Governing Limit State Research Articles

Structural rehabilitation of half-joints in RC bridges: a state-of-the-art review

Gerber road bridges provide clear advantages in terms of stress distribution and absorption of small settlements. For this reason, such bridge designs have been frequently used in Italy and abroad. This static arrangement is provided with connections among spans located in the half-joints, which are prone to the accumulation of deteriorating agents and are difficult to inspect. Furthermore, these bridges were designed based on old code provisions referring to loads lower than those prescribed by current codes. Hence, half-joints frequently need to be assessed and possibly strengthened. This paper reviews the available strengthening techniques based on both practice and experimental results, comparing them in terms of structural performance, failure mode and governing limit state. As result, a decision-making approach is proposed in order to guide intervention choices while accounting for design requirements and constraints. In fact, the presence of curbs and transverse beams close to half-joints prevents the utilization of externally bonded composites making steel-based techniques more suitable. Some remarks on intervention costs highlight the great impact of deteriorated half-joints due to the need for bridge lifting and carry out restoration interventions. Therefore, the need for repair should be carefully evaluated as it significantly influences the overall intervention cost.

Reliability-based serviceability limit state design of spread foundations under uplift loading in cohesionless soils

ABSTRACT The design of foundations is often governed by the serviceability limit state (SLS) requirements of the supported structure, particularly for large spread foundations. This paper aims to develop a reliability-based SLS design method for spread foundations under uplift loading in cohesionless soils. A probabilistic framework was adopted for the empirical characterisation of the compiled load-displacement curves and the quantification of the associated uncertainties. By using the obtained statistics of the curves, reliability analysis was carried out with Monte-Carlo simulations to calibrate the resistance factors within the load and resistance factor design (LRFD) framework. The calibration results showed that the embedment ratio of the foundation and the fitting errors of the empirical model, which were previously unaddressed in the literature, had notable effects on the calibrated SLS resistance factors. The relationship of the SLS with the ultimate limit state was assessed, including the governing limit state at each allowable displacement level, and the probability of ultimate failure of the foundation at the SLS condition. By considering the relationship between the limit states, the procedures for determining the design resistance factor and foundation capacity were proposed.

Mean Stress Effect in High-Frequency Mechanical Impact (HFMI)-Treated Steel Road Bridges

High-frequency mechanical impact (HFMI) is a post-weld treatment method which substantially enhances the fatigue strength of steel weldments. As such, the method enables a more efficient design of bridges, where fatigue is often the governing limit state. Road bridges are typically trafficked by a large variety of lorries which generate load cycles with varying mean stresses and stress ranges. Unlike conventional welded details, the fatigue strength of HFMI-treated welds is known to be dependent on mean stress in addition to the stress range. The possibility of considering the mean stress effect via Eurocode’s fatigue load models (FLM3 and FLM4) was investigated in this paper. Moreover, a design method to take the mean stress effect into account was proposed by the authors in a previous work. However, the proposed design method was calibrated using limited traffic measurements in Sweden, and as such, may not be representative of the Swedish or European traffic. In this paper, larger data pools consisting of more than 873,000 and 446,000 lorries from Sweden and the Netherlands, respectively, were used to examine the validity of previous calibration in both countries. The comparison revealed no significant difference between the data pools with regards to the mean stress effect. Additionally, previous calibration provided the most conservative mean stress effect and was considered adequately representative for both countries. The proposed design method was further validated using four composite case study bridges. It was also found that the mean stress effect was mainly influenced by the self-weight, while variation in the mean stress due to traffic had a minor influence on the total mean stress effect. Furthermore, it was found that the mean stress effect could not be accurately or conservatively predicted using FLM3 or FLM4.

Improved Ultra-Low Cycle Fatigue Fracture Models for Structural Steels Considering the Dependence of Cyclic Damage Degradation Parameters on Stress Triaxiality

The ultra-low cycle fatigue (ULCF) fracture initiation caused by cyclic large plastic strain in structural steels is often the governing limit state in steel structures when subjected to strong earthquake actions. Based on the author’s previous work, this paper presents the improved cyclic void growth model (CVGM) and degraded significant plastic strain (DSPS) model considering the dependence of cyclic damage degradation parameters on stress triaxiality. To this end, tests on circular notched specimens and coupon specimens made of Q345qC steel were conducted, and scanning electron microscopy studies were performed on fracture surfaces of specimens, analysis results of which show that the ULCF fracture of Q345qC steel exhibits the typical behaviour of “void nucleation, growth, and coalescence.” The cyclic damage degradation parameters of CVGM and DSPS model were calibrated at different stress triaxialities based on experimental results of specimens and complementary finite element analysis, and empirical formulas were subsequently established between cyclic damage degradation parameters and stress triaxiality. Finally, detailed finite element analysis results demonstrate that the improved CVGM and DSPS model can predict ULCF fracture behaviour with higher accuracy in comparison with original models.

Limit state behavior and response sensitivity analysis of endplate steel connections with shape memory alloy bolts

Shape memory alloys have been used in developing self-centering steel moment connections. This article presents a numerical study aiming at evaluating the cyclic response sensitivity and limit states of extended endplate steel connections with shape memory alloy bolts. Three-dimensional finite element models are developed and validated against a recent experimental study. Using a statistical design-of-experiment method, the effects of 21 design factors and their interactions on the cyclic response of shape memory alloy connections are assessed. The sensitivity of six response parameters is studied. In addition, four limit states for shape memory alloy connections are discussed, including beam local buckling, bolt excessive axial strain, endplate yielding, and column flange yielding. Results show that endplate thickness, shape memory alloy bolt diameter, beam web slenderness ratio, and shape memory alloy maximum transformation strain are the most influential factors. Furthermore, endplate yielding is found to be the governing limit state in almost 80% of the analyzed connections, whereas shape memory alloy bolt excessive strain and column flange yielding are observed in less than 20% and 5% of the connections, respectively. Beam local buckling is not governing in the analyzed shape memory alloy connections designed as per the AISC 358-16 and AISC 341-16 seismic design requirements for extended endplate connections and highly ductile members.

Structural design and behavior of prestressed cable domes

A cable dome system is a spatial network of cables and struts that are pin-jointed, and whose forces are eventually brought to balance by a perimeter ring beam and supporting walls or columns. This paper provides insights about the structural design and behavior of prestressed radial-type cable domes. Through a study of parametric effects, the paper emphasizes careful selection of geometric parameters and cable prestressing forces. A simplified planar model equivalent to that of a three-dimensional model is derived for efficient analysis and design under symmetric loading conditions. The equivalent planar parameters are obtained using the geometrical and nodal force equilibrium relationships, and the Principle of Virtual Work. Results from planar analysis are compared and validated with the three-dimensional analysis results. The calculation of initial member sizes and initial cable prestressing forces is explained. This is followed by a discussion of the structural behavior of cable domes under asymmetric snow loads and wind uplift and the ensuing stability issues. The analysis results revealed that either strut buckling or overall system stiffness were the dominant limit states, the former being the governing limit state in domes with fewer hoops. A design enhancement in the form of cable-stayed struts is as such recommended to not only increase the strut buckling strength, but also to substantially increase a dome’s load bearing capacity.

Review of Pedestrian Load Models for Vibration Serviceability Assessment of Floor Structures

Innovative design and technological advancements in the construction industry have resulted in an increased use of large, slender and lightweight floors in contemporary office buildings. Compounded by an ever-increasing use of open-plan layouts with few internal partitions and thus lower damping, floor vibration is becoming a governing limit state in the modern structural design originating from dynamic footfall excitations. This could cause annoyance and discomfort to building occupants as well as knock-on management and financial consequences for facility owners. This article presents a comprehensive review pertinent to walking-induced dynamic loading of low-frequency floor structures. It is intended to introduce and explain key walking parameters in the field as well as summarise the development of previous walking models and methods for vibration serviceability assessment. Although a number of walking models and design procedures have been proposed, the literature survey highlights that further work is required in the following areas; (1) the development of a probabilistic multi-person loading model which accounts for inter- and intra-subject variabilities, (2) the identification of walking paths (routes accounting for the effect of occupancy patterns on office floors) coupled with spatial distribution of pedestrians and (3) the production of a statistical spatial response approach for vibration serviceability assessment. A stochastic approach, capable of taking into account uncertainties in loading model and vibration responses, appears to be a more reliable way forward compared to the deterministic approaches of the past and there is a clear need for further research in this area.

Evaluation of the bolt and weld eccentricities of conventional single-plate shear connections

This study aims to investigate the accuracy of bolt eccentricity (eb) and the required weld size for connecting shear tab to the support presented in 15th edition of AISC Steel Construction Manual for conventional single-plate (CSP) connections. In addition, the available equation for prediction of the weld eccentricity (ew) was evaluated. For this purpose, by changing different parameters, 72 specimens were designed in accordance with the AISC Manual. The designs are in a way that the bolt fracture becomes the governing limit state. Investigated parameters include loading type, bolt pretensioning force, beam span (Lb), beam depth (db), the number of bolts (n) and the spacing between bolt and weld lines (a). All specimens were analyzed through finite element (FE) method using ABAQUS software. Results indicate that the manual prediction for eb is non-conservative and inaccurate. Although the available equation for ew was able to reasonably predict ew, this equation yields to a non-conservative prediction in most cases. Furthermore, results indicate that among all investigated parameters, only n, Lb and a have remarkable effects on eb and ew. In order to propose alternative equations for eb and ew in terms of effective parameters, artificial neural network was utilized which resulted in predictive models with acceptable level of accuracy. Regarding the weld size, a procedure was proposed in which the weld must fail after the bolt fracture. Results show that, using this procedure, leads to a safer weld design in comparison with the use of AISC Manual suggestion for weld design (w = 5/8tp).

Numerical analysis and punching shear fracture based design of longitudinal plate to concrete-filled CHS connections

The mechanical behaviour of longitudinal plate-to-concrete-filled circular hollow section (CHS) connections under axial tension, eccentric tension and in-plane bending is extensively studied by the experimentally validated finite element analysis (FEA) in this paper. A total of 336 connections with a wide range of parameters on geometrical configurations, material properties and load positions was conducted to investigate (a) the general applicability of the experimental conclusion for the governing limit state, (b) the shear stress profile on the failure face and (c) the design equations based on fracture analytical models under various loading conditions. FEA extended the validity of experimental conclusion that the only governing limit state was punching shear failure instead of the deformation limit of 3% chord diameter (D). With an aim of proposing design equations based on ductile fracture mechanics, the stress distributions on the fracture failure face and the inner concrete were investigated by the parametric study, and then were adopted in the analytical models. Finally, design equations based on semi-theoretical models for the ultimate strength of longitudinal plate-to-concrete-filled CHS connections under three investigated loads were proposed. It is found the connection-capacity predictions agreed with both test and FEA results well.

Mechanical behaviour of concrete-filled CHS connections subjected to in-plane bending

This paper presents an investigation on the mechanical behaviour of concrete-filled circular hollow section (CHS) connections. Four large-scale connection specimens were tested to failure under in-plane bending. The main test parameters included chord-wall slenderness and diameter ratio between brace and chord. The main failure mode observed from the tests was chord-wall punching shear failure. Meanwhile the chord-wall deformation was also investigated to determine the governing limit state. Complementary finite element (FE) methodology was validated against the experimental findings and the validated FE models were used to further study the mechanical behaviour and the strength design of the connections. The modified Mohr-Coulomb criterion (MMC) was introduced into the finite element models to capture steel fracture failure. Based on both experimental and numerical investigations, a theoretical analytical model with the consideration of the inner concrete was established and an ultimate strength design equation was proposed accordingly to predict the punching shear strength for concrete-filled CHS connections under in-plane bending.

Yield frequency spectra and seismic design of code‐compatible RC structures: an illustrative example

SummaryThe seismic design of an eight‐story reinforced concrete space frame building is undertaken using a yield frequency spectra (YFS) performance‐based approach. YFS offer a visual representation of the entire range of a system's performance in terms of the mean annual frequency (MAF) of exceeding arbitrary global ductility or displacement levels versus the base shear strength. As such, the YFS framework can establish the required base shear and corresponding first‐mode period to satisfy arbitrary performance objectives for any structure that may be approximated by a single‐degree‐of‐freedom system with given yield displacement and capacity curve shape. For the eight‐story case study building, deformation checking is the governing limit state. A conventional code‐based design was performed using seismic intensities tied to the desired MAF for safety checking. Then, the YFS‐based approach was employed to redesign the resulting structure working backwards from the desired MAF of response (rather than intensity) to estimate an appropriate value of seismic intensity for use within a typical engineering design process. For this high‐seismicity and high‐importance midrise building, a stiffer system with higher base shear strength was thus derived. Moreover, performance assessment via incremental dynamic analysis showed that while the code‐design did not meet the required performance objective, the YFS‐based redesign needed only pushover analysis results to offer a near‐optimal design outcome. The rapid convergence of the method in a single design/analysis iteration emphasized its efficiency and practicability as a design aid for practical application. Copyright © 2017 John Wiley & Sons, Ltd.

Finite element modeling strategies for sandwich composite laminates under compressive loading

This paper deals with the buckling behavior of composite sandwich columns under compressive loading. Namely, finite element (FE) modeling strategies are discussed with the aim to test a suitable and cost effective solution for assessing the buckling behavior of delaminated sandwich laminates.Indeed, pleasure craft industry is now facing the challenge of thinner and thinner skin laminates. Buckling, that in past years was not a governing limit state because of rather high thicknesses and of limited spans of structural elements, should be now assessed possibly accounting for actual defects, i.e. delaminations, and applying straightforward but cost-effective approaches, easy to implement in the everyday practice of composite hull structural design.A suitable test case, available in open literature, was selected and results of the proposed modeling strategy are compared with experimental ones as well as with other numerical estimates, showing its capabilities and addressing hints for FE application.

Computational evaluation of limit states of thin-walled channels made from steel foam

The objective of this paper is to explore the potential strength and serviceability implications of metallic foams, specifically steel foam, utilized as a thin-walled channel structural member. A typical advantage sought in the selection of a thin-walled member is minimal weight. However, the stability of the thin walls and the related limit states constrains the extent to which weight minimization may be utilized. As a material, steel foam (literally creating air voids in the steel microstructure) offers the potential to provide increased plate stiffness for a given weight and thus create even lighter thin-walled members and structures. In this work analytical material relationships are used to explore the structural potential for steel foam. First, the local buckling and yielding of an isolated steel foam plate is explored. Second, the local, distortional, and global buckling of a prototypical cold-formed steel channel using steel foam is examined. Finally, the strength and governing limit state of the channel as a function of relative density (i.e., the degree to which the material is foamed) is explored. The results show the key tradeoff made when foaming–stiffness per weight is increased, including stiffness related to member buckling modes; however, yield strength per weight decreases. Depending on the slenderness (in local, distortional, and global modes) of the member this tradeoff can be beneficial or detrimental.

Effect of relative failure consequences in reliability based dual performance design

During its design life, a structure has to satisfy several performance requirements. It is now common to express all safety requirements, as well as some functionality requirements, in reliability based formats. Failure consequences (hence target reliabilities), structural behavior, capacity, loads and modeling uncertainties and thus the limit states themselves are different at these various performance levels, and the design must take these aspects into account. This paper develops optimal partial safety factors over a range of structural configurations for the design of partially prestressed sections in flexure corresponding to two performance levels — cracking and collapse — satisfying respective target reliabilities. Detailed numerical examples and derivations are presented. The role of relative failure consequences at the two performance levels in determining the governing limit state, the “balance point” where both limit states are active, and the possible implication on maintenance strategies, meas...

Effect of Lüders Plateau on Fracture Response and Toughness of Pipelines Subject to Extreme Plastic Bending

The reeling technique presents an economical pipeline installation method for offshore oil and gas applications, especially for thick-wall (low D/t) pipelines. During reeling, the pipe is subjected to large plastic bending strains up to 3%. In thick-wall pipes, the tensile fracture response of the pipeline/girth weld would normally be the governing limit state. Seamless line pipes are preferred for the reeling applications in which the Lüders plateau is often exhibited in materials stress-strain response. In this paper, the fracture response of such pipelines is investigated from a continuum perspective using a nonlinear 3D finite element analysis. A typical pipeline with a hypothetical defect is considered, with the material having a range of Lüders strains and strain hardening indices. Results show that the Lüders plateau modifies the shape of the moment-strain response curves of the pipe, as well as the J-integral fracture response. It is observed that the response is always bounded between two limiting material models, which are (i) the elastic-perfectly plastic stress-strain response and (ii) the conventional elastic-strain hardening plasticity response, without a Lüders plateau. Also, the Lüders plateau was observed to decrease the crack opening stress ahead of the crack tip and thus the crack tip constraint. On the other hand, the presence of a Lüders plateau elevates the near tip plastic strain and stress triaxiality fields, thus promoting ductile fracture. A micromechanical damage integral model coupled with a modified boundary layer analysis was incorporated to study this aspect. Based on the findings of this study, it is believed that the presence of Lüders plateau could significantly alter the fracture response and toughness of pipes subject to relatively high strains.

Cyclic Void Growth Model to Assess Ductile Fracture Initiation in Structural Steels due to Ultra Low Cycle Fatigue

A new model is proposed to simulate ductile fracture initiation due to large amplitude cyclic straining in structural steels, which is often the governing limit state in steel structures subjected to earthquakes. Termed the cyclic void growth model (CVGM), the proposed technique is an extension to previously published models that simulate ductile fracture caused by void growth and coalescence under monotonic loading. The CVGM aims to capture ultra low cycle fatigue (ductile fracture) behavior, which is characterized by a few (generally, less than 20) reverse loading cycles to large inelastic strain amplitudes (several times the yield strain). The underlying mechanisms of low-cycle fracture involve cyclic void growth, collapse, and distortion, which are distinct from those associated with more conventional fatigue. The CVGM represents these underlying fracture mechanisms through plastic strain and stress triaxiality histories that can be modeled at the material continuum level by finite-element analyses. Development and validation of the CVGM is substantiated by about 100 notched bar tests, with accompanying finite-element analyses, metallurgical tests, and fractographic examinations of seven varieties of structural steels.

Safety Evaluation of Frames with PR Connections

An efficient nonlinear stochastic finite-element method is proposed for the design of frame structures, specifically applicable to steel structures. The assumed stress-based finite-element method is used to compute nonlinear structural responses and the corresponding response gradients. Nonlinearities due to geometry, material, and partially restrained (PR) connections are considered in the algorithm. Elastoplastic material behavior is considered and the PR connections are modeled by the four-parameter Richard model. The material properties, geometry, connections parameters, and external loads are considered to be random variables. Both the strength and serviceability limit states are considered. The efficiency, robustness, desirability, and application potential of the method are demonstrated by two examples. Several observations with design implications can be made from these examples. Frames designed for strength may not be safe when serviceability is considered. The presence of PR connections makes the frame more flexible, and serviceability could become the governing limit state. It is essential to properly consider the PR connections in the analysis and design of frames, since design forces change significantly. In many cases, the member sizes may change considerably. The assumption that the connections are rigid, which is routinely used in the profession, is not appropriate. The proposed algorithm can be used as an alternative to the currently available methods to analyze and design frames, and to evaluate the corresponding reliabilities. The design is expected to be more efficient using this approach.

Simplified Frame Design of Type PR Construction

Design of unbraced building frames using simple connections between beams and columns has been based historically on Type 2 Construction assumptions. Extensive research on the performance of this type of frame has led to the recommendation that Type 2 Construction should be limited to frames less than 10 stories tall, when the lateral load is resisted entirely by the unbraced frame. Moreover, it was shown that the governing limit state in such frames is overall frame instability under combined wind and gravity loads, initiated by extensive plastification of the leeward column stack. Two common features of this limit state are that girders are loaded to about half their bending capacity and the exterior columns are heavily overloaded in bending. The reason for this inappropriate apportionment of steel to the girders and exterior columns is that the simple connections do possess rotational stiffness and tend to decrease the in-span girder gravity moments by developing a fraction of the fixed-end moments, referred to herein as flexible-end moments. This paper describes a more appropriate model for gravity analysis of frames with flexible beam-to-column connections that enables a simplified design procedure for Type PR Construction.