Structural Design Codes Research Articles

Symbolic regression for strength prediction of eccentrically loaded concrete-filled steel tubular columns

Concrete-filled steel tube (CFST) columns are widely employed in high-rise buildings, long-span bridges, and seismic-resistant structures due to their superior load-bearing capacity, structural efficiency, and resilience under extreme loading conditions. This study uses symbolic regression with structural design code provisions to predict the eccentric strength of concrete filled-steel tubular columns with circular shape (CCFST) and rectangular shape (RCFST). Previous studies have used two distinct approaches for estimating eccentric strength: explainable models based on theoretical derivations and black-box models derived from machine learning (ML) methods. This study proposes a hybrid model derived from the design code standards, with performance enhanced by the symbolic regression technique. This model is based on a comprehensive experimental database of 464 tests for CCFST columns and 313 tests for RCFST columns under eccentric loading from various research papers. The developed code-based symbolic regression (C-SR) displays both robust and interpretable, demonstrating high prediction accuracy with mean values of the prediction-to-actual ratios of 1.006 and 0.997 and coefficient of variation (CoV) values of 0.117 and 0.098 for CCFSTs and RCFSTs, respectively, while providing explainable mathematical expressions that align with the mechanical principles of code provisions. The developed C-SR model is benchmarked against EC4 and AISC360 standards and evaluated against the various ML techniques, demonstrating acceptable performance. The results highlight the C-SR model’s effectiveness in providing reliable predictions and valuable insights for practical engineering applications.

A Simplified Analysis Model for Predicting the Crack Width and Deflection of Reinforced UHPC Shallow T-Shaped Beams Under Four-Point Bending

To predict the mid-span deflection and crack width of reinforced ultra-high-performance concrete (R-UHPC) shallow T-shaped beams, a simplified analysis model comprising a bilinear curve with several characterization points is proposed in this paper. The proposed model is distinguished from existing deflection and crack width prediction methods by its consideration of several significant factors, including the tensile stiffening effect, tension contribution of UHPC post-cracking, nonconstant bond behavior of the interface, and shrinkage and creep effect. To obtain closed-form solutions, the proposed simplified analysis model directly incorporates the bond properties from bond tests, thereby eliminating the reliance on constant bond stress simplification and the subsequent necessity for member calibration, which is commonly required in existing design codes for UHPC-based structures. To validate the proposed model, six reinforced UHPC shallow T-shaped specimens with dimensions of 3.7 m × 0.7 m × 0.22 m, varying reinforcement ratios and fiber types within UHPC, are utilized and tested statically under four-point bending conditions. The experimental values obtained from these tests are then compared with the theoretical calculations derived from the simplified analysis model. The ratios of mid-span deflections and crack widths at reinforcement yielding, calculated using the simplified analysis model, to the counterparts from experimental values are found to be within a range of 0.9 and 0.95, respectively. The average percentage of differences between experimental and predicted values for the deflections and crack widths at reinforcement yielding are 4.2% and 5.8%, respectively. These findings demonstrate that the simplified analysis model proposed is accessible and accurate for predicting the deflection and crack width of reinforced UHPC shallow T-shaped beams, which has the potential to be a valuable reference for the design and calculation of such beams.

Structural reliability assessment of a historical reinforced concrete building using numerical analysis and NDT techniques

AbstractThis paper presents a case study of a methodology for assessing the structural reliability of an early reinforced concrete structure using a combination of primarily non‐destructive diagnostic and advanced numerical analysis methods. The case study examines the historical Csíky Gergely Theater in Kaposvár, Hungary, built in 1911. At that time, the design methodology and construction process were carried out using a relatively rudimentary standard framework. This study demonstrates that a multi‐phase assessment procedure integrating numerical analysis and primarily non‐destructive testing techniques can significantly reduce structural analysis uncertainty. This approach allows for an optimal selection of the reliability index (βtarget), even when deviating from design standards. Based on this modified reliability index and considering the diagnostic and material test results, the partial factors used for the assessment can be optimally adjusted, and in most cases reduced, compared to those in design codes for new structures. Consequently, the extent of structural interventions needed to increase the load‐bearing capacity can be minimized.

Implementing Steel Design in Educational Software: The Linear Elements Structure Model Program

The Linear Elements Structure Model, or LESM for short, is a user-friendly, free-to-use, and open-source educational software for the structural analysis of models composed of linear elements. Aimed at aiding students, teachers, engineers, and architects to understand the behavior of structures better and improve their workflow, its intuitive and straightforward GUI (Graphical User Interface) allows a simple yet effective approach to modeling, running calculations of linear-elastic static and dynamic effects, and visualizing the internal stresses and strains in two-dimensional and three-dimensional trusses and frames. This paper expands upon the capabilities of LESM by detailing the implementation of steel design for bidimensional frames in compliance with the Brazilian steel structure design code, NBR8800:2008, within the current version of the software, building upon previous efforts to enhance LESM's functionality through object-oriented programming in the MATLAB environment. With the feature of steel design initially conceived as an extension for a prior version of the software, the LESM program has since been updated and reworked with more straightforward and quicker user interaction, a more optimized source code, and the addition of new features. By comparing past and current versions of the software and examining the source code of the steel design extension, it was possible to successfully integrate the steel design feature into the latest iteration of LESM, broadening the program’s scope of use, both for the academic and industrial sectors in the field of analysis and design.

Seismic Collapse Risk Assessment and Fragility Analysis of Reinforced Masonry Core Walls with Boundary Elements Using the FEMA P695 Methodology

In the past, the primary objective of structural design codes was centred around ensuring human life safety, with a strong focus on preventing structural collapse. This approach predominantly relied on force- or strength-based criteria as the basis for design. Nevertheless, a notable shift has occurred recently, transitioning the design philosophy from 'strength' towards a 'performance'-based approach. This shift signifies a growing recognition that strength and performance are not identical. However, to adopt the performance-based seismic design approach, it is essential to develop precise models for estimating damage and potential losses associated with various seismic force-resisting systems (SFRSs). Fragility functions are widely interpreted among the most prevalent damage and loss models. They establish a crucial link between specific demand parameters and the likelihood of exceeding various damage states. Although reinforced masonry (RM) structures have recently gained popularity, the seismic design of mid- to high-rise RM structures is still challenging because it requires a reliable SFRS capable of providing the needed ductility and capacity. Therefore, the main objective of this study is to evaluate the key seismic performance parameters (i.e., system overstrength and ductility) and to perform a collapse capacity risk assessment of reinforced masonry core walls with boundary elements (RMCW+BEs) as the main SFRS in RM structures. The current study utilizes the applied element method (AEM) implemented in the Extreme Loading for Structures software (ELS) to model three RM structures with various heights (10-, 15-, and 20-story buildings). Nonlinear pseudo- static pushover analysis was performed to quantify the ductility and overstrength of the proposed RM system following the FEMA P695 guidelines. In addition, an incremental dynamic analysis (IDA) was carried out to assess the seismic collapse risk of RMCW+BEs by generating system-level-based fragility curves. The results showed that the proposed RM system provides the needed ductility, overstrength and deformation capacity for a ductile SFRS for typical mid- and high-rise RM buildings. Furthermore, the developed collapse fragility curves verified excellent seismic performance, negligible collapse probability values and high reserved collapse capacity at the maximum considered earthquake (MCE) design level. The findings of this study significantly contribute toward adopting RMCW+BEs as an effective SFRS for typical RM buildings in the next generations of North American masonry design standards.

Automated extraction method of STM for 3D topology optimization based on moving morphable components

The Strut-and-Tie Method is considered a helpful tool for the analysis and design of reinforced concrete structures and has been incorporated into different structural design codes. However, the low efficiency of the construction of the three-dimensional (3D) Strut-and-Tie model (STM) has been a key problem limiting the widespread use of the STM. To realize the efficient construction of STM, an automated extraction method based on the moving morphable components (MMC) is established. The presented method is divided into four parts: 3D topology optimization, curve skeleton extraction, spatial frame extraction, and shape optimization. To improve the computational efficiency, the 3D topology optimization and curve skeleton extraction are based on the MMC method and the Laplacian method based on the mean curvature flow (MCF), respectively. A spatial frame consistent with the topological form of the optimization result is formed by point identification and connection. In shape optimization, the truss-like index that can reflect the proportion of shear forces in the internal forces of the bars is introduced. The results of numerical examples show that the method efficiently constructs the STM with reasonable stress and regular geometry. A smooth and medial curve skeleton is extracted from the optimized structure by the Laplacian extraction method. Shape optimization constrained by the truss-like index enhances the regularity of STM and realizes the change of optimized structures from frames to trusses.

Seismic collapse risk assessment and fragility analysis of reinforced masonry core walls with boundary elements using the FEMA P695 methodology

In the past, the primary objective of structural design codes was centred around ensuring human life safety, with a strong focus on preventing structural collapse. This approach predominantly relied on force- or strength-based criteria as the basis for design. Nevertheless, a notable shift has occurred recently, transitioning the design philosophy from 'strength' towards a 'performance'-based approach. This shift signifies a growing recognition that strength and performance are not identical. However, to adopt the performance-based seismic design approach, it is essential to develop precise models for estimating damage and potential losses associated with various seismic force-resisting systems (SFRSs). Fragility functions are widely interpreted among the most prevalent damage and loss models. They establish a crucial link between specific demand parameters and the likelihood of exceeding various damage states. Although reinforced masonry (RM) structures have recently gained popularity, the seismic design of mid-to high-rise RM structures is still challenging because it requires a reliable SFRS capable of providing the needed ductility and capacity. Therefore, the main objective of this study is to evaluate the key seismic performance parameters (i.e., system overstrength and ductility) and to perform a collapse capacity risk assessment of reinforced masonry core walls with boundary elements (RMCW + BEs) as the main SFRS in RM structures. The current study utilizes the applied element method (AEM) implemented in the Extreme Loading for Structures software (ELS) to model three RM structures with various heights (10-, 15-, and 20-story buildings). Nonlinear pseudo-static pushover analysis was performed to quantify the ductility and overstrength of the proposed RM system following the FEMA P695 guidelines. In addition, an incremental dynamic analysis (IDA) was carried out to assess the seismic collapse risk of RMCW + BEs by generating system-level-based fragility curves. The results showed that the proposed RM system provides the needed ductility, overstrength and deformation capacity for a ductile SFRS for typical mid- and high-rise RM buildings. Furthermore, the developed collapse fragility curves verified excellent seismic performance, negligible collapse probability values and high reserved collapse capacity at the maximum considered earthquake (MCE) design level. The findings of this study significantly contribute toward adopting RMCW + BEs as an effective SFRS for typical RM buildings in the next generations of North American masonry design standards.

Comparative Analysis of Seismic Design Standards for Structures and Safety Standards for High-rise Concrete Building Structures

The core of this study is the comparative analysis of I S. 1893 (Part One): 2016 Edition (Code for Seismic Design of Structures) and I S. 16700:2017 (Code for Safety of High rise Concrete Building Structures). In addition, the study aims to uncover the key factors that contribute to poor performance of buildings in earthquakes, with the aim of improving the safety performance of structures in earthquakes in the future. As a research case, we selected a specific reinforced concrete moment shelving frame (SMRF) building at Jabalpur Airport. The building structure was modeled and analyzed using SAPpro V20i software. According to software calculations, we obtained the time history analysis results of the structure in two directions and ensured that they comply with the two Indian standards mentioned above. Subsequently, by comparing the structural responses under the two standards, we evaluated the significant differences in foundation shear force, displacement, and mass participation. The research results indicate that compared to I S. 1893 (Part One): 2016, following I S. The performance of the 16700:2017 structure in earthquakes is relatively poor.

Comparative analysis of hydrodynamic loads on bridge piers: assessing standards through numerical modeling

Currently, there is an alarming difference in the estimated actions on piers resulting from flash-floods and tsunamis as prescribed by international structural design codes. Previous studies have explored the interaction between surge waves and piers from a fluid-dynamics perspective, but there is no assessment about the relevance of the methods used in Structural Design to determine the hydrodynamic pressure resultants. To determine the degree of conservatism embedded in design, results from the different approaches are compared against validated numerical simulations. Three-dimensional numerical analyses were conducted using the OpenFOAM platform, employing the Large Eddy Simulation turbulence modeling approach to simulate the dam-break wave impacting the pier. The findings revealed that the maximum force was not necessarily caused by the stream’s first strike and could be sustained over time. The hydrodynamic pressure center consistently occurred at two-thirds of the stream depth, significantly impacting the overturning moments experienced by the pier. Identified inconsistencies between Codes underscore the need for revision of nonconservative approaches in predicting the design forces.

A limit state approach for considering greenhouse gas emissions in the structural design of buildings: Environmental Impact Limit State (EILS)

Recent reports underscore the growing significance of embodied greenhouse gas emissions in the building industry, necessitating sustainable structural designs to combat climate change. However, the current building and structural design codes require satisfying Ultimate and Serviceability Limit States (ULS and SLS) without setting limitations on embodied emissions in the design process of structural members. Thus, this study proposes an Environmental Impact Limit State (EILS), specifying allowable and design emissions for structural components, to be used alongside ULS and SLS. The EILS combines nominal emission intensities from parametric analysis with fuzzy-logic-based uncertainty factors, enabling standardized consideration of environmental impacts in sizing structural elements. The EILS calibration is demonstrated for flat slab and shear wall systems following Canadian codes. The calibration involved an extensive parametric study (450, 975, and 2160 configurations for flat slabs, columns, and shear walls) to evaluate the impact of design and loading parameters. A detailed numerical example is presented to showcase the incorporation of EILS in the design process, achieving emission reduction on magnitude of 25 % compared to non-EILS design process.

Automated Compliance Checking System for Structural Design Codes in a BIM Environment

Automated Compliance Checking System for Structural Design Codes in a BIM Environment

Nonlinear modeling and time-history analysis of dry-assembled precast concrete frames with buckling-restrained braces

A combination of dry-assembled precast concrete frames and buckling-restrained braces (BRB) is a viable choice for achieving the full potential of building industrialization and promoting the popularization of precast structures in earthquake-prone zones. A recent study has tested the seismic performances of a dry-assembled precast concrete frame with BRBs (BRB-DPCFs) under cyclic quasi-static loading. To study the comparative seismic behaviors of BRB-DPCFs and the monolithic concrete frames with BRBs (BRB-MCFs) under ground motion records, buildings between 3 and 12 stories in height were designed based on GB50010-2016, Chinese code for design of concrete structures, and investigated numerically. This investigation includes two-dimensional nonlinear time-history analyses of BRB-MCFs and BRB-DPCFs under two seismic hazard levels. BRB-DPCF demonstrated a larger maximum story drift compared to BRB-MCF, while the maximum residual story drift of the former is negligible in comparison to the latter at a higher building height or under a higher seismic intensity. The two systems show similar drift concentration factors, which was observed irrespective of the hazard level and the specific height of the building.

In-plane compressive behavior of cross-laminated bamboo and timber with variable heights

This paper investigates the in-plane compressive behavior of 5-layer cross-laminated bamboo and timber (CLBT) wall elements with variable heights. Five different heights of CLBT specimens, ranging 400 mm – 3800 mm, were designed for the experiment, with conventional 5-layer cross-laminated timber (CLT) specimens used as controls. Theoretical calculations based on timber structure design codes were employed to analyze the ultimate bearing capacity in compression, complemented by finite element simulations based on Abaqus that also explored the failure characteristics. The results indicated that CLBT wall panels had significantly better compressive performance compared to those of CLT wall panels. For wall panels of around 3.0 m and 6.0 m in height, the compressive strength of the CLBT was approximately 65 % and 40 % higher than that of the CLT, respectively. For specimens showing buckling instability, CLBT demonstrated more concentrated failure in the end regions, contrasting with CLT, which failed primarily in the central region. The outcomes of this study clearly delineate the superiority of CLBT over CLT when used as wall panels, providing valuable references for their potential engineering applications.

Numerical and experimental verification of column web in transverse compression

This paper focuses on the problem of steel members of open double symmetrical cross-sections in transverse compression. First, the problem is introduced with examples of its application in steel structures of buildings and followed by the overview of selected substantial literature resources and current design codes provisions. The essential part of the paper is a presentation of results of experimental tests and advanced numerical analysis of members subjected to selected cases of transverse compression. Where possible, the results are compared with resistances obtained using provisions in currently valid design codes for steel structures. The influence of selected parameters on the resistance in transverse compression is quantified within the evaluation with specific attention paid to plate buckling of the web. Based on data obtained from the experimental and numerical investigations, the most notable findings are summarized.

Reliability design for bearing capacity of steel plate strengthened RC beams based on the improved design value method

AbstractThe partial factor method is widely employed as a design approach for structural reliability and serves as a crucial foundation for structural design codes. However, in practical applications, this method has gradually revealed shortcomings, such as issues with generality and insufficient precision in reliability control. In this article, an improved design value method for the bearing capacity design of steel plate strengthened RC beams was established. Additionally, considering the impact of the live‐to‐dead load effect ratio on the partial safety factor of resistance, a simplified expression for the ultimate limit state design of bearing capacity was proposed. The results show that the reliability index calculated using the partial factor method for the bearing capacity of steel plate strengthened RC beams has a significantly larger relative error. In contrast, the reliability indexes calculated based on the improved design value method are all greater than the target reliability index, ensuring the requirements of reliability design and providing a higher degree of precision in reliability control.

Numerical Study and Design Method for Lateral Torsional Buckling of High-Strength Steel Beams

Given the increasing use of high-strength steels in building constructions, the stability design of high-strength steel beams has become a crucial consideration. However, the current standards of various countries are based on analyses and fittings derived from conventional steel, rendering them unsuitable for high-strength steel. Moreover, existing research indicates that these standards underestimate the ultimate load-bearing capacity of high-strength steel beams. A finite element model was established to investigate lateral torsional buckling in high-strength steel beams. The obtained results were then compared with test results from experiments conducted on Q460GJ and Q690 steel beams. The reliability and accuracy of the established finite element model were validated. Through parametric studies, the impact of depth-to-width ratio, boundary condition, and steel grade on the stability coefficient was evaluated. It was observed that at the same non-dimensional slenderness, an increase in the depth-to-width ratio or a reduction in support constraints led to a decrease in the stability coefficient. It should be noted that the steel grade had little effect on the stability coefficient. Comparisons with the current steel structure design codes, such as EN1993-1-1, GB50017-2017, JGJ/T483-2020, and ANSI/AISC360-22 revealed an underestimation of the stability coefficient for clamped high-strength steel beams under uniformly distributed loads. Based on finite element simulations, stability coefficients for high-strength Q460, Q690, and Q960 clamped beams were determined. Similar to the stability coefficient proposed in GB50017-2017 for the lateral buckling stability design of steel beams, a lateral buckling stability coefficient for high-strength steel clamped beams subjected to uniformly distributed loads was proposed.

Seismic fragility analysis of girder bridges under mainshock‐aftershock sequences based on input‐output hidden Markov model

AbstractCurrent seismic design codes for bridge structures do not account for the influence of aftershock sequences, which, to some extent, overestimate the seismic performance for bridges subjected to mainshock‐aftershock (MS‐AS) scenarios. To address the great need for ground motion sequences tailored to specific research sites for fragility analysis, this study proposes a method for generating artificial MS‐AS ground motion sequences based on the evolutional bimodal Kanai–Tajimi model and the Epidemic–Type Aftershock Sequence model. We establish a framework for MS‐AS fragility analysis using an input–output Hidden Markov Model (IOHMM), where the damage states (DS) of bridge piers are considered unobservable and are inferred statistically through damage indices in an unsupervised manner. Model parameters are trained using intensity measure (IM) sequences and damage index (DI) sequences. Fragility curves for both the mainshock and state‐dependent aftershocks considering multiple aftershocks are formulated based on the initial state probability and state transition probabilities of the proposed IOHMM. The fragility analysis results reveal that as the initial seismic damage level increases, the probability of aftershocks causing higher damage levels in the structure also increases, highlighting the significant impact of aftershocks on structural damage increments. Furthermore, we extend the proposed model to a bivariate seismic intensity measure and develop fragility surfaces. The proposed framework provides a novel approach and insights for tackling seismic fragility under multiple aftershocks.

Codes and standards for structural design - developments and future potential

To date our built environment is broadly developed and maintained on the basis of structural design standards. Most design standards contain simplified semi-probabilistic safety concepts that help daily structural engineering decision making using simple calculus. In this paper research about the rational basis for the calibration of these simplified code formats is reviewed and the potential for further developments is presented.

Classification and ultimate capacity of duplex stainless steel H-section under cyclic loading

Stainless steel materials are high ductility and strain hardening under cyclic loading, which is promising in seismic design. However, the current European stainless steel structure design code prEN 1993-1-4(EC3) ignores this favorable effect in the cross-section classification, as well as the lack of prediction formulas for the ultimate capacity of H-section under cyclic loading. In this paper, parametric analysis was carried out for H-section to extend the database based on the existing test results after calibration of the finite element model. The cross-section classification criteria of duplex stainless steel beams and beam-columns around major-axis under cyclic loading were investigated, and the EC3 classification of stainless steel H-section was evaluated. The predicted results for EC3 are conservative due to not considering the constraints of the cross-section component plates and the favorable conditions for the material strengthening of stainless steel under cyclic loading. Based on this, classification criteria for stainless steel H-section under cyclic loading were proposed and summarized. Subsequently, the method of calculating the ultimate capacity methods under cyclic loading suggested by EC3, Chen and Zhou et al. were evaluated. The results show that EC3 is on the conservative side, with actual results being generally 1.5 times higher than the predictions. In contrast, Chen and Zhou et al.'s method is on the unsafe side of the prediction. Finally, improvement suggestions are given for EC3 and the continuous strength method by considering the over-strength factor under cyclic loading, respectively, with results exhibiting high accuracy.

Reliability-based calibration of companion load combination factors by considering concurrent wind and ice loading for structural design

Transmission towers and overhead transmission lines are designed and constructed by considering the combined ice load and wind-on-ice load if the ice accretion hazard is not negligible. The structural design codes provide clauses with a range of values to evaluate such a combined load. However, it is unclear which of the values suggested in the codes one should use for specified regions, and the reliability-based calibration of such a combination is unavailable. To fill this gap, in the present study, we carried out the reliability-based calibration of the companion load combination factors by using statistics of the ice accretion thickness and concurrent wind speed available from more than 250 meteorological stations in Canada. For the calibration, a nonlinear combination problem needs to be considered since the wind-on-ice load depends on the accreted ice thickness, making this calibration task differ from those commonly reported in the literature, which is focused on the linear load combination problem. A parametric investigation was also carried out to assess the effect of using different return periods and the correlation between ice accretion and concurrent wind speed on the companion load combination factors. The calibration results were used to recommend the load combination format, the companion load combination factors, and the ratio of the square equivalent concurrent wind speed to the return period value of the annual maximum wind speed, which is commonly implemented in design codes.