Strength Limit State Research Articles

Generalised component method for bolted bearing type connections

AbstractThis paper develops a new generalised component method (GCM) model for bolted bearing type connections that predicts their full‐range response and all relevant strength limit states, including the bolt shear, bearing, shear‐out, net section fracture and block shear limit states. The proposed model divides a bolted bearing type connection into components that significantly contribute to its deformation and/or strength limit states. For each component, the force‐deformation curve is derived, including the post‐ultimate response, and expressed as a trilinear relationship. By assembling all components (springs) into the connection model, the multi‐linear force‐displacement response of the connection can be predicted, including the ultimate strength and ultimate deformation capacities. The proposed GCM can consider the interaction of adjacent bolts in modelling multi‐bolt connections. The new GCM is shown to accurately predict force‐displacement responses obtained from experimental tests and non‐linear finite element analyses. It is also shown to predict experimental responses significantly more accurately than the current component method implemented in Eurocode 3‐1.8.

Probabilistic safety assessment of truss members designed by TCVN 5575:2012

This study aims to evaluate the probabilistic safety levels of truss structures designed using the TCVN 5575:2012. A planar structure was designed according to the strength limit state (tension and compression) in the design code. Monte Carlo simulations were then executed to assess the failure probability of the design solutions designed following TCVN 5575:2012. The results help evaluate safety in terms of probability and uniformity. Accordingly, the probability safety levels are compared with those specified in international specifications. The results obtained in this study reveal that the reliability indices for compression bars are higher than those for tension members (approximately 20%). In addition, the reliability indices for the tension members were relatively close to the specified target in the American specification. In contrast, compression bars designed using the TCVN result in a higher reliability index than the target specified in the American code.

A probabilistic design approach to the reinforced fill over a void problem

Current design methods for the problem of a thin reinforced fill over a void are based on analytical solutions which are most often solved using an allowable (working) stress deterministic (factor of safety) approach. However, in practice there are uncertainties in the estimate of the input parameter values that appear in the analytical equations. The paper shows how margins of safety for the limit states that appear in the wellknown BS8006 method can be computed using Monte Carlo simulation or an equivalent closed-form solution for reliability index. Reinforcement strain, strength and stiffness limit states are formulated to include input parameter uncertainty and model accuracy. The probabilistic limit state solutions are expressed by simple equations that are easily implemented in an Excel spreadsheet. The paper shows that using a probabilistic approach provides a more nuanced appreciation of the margins of safety for these limit states than deterministic factor of safety approaches. The probabilistic approach demonstrated in this paper is also in alignment with the movement toward reliability theory performance-based design of reinforced soil structures.

Experimental investigation of torsional strengths of aluminum alloys: Circular and rectangular solid sections

An experimental investigation of aluminum alloy rods and bars subjected to torsional loading is presented. The test specimens were 6061-T6 and 5050-H32 alloys with solid circular and solid rectangular cross-sections. The test plan included torsion tests until rupture, for 5 sets of 6061-T6 specimens with circular and rectangular cross-sections, and 4 sets of 5050-H32 specimens with rectangular cross-sections. Each test series included six specimens, for a total of 54 torsion tests. Experimental torque and angular deformation data were recorded and subsequently analyzed to investigate the torsional stiffness, strength, and ductility of the specimens, including consideration of initial-yield, full-yield, and rupture strengths, as well as total angular deformation at failure. A methodology was developed to estimate the full plastic torque, associated with yielding throughout the cross-section, from the measured experimental data. Results were compared with nominal strengths predicted using the material properties required within the Aluminum Association’s Specification for Aluminum Structures (SAS). Use of these properties in conjunction with SAS’s first-yield criterion produced results that were overly conservative in general, demonstrating the importance of exploring changes to the Specification. Recommendations are made for adjustments and extensions to the SAS, which support an ultimate strength approach consistent with its strength limit states design methodology.

Quasi-static tests and numerical simulations of ductile seismic behavior for scoured bridge pile group foundations considering pile uplift

Scour is the main hazard for coastal bridges. Compared to the fully embedded pile group foundation before scour, the scoured pile group foundation is more prone to the inelastic damage and pile uplift when subjected to earthquakes. However, the seismic behavior of the scoured bridge pile group considering both the ductile and uplift behavior of piles is yet to be documented. This study aims to reveal the ductile seismic behavior of the scoured pile group foundation considering the pile uplift behavior. To this end, quasi-static tests were performed on two reinforced concrete (RC) 3 × 2 pile group foundation specimens embedded in homogeneous sand with and without pile uplift. The lateral loads were separately applied to the cap center of the pile group and the top of the pier to reproduce the pile uplift effect on the foundation. The experimental result of these two specimens was comprehensively compared and discussed. Furthermore, the finite element models for the quasi-static tests were developed and validated. The experimental result indicates that the pile group without uplift shows ductile properties, whereas that with uplift exhibits both ductile and self-centering behavior. The uplift of piles reduces the lateral strength and residual lateral deformation of the ductile foundation. Moreover, the pile group with the pile uplift has a more considerable displacement ductility at the first yielding limit state of belowground piles but a smaller displacement ductility at the peak lateral strength and ultimate residual strength limit states. The findings of this study provide insights into the seismic design/assessment of scoured bridges in coastal regions.

Probabilistic analysis for the reinforced fill over void problem

Analytical and numerical solutions for the problem of geosynthetic-reinforced fills over a void have been the subject of investigation for the last four decades. A common feature of this prior work is that all methods have treated the analytical solutions as deterministic. While the treatment of some input parameters must be taken as deterministic, there are other parameters that have uncertainty. Furthermore, the underlying mechanistic models for load and resistance terms in the limit state equations for the reinforced fill over a void problem can be expected to have different accuracy. This paper revisits the problem of geosynthetic-reinforced fills over voids from a probabilistic point of view for reinforcement tensile strain, tensile strength, and geosynthetic stiffness limit states. Particular attention is paid to the method used to select the isochronous stiffness of the reinforcement and the associated uncertainty in the magnitude of that value. The paper demonstrates how the factor of safety from deterministic past practice can be linked quantitatively to the reliability index used in contemporary probabilistic design. Finally, the paper demonstrates the advantage of using product-specific constant-load creep test results to maximise margins of safety for strength and stiffness limit states in both deterministic and probabilistic frameworks.

Compressive behaviour of circular steel tube confined reinforced concrete (STCRC) columns considering shrinkage and creep

Thin-walled steel tube confined reinforced concrete (STCRC) columns are increasingly used in high-rise and heavily loaded structures. One concern is whether concrete shrinkage affects the load resistance of STCRC columns, as the confinement to the concrete may become less effective when the concrete shrinks. This paper presents ultimate tests on STCRC columns after subjected to 490-day-sustained-loading or 490-day-shrinkage. The compression tests are conducted on specimens with different steel ratios, reinforcement ratios, concrete strengths and steel-concrete interfacial bonding conditions, or with long-term load first applied at different concrete ages. The sustained load history and the shrinkage effects on the short-term axial stiffness, ultimate strength, and peak strain of STCRC columns are investigated. The development of confinement effects and the tube's axial stiffness contribution after shrinkage and creep history are compared against those test results without experiencing shrinkage or long-term load history. A non-linear finite element model is finally developed for the ultimate response prediction of STCRC columns with the consideration of the creep and shrinkage history, and its accuracy is compared against the test data. The results show that concrete shrinkage and creep significantly affect the occurrence and development of the confinement effects, but not the confining pressure at the peak load. The axial stiffness and peak strain of STCRC columns are sensitive to time effects, while the ultimate strength is not. Under service loading, the tube's contribution to the axial stiffness of STCRC columns is negligible due to concrete shrinkage, while at the ultimate strength limit state condition, the column compression resistance is barely influenced by shrinkage and creep effects. The proposed FE model achieves reasonable accuracy in evaluating the ultimate responses of STCRC columns considering the shrinkage and creep effects.

Design Demand of RC Building as per Soil Type

The RC-framed building is one of the most common construction techniques for seismic-resistant structures due to its ductile nature. But the seismic performance of the RC structure is affected by various factors among which site soil condition is vital. The sub-soil condition affects the time period of the structure which eventually impacts the earthquake force in the structure, thus making variations in seismic loadings. Although several studies have been performed and design elastic spectra have been defined as per soil types in the design codes, there are no studies quantifying the effect of design demand in the buildings due to variation of soil type in the context of Nepal and NBC 105:2020. Therefore, this study aims to present the variation in design demand for moderately high-rise RC buildings in different soil types. A representative sample building has been taken and analyzed in the Finite Element platform SAP 2000. Numerical analysis is performed using linear static and response spectrum methods. Based on the study, variation in the base shear, story displacement, inter-story drift, and section size to meet the limit state of strength are compared for soil types A, B, C, and D.

Structural design of hybrid steel-timber buildings for lower production stage embodied carbon emissions

Using cross laminated timber (CLT) floor panels in combination with steel framing has been identified as a promising new structural configuration that can reduce the embodied greenhouse gas emissions of buildings. This project evaluated efficient structural design of hybrid steel-timber floor sections for a wide range of design parameters to determine the reductions in global warming potential possible relative to a conventional steel-concrete cross section. Each of the structural designs was checked for strength limit states, deflection, and minimum fire rating of either unrated, 1-h, or 2-h for a range of deck spans between 2.3 m and 4.6 m and beam spans between 5.5 m and 13.5 m. For an unrated floor assembly there is little global warming potential benefit to use steel-timber floors if a topping slab is included on top of the CLT slab. Whereas, using steel-timber configurations without a topping slab result in the largest global warming potential reductions. For the 1-h and 2-h ratings, even steel-timber configurations with a 64 mm thick topping slab had up to 20% reduction in global warming potential compared to the steel-concrete alternative. Additionally, several considerations that can drastically affect the global warming potential results were discussed. The results from this project demonstrate the best practices for structural design of hybrid steel-timber buildings to reduce global warming potential of the superstructure frame by between 5% and 35% relative to conventional steel and concrete construction.

A study on the probabilistic safety assessment of the truss structure designed by the LRFD code

The probabilistic analyses provide a more rational approach for the safety assessment of structures since they consider the uncertainties in the calculations. Consequently, the design specifications of engineering structures are gradually transformed from the allowable stress design to the reliability-based specifications such as load and resistance factors design (LRFD) or partial safety factor design. The partial safety factors and the load andresistance factors provided in the reliability-based design codes are successfully determined from probabilistic frameworks. However, these specifications are classified into semi-probabilistic-based codes because no probabilistic analysis is required in the design practice. Thus, the actual reliability index of the design solutions maynot be as close to the target value as expected. This study employs the fully probabilistic analysis as an additional analysis to examine the reliability index of an LRFD-based design of the truss structure. A planar truss,which is designed following the semi-probabilistic code, is thoroughly examined. Several feasible sections are first designed using the LRFD code. Then, the actual reliability indexes of truss structures are evaluated to check if they meet the target reliability index specified in the reliability-based design codes. The tension and compression members concerning the strength limit state and the maximum deflection presenting for service ability are investigated as representative performances. The results of the probabilistic analyses indicate thatthe reliability indexes for the strength limit state are higher than the target value stipulated in the LRFD code. Compared to the tension members, more redundancy in terms of reliability index is observed for compression elements, although they are both designed at the limit state. Moreover, the reliability index obtained for theserviceability limit state is strongly dependent on the component (i.e., floor or roof) where the truss is utilized.

Characterization studies on calcium silicate boards and fibre cement boards used as sheathing in light gauge steel framed systems

This paper presents a systematic mechanical characterization study on two types of board materials reinforced with lignocellulosic fibres used as sheathing in light gauge steel framed building, namely calcium silicate board (CSB), and fibre cement board (FCB), under tensile, compressive and shear loading. The ASTM and EN standards for wood-based panels recommend the preparation of the test specimen by bonding additional numbers of boards along thickness to eliminate global buckling under compression and shear loading. However, it is observed that the FCB and CSB specimens still suffers premature bearing failure at the loaded ends and delamination of the boards at the glued interface which often fails to characterize the actual material behaviour. To overcome this limitation, the paper proposes a unified coupon made of single (virgin) thick board and the use of combined loading compression fixtures and large panel–shear test fixtures to simulate the desired failure modes and obtain complete stress–strain response under compression and shear loading, respectively. The scope of the work majorly encompassed an extensive experimental program comprising of total 115 specimens made of FCB and CSB of thicknesses 8 mm, 10 mm and 12 mm, tested along both longitudinal and transverse directions to evaluate the constitutive properties and strength limit states. The results show that the FCB exhibits higher strength and stiffness than the CSB specimens. Further, a nonlinear stress–strain model was established to represent the response of the board material under compression.

Designing Lightweight Stadium Roofing Structures Based on Advanced Analysis Methods

The current structural engineering practical standards are unable to offer an universal structural design standard for long-spanning lightweight stadium roofing structures. As such, the design procedure of a particular stadium roof is not replicable to another. This research aims to present a novel design procedure for lightweight stadium roofing structures considering the Lakhwiya stadium the Optus Stadium and the CommBank Stadium as experimental cases. Using the finite element analysis (FEA) software Strand7, the cases will be modelled and analysed. Varying load cases and combinations such as ultimate strength (ULS) and serviceability limit states (SLS) based on the Australian Standard AS1170.0:2002 will be calculated and subsequently applied. Linear static analysis will then be undertaken where critical members will be identified within the model. Based on this, preliminary member sizing and design feasibility checks will be conducted in order to ensure structural stability and compliance to the Australian Steel Structure code AS4100:2020. A linear buckling analysis is also conducted based on the selected sizes from the initial stage to determine critical loads. Advanced analysis including non-linear buckling computation is comprehensively managed. Some of the crucial parameters such as maximum displacement, maximum/minimum principal stresses, critical buckling loads, as well as load factors are examined. The main novelty of this study is to determine a clear road map to design stadium roofing systems subjected to a combination of different types of the loading.

Pullwinding technique for realizing hybrid roving architecture in pultruded GFRP composites

In this work, pullwinding technique is adopted to realize the hybrid roving architecture in pultruded GFRP composites so as to improve their transverse properties as well as the flexural performance of GFRP beams. First, small-scale material characterization tests and large-scale four-point bending tests were conducted to evaluate the mechanical performance of pullwound composites and the flexural behavior of pullwound box-beams. Second, analytical study was performed to calculate the strength and modulus of laminated plates with hybrid roving architectures. Then, finite element modeling was conducted to assess the strength and stability limit states of pullwound beams. The hybrid roving architecture could effectively reduce the material orthotropy, thus improving the transverse properties of GFRP composites as well as the flexural performance of GFRP beams. In the end, a design procedure is proposed to facilitate the design of roving architecture of pullwound composites to achieve the desired mechanical properties.

Erratum for “Revisiting the Net-Section Tensile Rupture Strength Limit State of Single-Bolt Connections in Pultruded Structures” by Abdul-Hamid Zureick and Blaine Weinmann

Erratum for “Revisiting the Net-Section Tensile Rupture Strength Limit State of Single-Bolt Connections in Pultruded Structures” by Abdul-Hamid Zureick and Blaine Weinmann

Design Optimization of PCI Girders: A Parametric Study

This study investigates the effect of superstructure configuration on the optimum design of slab on Precast I (PCI) girder bridges. For this purpose, more than 20,000 bridge cases of varying superstructure configurations are considered to investigate the effects of various superstructure parameters such as girder spacing, span length, slab thickness and girder types on the optimum design of slab on PCI girder bridges. PCI girders are designed conforming to the AASHTO LRFD for flexure using stress limits at the service limit state, then checked at ultimate for flexure and shear using factored loads at the strength limit state. A modified harmony search optimization algorithm is used to obtain optimum bridge design parameters using standard AASHTO PCI girders according to these AASHTO LRFD requirements. Those girders are designed taking into consideration geometrical constraints, stress constraints and constraints related to the conformity of the design with the AASHTO LRFD code. Various sensitivity analysis are performed to investigate the effect of different geometrical factors on the design of the girders, and easy-to-use design aids were developed. The outcomes of this study may facilitate the bridge engineers to choose optimum design parameters such as girder types and spacing as well as number strands for a certain span length before the design of slab on PCI girder bridges.

Reliability Analysis of Steel Bridge Girders Strengthened with CFRP Considering the Debonding of Adhesive Layer

One issue to consider while designing and constructing steel girders reinforced with carbon fiber-reinforced polymer (CFRP) plates in bridges is debonding failure. Previous studies showed that the parameters such as characteristics of material, load, adhesive, and CFRP plates have an effect on the failure probability of steel girder, which is represented by the reliability index. Therefore, this study analyzes the reliability indices of steel girders in bridges strengthened with CFRP plates to clarify the effects of debonding failure. Debonding and strength limit states are used to compare differences in reliability indices of different design scenarios. Strength and debonding margin the functions for the strength limit state and debonding limit state will be established in this study. The probability of failure is determined by a Monte Carlo simulation (MCS). It is found that the reliability index of debonding limit state is much lower than that of the strength limit state. This shows that the debonding failure should be considered significant in the reliability analysis of steel bridge girders strengthened with CFRP plate.

Strength and Deflection Reliability Estimation of Girder Steel Portal Frames Using the Bayesian Updating Method

Uncertainty is ubiquitous in any engineering system at any stage of product development and throughout a product's life cycle. As information and sensor technology develops, more and more data about engineering systems are gathered. A strong technique for calibrating models using new information and observations is Bayesian updating. The applied loads, yield strength, plastic section modulus, span, cross-section dimensions, and modulus of elasticity from the international literature have been updated through the local literature and a data survey for the interior girder portal frames to investigate the reliability index and the probability of failure of the system. First Order Reliability Method (FORM) and Monte Carlo (MC) simulations have been used to estimate the reliability and probability of failure of strength and serviceability limit state function. The results reveal that for shear force, the reliability index increased significantly from 9.03 to 16.01. At the same time, the reliability index of the bending moment and deflection increased from 4.34 to 5.30 and from 6.90 to 7.66 respectively.

Implication of bridge resilience design and lessons from negative examples

AbstractBridge resilience is a newly proposed bridge design criterion that involves robustness, redundancy and reparability targeting on the rapidity of functionality restoration after suffering extreme actions and long-term durability deterioration. It stipulates a lower probability of reaching the ultimate limit state or strength limit state, which have been only partly involved in bridge design codes around the world. In AASHTO LRFD Bridge Design Specifications and Eurocodes, there are some design principles related to bridge resilience. Yet, it is also necessary to give more requirements for structural ductility and collapse resistance when the actual load exceeds the load combination in the code. This paper focuses on the resilience-based principles for bridge design, and exposes some problematic bridge structural systems and details, such as bridges most likely to overturning, steel bridges with fracture critical members, arch bridges with suspended desk, Morandi cable-stayed bridges, poor details for seismic vulnerability, etc. Whereas overturning is one of the worst anti-resilience scenarios, the resilience design against bridge overturning is highlighted through a detailed discussion including the calculation methods of anti-overturning factor, overturning stability of curved bridges, reasonable disposition of supports, and anti-overturning countermeasures.

Experimental Study on External Loading Performance of Large Diameter Prestressed Concrete Cylinder Pipe

A prestressed concrete cylinder pipe (PCCP) is created with a complex composition of concrete core, welded steel cylinder, prestressed steel wire, protective mortar and anti-corrosion coating. Due to the economy and complexity of structural prototype tests, the ultimate loading test on PCCP is rarely conducted. In this paper, the three-edge bearing test was carried out on a 3.2 m diameter PCCP with embedded steel cylinder. The strains of concrete core, prestressed steel wire and protective mortar were monitored, and the distribution and width of the concrete cracks were recorded. The test results show that the cracking on the inside concrete at the crown zone occurred before those on the invert zone of the pipe. The prestressed steel wire postponed the tensile stress of out-side concrete at the springing line until subjected to the calculated cracking load (Pc). Due to the moment redistribution caused by the cracking on the inside of the concrete at the crown/invert, the protective mortar at the springing line was cracked at 1.2 Pc and exhibited visible cracking after 1.4 Pc. The prestressed steel wire reached the elastic and strength limit states of 1.4 Pc and 1.6 Pc, respectively. The PCCP designed by the limit state design method can resist the increased external loads after reaching the serviceability limit state. The final failure load of the test pipe is greater than 1.6 Pc, and there is sufficient safety in actual operation. Due to the fact that the damage to the concrete at the crown/invert zone may become a fuse of PCCP failure, the tensile stress of the inside concrete at the crown/invert zone of the PCCP should be accurately verified in the design process.

Structural Considerations and Implications Related to Foundation Movements in AASHTO LRFD

In the United States, highway bridge design practice is based on the LRFD method developed by AASHTO. In AASHTO LRFD, which is based on the concept of limit states, the effect of foundation movements on structural elements is expressed as a force effect rather than a geotechnical resistance. In fact, all design codes worldwide recognize this observation by including a representation of structural effects of foundation movements as a force. AASHTO LRFD uses the designation “ SE” for the geotechnical demands to be considered. An associated load factor, γ SE, is specified for each load combination where SE is applicable. The product of γ SE and SE is the factored demand, or factored force. The structural effect of foundation movements is manifested in the form of additional force effects such as induced torques, moments, and shears in a bridge structure that can lead to adverse consequences such as cracking. In AASHTO LRFD, the SE load factor occurs in four out of the five load combinations for Strength Limit State and three out of the four load combinations for Service Limit State. This paper presents a study that explores the structural considerations and implications related to use of SE load factor and the effects of foundation movements in AASHTO LRFD.