridge 150 m wide by 9 m. The planning method used is LRFD (Load Resistance Factor Design) and uses the Staad Pro v8i assist program. In this planning the author planned floor plates, elongated girders, transverse girders, parent girders, wind bonds, cables, joints and elastomers. From the results of the analysis obtained the structure of the building over the bridge for floor plates using the principal bones D10-200 and reinforcements for D13-200, the elongated steel gelagar profile WF 500 x 200 x 10 x 16, the steel transverse gelagar profile WF 800 x 350 x 16 x 36, the parent steel gelagar profile WF 700 x 300 x 13 x 24, steel steel bond double profile L250 x 250 x 35, for the dimensions of dyform cable D38, for laying using elastomer size 120 cm long, width 120 cm, height 26 cm

Study of Yielding Zone on Reinforced Concrete Bridge Parapet Design for Vehicular Impact

Reinforced concrete bridge parapets have important safety roles in the highway system. Currently AASHTO and FHWA require all new permanent installation of bridge rails on the National Highway System to be compliant with Manual for Assessing Safety Hardware (MASH) requirements. Therefore, there is an immediate need to update Section 13: Railings of the AASHTO LRFD [Load and Resistance Factor Design] Bridge Design Specifications to incorporate the MASH requirements. However, the current provisions for designing and analyzing concrete parapets in AASHTO using yield-line theory have been found to possess many inherent limitations, including an inaccurate yield-line pattern for computing nominal resistance to transverse load. This paper presents an evaluation of AASHTO’s yield-line pattern using both dynamic finite element analysis (FEA) and an analytical investigation based on theory of plates. In the dynamic FEA, a three-dimensional numerical model of a parapet section was created and analyzed using non-linear material properties. In the analytical approach, MATLAB was used to compute the stresses throughout a plate having properties equivalent to those of a reinforced concrete parapet. Computed stress values on the plate were graphically displayed to locate areas of highest stress concentration or yielding zones, where yielding of rebars has a high chance of occurring during impacts. The outcomes of the two independent analyses were found to be in very good agreement. The goal of this study is to predict reliable boundaries of the yielding zones, which will provide a strong foundation for developing a more precise yield-line pattern.

Database classification for LRFD of spread foundations under uplift loading in cohesionless soils

The load and resistance factor design (LRFD) approach considers the uncertainties of foundation capacity predictions by assessing the probability distribution of the model factors (i.e. model statistics). The model statistics are dependent on the selected load test database, and specific design parameters of the foundation. While previous studies have focussed on the compilation of extensive databases, there has been limited research on the classification of the database in terms of the design parameters that can affect the model statistics. Thus, this study aims to use unsupervised clustering methods to classify the database for uplift load tests of spread foundations in cohesionless soils. Three different clustering algorithms (hard K-means, fuzzy C-means, and self-organising map) were used to categorise the database by inputting the following parameters: the embedment ratio of the foundation, the friction angle of the soil, the normalised foundation width, and the model factors obtained from the calculation models in existing design codes. This study considers an existing database, NUS/SpreadFound/919, along with additional load test data collected from the literature. First, the database was divided into seven data groups, which were classified in terms of the uplift failure behaviour of the foundation (shallow, intermediate, and deep) and the strength parameter of the soil (loose and dense). Second, an example LRFD calibration was carried out, and it was shown that higher resistance factors were yielded when the classified data groups were used, compared to when the whole database was used. This demonstrated that the use of clustering is feasible for classifying the database to obtain more economic and optimal LRFD solutions.

Reliability-based design of fiber reinforced concrete slabs-on-ground in flexure as per ACI 360

Modern design codes apply the Load and Resistance Factor Design (LRFD) format to account for all uncertainties involved, primarily manufacturing, fabrication, and modeling errors. In this format, load effects are scaled-up by load factors while a resistance factor scales down the resistance. In this way, the LRFD design format ensures that all designs meet, consistently, a certain safety level. To determine the most appropriate factors, a reliability-based procedure is required, in which a target reliability index is selected, which corresponds to an acceptable probability of failure. Unlike most of the American Concrete Institute (ACI) design codes, which adopted the LRFD design format, the current ACI 360R for slabs-on-ground design is based on the concept of safety factors. The present work aims at calibrating the resistance factor,ϕ, for the flexural design of fiber reinforced concrete slabs-on-ground. A total of 56 laboratory tests gathered from previous studies were analyzed to determine the statistical parameters of the resistance model. Then a series of reliability analyses were conducted to calibrate the resistance factor. In the calibration process, dead and live loads with and without impact were considered in the load combinations. This study suggests that for a flexural design of fiber reinforced concrete slabs-on-ground subjected to dead and live (with or without impact) loads, to meet the target reliability index, a resistance factor ϕ = 0.8 is recommended. An example is presented to showcase the application of LRFD for the design of FRC slabs-on-ground.

Resilience-Based Design of Infrastructure: Review of Models, Methodologies, and Computational Tools

The quest to answer the longstanding question of how safe is safe enough has led to an evolution of design philosophies. The traditional philosophy has been based on ensuring that system capacity exceeds demand. This philosophy has been manifested in such design methods as allowable stress design (ASD) and load and resistance factor design (LRFD). The level of safety in these methods is commonly calibrated to the acceptable practice using structural reliability methods. Such an approach to design aims to balance life safety and construction costs and works relatively well for service loads under which strength is nearly always a sufficient representative of system capacity. Under extreme loads, however, not only do factors such as ductility or energy-dissipation capacity come into play, but also the consequences of failure are vastly larger and may go beyond the failure site. For this reason, the more modern design philosophy of performance-based design emerged. According to this philosophy, a system is designed to meet a target performance, defined by limits on its performance metrics. These metrics were initially defined on structural responses, such as deformations and accelerations, and later evolved into risk measures based on monetary loss, downtime, and casualties. This philosophy is gradually making its way into modern design codes. Typical performance-based criteria focus primarily on what transpires during extreme loads. The need to incorporate the recovery of the system after such events has prompted the design philosophy to make another leap into resilience-based design (RBD). Resilience is defined herein as the ability to recover, within a predetermined period of time, in the aftermath of extreme events. Resilience transcends risk, i.e., a resilience analysis incorporates not only a risk analysis but also a recovery analysis. This paper provides a review of RBD in continuation of PBD and further introduces various applications of RBD into the design and assessment of civil infrastructure. The review covers the state of the art in resilience quantification approaches and associated computational platforms.