Strength Limit State Research Articles

Reliability-Based Evaluation of U.S. Design Provisions for Composite Steel Deck in Construction Stage

This paper presents a reliability-based evaluation of the American National Standards Institute/Steel Deck Institute (ANSI/SDI) C1.0 and Structural Engineering Institute/American Society of Civil Engineers (SEI/ASCE) 37 design provisions for composite steel decks in the construction stage. Reliability of the allowable stress design (ASD) and load and resistance factor design (LRFD) methods at the strength and deflection limit states was evaluated in terms of reliability indices employing the first-order reliability method. A large number of composite slab configurations, which cover the range of slab parameters typically used in the U.S. construction practice, were investigated. Obtained results demonstrate that the current design provisions for steel decks in the construction stage are overconservative. Modifications of the ANSI/SDI C1.0 construction load requirements are proposed. The modified load requirements result in longer maximum unshored construction spans and acceptable reliability. Safety of the deck designed according to the modified load requirements is more uniform across the typical design parameters when compared with the current design provisions.

변형률계를 이용한 강재보의 건전도 평가 시스템 개발에 관한 연구

This study aimed to develop a Structural Health Monitoring System for steel beams in the manner of suggesting and verifying a theoretical formula for displacement estimation using strain gauges, and estimating the loading points and magnitude. According to the results of this study, it was found that when a load of 160kN (56% of the yield load) was applied, the error rate of the deflection obtained with a strain gauge at the point of maximum deflection compared to the deflection measured with a displacement meter was within 2%, and that the estimates of the magnitude and points of load application also showed the error rate of not more than 1%. This suggests that the displacement and load of steel beams can be measured with strain gauges and further, it will enable more cost-effective sensor designing without displacement meter or load cell. The Structural Health Monitoring System program implemented in Lab VIEW gave graded warnings whenever the measured data exceeds the specified range (strength limit state, serviceability limit state, yield strain), and both the serviceability limit state and strength limit state could be simultaneously monitored with strain gauge alone.

Experimental evaluation of GFRP bars as reinforcement for concrete bridge decks: Negative bending low cycle fatigue study

Bridge deck durability is often compromised due to corrosion of the steel reinforcement. The use of glass fiber reinforced polymer (GFRP) bars as a substitute for steel is a possible solution to this problematic condition. GFRP is an elastic brittle material with a high tensile strength, and modulus of elasticity that is approximately 20% that of steel reinforcement. Considering these material properties, meaningful data is required to demonstrate compliance with imposed design limits at all relevant limit states. Experimental evaluation of GFRP bars as structural reinforcement for highway bridge decks must recognize and duplicate the load and support conditions specific to this application. Laboratory testing should consider load magnitudes associated with AASHTO service, strength and fatigue limit states, indeterminacy of the deck in the transverse direction, two-way distribution of wheel loads, and load application and deck support conditions as affected by truck tire contact area and girder flange stiffness, respectively. In this research study 2-span continuous concrete beams doubly reinforced with GFRP bars are tested under load and support conditions designed to simulate performance of the GFRP reinforcement in a highway bridge deck environment. Monotonic, cyclic, and low cycle fatigue loading are applied to establish behavior of the experimental deck as related to an actual bridge deck load condition. Test results related to strength, deflection, and crack width are presented.

Proposed load combination factors for bridges with high dead-to-live load ratios

The combination of dead load and live load is very important in design of bridge superstructure as, in practice, it controls the strength limit states. The basic set of load factors for the Strength I limit state is 1.25 for dead load and 1.75 for live load and dynamic load. For design cases when the dead load dominates, i.e. for Strength IV limit state, the dead load factor is 1.5. The acceptability criterion for load and resistance factors in the AASHTO LRFD Code is closeness to the target reliability index, which is assumed to be 3.5 for steel and concrete girder bridges. However, the reliability analysis performed for a full range of dead load to live load ratios indicates that when live load is about 10-20% of the total load, the reliability indices are about 3.0 which is lower than the target value of 3.5. This is an indication that the reliability level is insufficient and there is a need for increasing load factors. On the other hand, for dead load constituting about 100% of the total load (i.e. no live load), the reliability index is much higher than 3.5, which means that the load factor 1.5 can be reduced. Therefore, it is proposed to change the current Strength IV load factors to dead load of 1.4 and live load factor 1.4. The result is a more uniform reliability level for all combinations of dead load and live load. The results of reliability analysis are presented in graphs.

Experimental behaviour of LVL–concrete composite floor beams at strength limit state

This paper reports the outcomes of short-term collapse tests performed on eleven laminated veneer lumber (LVL)–concrete composite floor T-beams. Different variables such as span length (8 and 10 m), connection and concrete types, and design level (well- and under-designed, in terms of connector numbers) were investigated. During 4-point bending tests, mid-span deflection, connection slips and strains were measured. Connection types investigated include triangular and rectangular (150 mm and 300 mm long) notches cut in the timber and reinforced with a coach screw, and modified toothed metal plates pressed on the edge of the LVL joists. All of the beam specimens were designed using the effective bending stiffness or γ -method, in accordance with Annex B of Eurocode 5. The same method was used for an analytical–experimental comparison of the beam’s performance at ultimate (ULS) and serviceability (SLS) limit state. All well-designed beams provided more than 95% composite action even though there were relatively few connectors (e.g. six 300 mm long notches on the 8 m span beam). The ULS and SLS live load capacity of the beams was found to be approximately 90% of that of a fully composite beam. Correction factors providing a 15% increase for deflection and a 13% reduction of the effective bending stiffness are proposed for calculations using the transformed section method for all well-designed beams, i.e. beams designed using the γ -method according to Annex B of Eurocode 5. Although the γ -method was found to be significantly underestimate the ULS strength, it provided an accurate prediction of the short-term deflection. In terms of the connection type, the 300 mm rectangular notches provided the best performance, with high stiffness and strength beyond the ULS load level, and requiring fewer connectors along the beam. The triangular notch was found to be a viable alternative, with more connectors but was easier and faster to cut than a rectangular notch. Metal plate connectors provide a practical construction possibility, but the beam stiffness was found to rapidly deteriorate beyond the ULS load level.

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.

Reliability-Based Transmission Line Design

It is well known that environmental loads, e.g., wind and ice, acting on power transmission lines are highly uncertain, as are the structural strengths of the towers supporting the lines. The design of such systems must take uncertainty into account in order to achieve acceptable reliability at a reasonable cost. The paper presents a simulation-based methodology for the optimal design of a transmission line which considers uncertainties in both environmental loads and structural resistance. The methodology is developed and illustrated for the simple problem of determining the optimal span length required for designing against tower failure. Wind, ice, and tower resistances are simulated over the extent of the transmission line and over the design life of the transmission system. Total expected system cost, along with the estimated probability of lifetime failure, are produced for a range of possible span lengths, allowing an informed decision regarding the optimum span length for the tower strength limit state.

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.

A comparative study of AISC-360 and EC3 strength limit states

A study has been undertaken to evaluate the similarities and differences between the steel building design specifications used in the United States and Europe. Expressions for nominal strength presented in the AISC-360 Specification and the Eurocode 3 Specification were compared for fundamental limit states. In particular, rules for cross-section classification, tension members, compression members, I-shaped members subjected to flexure, I-shaped members subjected to shear, and fasteners were studied. Results of the investigation revealed that, in general, both specifications provide nominal capacities that are close to each other. Significant differences were reported for some limit states such as flexure in I-shaped members with non-compact flanges, shear and lateral torsional buckling in I-shaped members, and bearing strength at bolt holes. In this paper, the details of the comparative study are presented along with observations that are useful for practicing engineers.

Glulam beams reinforced with FRP externally-bonded: theoretical and experimental evaluation

The glued- laminated lumber (glulam) technique is an efficient process for the rational use of wood. Fiber-reinforced polymer (FRPs) associated with glulam beams provide significant improvements in strength and stiffness and alter the failure mode of these structural elements. In this context, this paper presents guidance for glulam beam production, an experimental analysis of glulam beams made of Pinus caribea var. hondurensis species without and with externally-bonded FRP and theoretical models to evaluate reinforced glulam beams (bending strength and stiffness). Concerning the bending strength of the beams, this paper aims only to analyze the limit state of ultimate strength in compression and tension. A specific disposal was used in order to avoid lateral buckling, once the tested beams have a higher ratio height-to-width. The results indicate the need of production control so as to guarantee a higher efficiency of the glulam beams. The FRP introduced in the tensile section of glulam beams resulted in improvements on their bending strength and stiffness due to the reinforcement thickness increase. During the beams testing, two failure stages were observed. The first was a tensile failure on the sheet positioned under the reinforcement layer, while the second occurred as a result of a preliminary compression yielding on the upper side of the lumber, followed by both a shear failure on the fiber-lumber interface and a tensile failure in wood. The model shows a good correlation between the experimental and estimated results.

Performance-Based Design of Drilled Shaft Bridge Foundations

The design of deep foundations for bridge structures should ideally consider the interaction between the soil and the foundation element to properly model the side and tip resistance components. A soil-structure interaction model, such as the t-z model method, can be utilized to develop a load-displacement curve for a deep foundation subjected to axial loads. The load-displacement curve represents the behavior of the deep foundation over a range of applied axial loads. More importantly, however, the load-displacement curve can be analyzed by using performance-based design criteria, such as a tolerable displacement corresponding to the service limit state. The tolerable displacement of an individual deep foundation element can be selected to correspond to a movement that would cause adverse performance, excessive maintenance issues, or functionality problems with the bridge structure. In this paper, a performance-based soil-structure interaction design approach for the strength and service limit state axia...

Establishing concrete cracking strength interval using possibility theory with an application to predict the possible reinforced concrete deflection interval

Concrete cracking is a challenging and uncertain design criterion that significantly affects our ability to predict the serviceability of reinforced concrete (RC) structures. It is evident that the concrete cracking strength depends on the test method, such as flexural strength, splitting tensile strength and direct tension. Moreover, prediction models proposed by design codes have wide variation. The uncertainty of the cracking strength determined experimentally or numerically reduces confidence in serviceability limit state design when compared with strength limit state design. However, this uncertainty cannot be claimed as a random uncertainty but rather as an epistemic uncertainty. Intervals can be used to describe this uncertainty using possibility theory, a mathematical framework to represent a kind of epistemic uncertainty known as non-specificity. A methodology is introduced here to establish a concrete cracking strength interval. A case study to use this cracking strength interval to predict an RC deflection interval is presented.

Component sizing approach for the sandwich plate system

The sandwich plate system (SPS) is a bridge deck system consisting of steel face plates bonded to a rigid polyurethane core. SPS bridges are typically constructed as a series of pre-fabricated SPS deck panels compositely connected with traditional steel girders. The decks are thin, lightweight and modular, and can be tailored to numerous applications including both new bridge and rehabilitated bridges. With new system, there exist hurdles in the implementation; for SPS, the primary challenge is the lack of an established design method for the panel cross-sections. Presented herein is a method for sizing SPS panel sections for bridge applications. This method is limited to the selection of steel plate and core dimensions, subjected to American Association of State Highway and Transportation Officials (AASHTO) limit states of serviceability, strength and fatigue and does not consider connections or bond aspects of the system. The sizing approach considers the deck panels as plates with variable boundary conditions subjected to the loading conditions of the AASHTO Load Resistance Factored Design (LRFD) bridge design specification. Results from this study indicate that the component sizing for SPS deck panels is controlled by stiffness and that plates selected to satisfy the AASHTO limiting deflection criterion will also be adequate for the remaining serviceability, strength and fatigue limit states.

Realistic risk assessment of axially loaded pile–soil system using a hybrid reliability method

The behaviour of an axially loaded pile embedded in a non-homogeneous soil deposit considering the pile–soil nonlinear interaction effect is realistically evaluated, and a new efficient and accurate hybrid reliability method is proposed for estimating the corresponding risk. The complicated problem is first deterministically formulated and then the uncertainties associated with the various design variables are considered explicitly. The hybrid reliability approach intelligently integrates the concepts of the response surface method, the finite difference method, the first-order reliability method, and an iterative linear interpolation scheme. The soil around the pile is represented by a series of springs. The system is expected to represent a realistic and efficient load-transfer mechanism. The soil–pile dual system is then deterministically analysed using the finite difference method. Uncertainties associated with load conditions, material and sectional properties of the pile and non-homogeneous soil properties are then incorporated in to the deterministic formulation resulting in the hybrid reliability approach. The risks corresponding to both service ability and strength limit states are estimated. With the help of an illustrative example, the applicability, accuracy and efficiency of the proposed algorithm in the safety assessment of axially loaded pile–soil systems are demonstrated. The reliability evaluation procedure is verified using the Monte Carlo simulation technique.

Strength and ductility of reinforced concrete slabs containing welded wire fabric and subjected to support settlement

This paper describes a numerical investigation of the impact of steel ductility and support settlement on the strength and ductility of continuous one-way reinforced concrete slabs containing low ductility welded wire fabric (WWF). A finite element model is developed for the investigation using the software ATENA and the results of a series of concurrent laboratory experiments are used to validate the numerical solution. A parametric investigation is conducted using the numerical model to investigate the various factors that influence structural behaviour at the strength limit state. The ductility of the main flexural reinforcement has a profound impact on the ultimate load behaviour of continuous one-way slabs subjected to support settlement, particularly when the reinforcement consists of cold drawn welded wire fabric. Both the strain at peak stress ( ε s u ) and the tensile strength to yield stress ratio ( f s u / f s y ) of the tensile reinforcement have a significant effect on the strength and ductility of reinforced concrete slabs, both with and without support settlement. When ε s u ≥ 5 % and f s u / f s y ≥ 1.08 (i.e. for normal ductility reinforcement), the reduction of strength caused by support settlements of up to span/100 is small and, for design purposes, can be ignored, even when significant redistribution of actions has been assumed. However, for low ductility reinforcement (i.e. when ε s u < 3.5 % and f s u / f s y < 1.05 ), support settlement may result in a significant loss of load carrying capacity. The load-deflection curves are brittle, even for the slabs with zero support settlement, and the slabs have little ability to undergo plastic deformation at or close to the peak load. In all cases with low ductility steel, fracture of the steel occurs at one of the critical sections at deformations not much larger than that at the formation of the first plastic hinge and failure is catastrophic, with little warning.

Performance-Based Design of Deep Foundation Systems in Load and Resistance Factor Design Framework

Performance-based design methods are increasingly being used for the design and analysis of structures. For performance-based design of deep foundation systems, limiting tolerable movements are one of the design criteria that can be used in lieu of the usual ultimate load capacity. The limiting tolerable movement is often selected to correspond to a movement that will cause damage to a structure but will not produce a collapsible failure of the structure. Performance-based design principles can be extended to include the axial design of deep foundation systems under strength and service loading conditions. In this extended approach, limiting tolerable settlements can be selected to correspond to a movement that will either cause excessive stresses in the structure or render a structure functionally inoperable because of serviceability limits. A performance-based design approach for axial design of deep foundations under the strength and serviceability limit states was developed. The design approach is integrated with the load and resistance factor design framework to develop an efficient and consistent methodology for satisfying both limit state criteria.

Effect of Fiber-Reinforced Polymer Configuration on Reliability of Flexurally Strengthened Concrete Beams

External bonding of composite materials in the form of strips, plates, and laminates to add tensile capacity in deficient zones has proved to be an efficient strengthening technique. The performance of composite materials in strengthening ailing infrastructure components has made them a mainstream alternative in some applications such as strengthening concrete structures. The technique is mature enough that design standards have been published. Few researchers have investigated the reliability of concrete structures strengthened with fiber-reinforced polymer (FRP). The results of these reliability investigations were incorporated in some of the recently published design guidelines. It is a well-known fact that FRP debonding is the dominant mode of failure. Nevertheless, the impact of different FRP configurations on the reliability of strengthened concrete beams in flexure has not yet been investigated. An analytical study is presented of the reliability of FRP-strengthened concrete beams in two of the most popular configurations: U-wrap and soffit-only. Material, fabrication, and model uncertainties are accounted for in a strength limit state function to analyze the reliability of strengthened reinforced concrete beams by using the first-order reliability method. Results from this study show that the reliability of U-wrap configurations is higher than that of soffit-only configurations. This finding can be used in establishing different resistance factors for each case such that the use of more materials in the U-wrap configuration is rewarded by the ability to predict its performance better.

Design moment of shear connections at the ultimate limit state

Shear connections develop moment under the rotational demand imposed on them by the supported beam. This paper proposes a semi-analytical approach for computing the moment of single-angle, double-angle and end-plate shear connections corresponding to the strength limit state of their supported beam. The connection moment equations are derived based on the observed yieldline mechanisms from various experimental tests on the shear connections. The approach takes into account major parameters such as connection plate thickness, angle length, bolt gauge and steel yield strength. The obtained equations can also be used to estimate the compression zone depth and tension zone force. Good agreement between the theoretical analysis results and the various test data is demonstrated. Finally, suggestions are given for applying the approach to design shear connections.

Web crippling strength of a steel sandwich panel with V-shaped webs

Steel sandwich panels with V-shaped web flutes (V-core panels) serve the structural functions of a proposed energy-efficient roof system for residential construction. Due to its intended use as a flexural member spanning between a ridge beam and a structural wall, and required slender webs for weight considerations, web crippling under end one-flange loading is a critical strength limit state for the V-core panels. Although the 2001 North American Specification for the Design of Cold-Formed Steel Structural Members provides a design procedure to address web crippling, those design rules were developed for members whose cross sections are different from that of V-core panels. Consequently, nine specimens were tested to collect data on V-core panels subjected to end one-flange loading. Test observations suggested that V-core panels behave very similarly to multi-web decks that are strapped and unfastened to the supports. Experimental data reported in the literature was used to modify the web crippling strength equation in the Specification to reflect these particular conditions. The modified equation was found to adequately predict the measured web crippling strength of V-core panels.

Single-angle all-bolted shear connections

This paper describes an experimental test of 19 full-scale single-angle all-bolted shear connections. The primary purpose of the study was to determine the shear strength of the two bolt groups associated with the two legs of the connection angle. The tested connections were made of an equal-leg angle and a vertical row of bolts at each leg. The angle had a leg width of 102 mm and a thickness of 9.5 mm. The bolts were 19 mm diameter high-strength A325 bolts. The number of the bolts in one vertical row was from 2 to 8 inclusive. The observed failure mode of the tested connections was the shear rupture of one of the bolt groups. The test found torsional or lateral restraints to the supported beam had a significant impact on the load carrying capacity of the connections. Test results indicated that the current North American design practices could lead to underdesigned single-angle connections having the number of bolts less than or equal to three. Furthermore, a yield line method was adopted for estimating the connection moment at strength limit state.