Limit State Design Research Articles

Application of Low Modulus CFRP Fabric for Steel Beams Strengthening: Experimental and Design Validation

This paper presents experimental results of steel beams strengthened with low-density and low-modulus CFRP fabrics, with the objective of, (i) checking the capability of the fabric type CFRP in strengthening; (ii) assessing and understanding the failure modes for design improvement; and (iii) validating the design methods for the practical application. A total of eighteen full-scale 2.5-meter-long beams strengthened with CFRP were tested. The governing failure modes of the CFRP-strengthened steel beams were debonding, rupture, and wrinkling. The experimental moment capacities were compared with the design predictions using the limit state suggested in the ACI guideline and two new design limit states. The comparison of design predictions indicated that the use of the limit state suggested in the ACI guideline unconservatively predicted the design moment capacity while the two new design limit states were conservative. Further, it is evidently assessed that the low modulus CFRP fabric can be used for the strength upgrade of the steel beams. A detailed design example is presented for the CFRP-strengthened steel beam using different limit states for a better understanding of the readers.

An Alternative Approach to Dynamic Earth Pressure Coefficients to Improve the Seismic Limit State Design of Earth-Retaining Structures

An Alternative Approach to Dynamic Earth Pressure Coefficients to Improve the Seismic Limit State Design of Earth-Retaining Structures

Strength Lab AI: a mixture-of-experts deep learning approach for limit state analysis and design of monolithic and laminate structures made of glass

Strength Lab AI: a mixture-of-experts deep learning approach for limit state analysis and design of monolithic and laminate structures made of glass

An improved method for statistics estimation of out-of-plane load resistance of masonry walls using design-code models and mechanics-based finite element models

The susceptibility of masonry walls to out-of-plane failure under seismic loading presents a significant engineering concern. In adherence to contemporary limit state design philosophy and as mandated by performance-based design guidelines, it is crucial to accurately estimate statistics parameters such as the mean and variance of out-of-plane resistance. To achieve this, two deterministic models are often considered within the Monte Carlo simulation framework: design-code models, known for their computational efficiency but potential for significant model error, and mechanics-based finite element models, noted for their accuracy but computational intensity. Relying solely on either model for statistics estimation presents challenges due to their respective inherent limitations. This study introduces an improved strategy that synergizes the strengths of both models, resulting in enhanced statistics estimators for the out-of-plane resistance of masonry walls. The proposed methodology involves the use of the control variate method by integrating numerous design-code model evaluations to boost computational efficiency while incorporating a limited number of finite element model evaluations to ensure accuracy. The constructions of the proposed estimators follow rigorous optimization procedures to minimize associated errors and variances. Theoretical derivations are provided for essential elements in the estimator constructions, such as model evaluation numbers for finite element and design-code models and control variate coefficients. Moreover, the accuracy of the proposed estimators is compared with that of the crude Monte Carlo estimator. A key benefit of the proposed estimators is their unbiased nature, and their accuracy is not compromised by the discrepancies between the finite element model and the design-code model. To demonstrate the practicality of these estimators, two case studies are illustrated: one focusing on unreinforced masonry walls and the other on reinforced masonry walls. The results indicate that design-code model-based estimators exhibit large bias, and compared to the estimators that solely rely on the finite element model, the proposed estimators achieve higher accuracy given the same computational budget.

Response surface method-based efficient approach for the load and resistance factors calibration of breakwater foundation considering soil spatial variability

This study aims to propose an efficient approach to calibrate the load and resistance factors (LRFs) for the limit state design of breakwater foundations. The spatial variability of soil was considered by employing the Cholesky decomposition technique. To overcome the low computational efficiency of the Monte Carlo simulation (MCS), a response surface method (RSM) was utilized. Additionally, an efficient algorithm, namely the adaptive boundary-based particle filtering algorithm (ABB-PFA), was proposed with the use of RSM to automatically and quickly search optimal nominal values of random variables in the LRF calibration process. Noticeably, the optimal number of particles and values of the modification factor used in the ABB-PFA were observed to enhance the efficiency of the calibration process. The results showed that the computational efficiency of the calibration process is significantly increased by utilizing the response surface method and the proposed ABB-PFA. The efficiency increases the most if the number of particles is one and the value of the modification factor is 0.5 or 0.6. The influences of the random field element size on the efficiency of the calibration process were also investigated. By using the appropriate size, the efficiency is significantly increased while still obtaining a high accuracy of the LRFs calibration process.

Seismic design rules for lightweight steel shear walls with wood panel sheathing within the Eurocode format

Within the 2nd-generation of Eurocodes several new lateral force resisting systems (LFRS) typically used in lightweight cold-formed steel (CFS) buildings have been introduced, including shear walls with wood sheathing (SWWS). Therefore, extensive studies have been carried out to define the seismic design parameters according to the format of European code for seismic design, i.e. Eurocode 8. In current version of the 2nd-generation Eurocode 8 (prEN1998-1-2, CEN 2022), in case of SWWS the behaviour factor has been defined based on the FEMA P695 (FEMA, 2009) [3] methodology, whereas the other seismic design parameters have been set based on assumption validated with analyses on limited case studies. To overcome this lack, specific research devoted to defining the main seismic design parameters for SWWS belonging to Ductility class 3 (DC3) according to prEN1998-1-2 (CEN 2022) has been carried out at the University of Naples “Federico II”. The research shows that the Easley et al. (1982) method gives consistent in-plane horizontal wall resistance predictions if the shear resistance of wood panel-to-steel sheet screw connections (sheathing connections) is evaluated with reliable approaches and formulas for the evaluation of the shear resistance of sheathing connections have been calibrated. Based on the results obtained from this research, a partial safety factor for resistance evaluation of SWWS according to limit state design (LSD) equal to 1.3 is proposed and an overstrength (expected resistance) factor for the design of non-ductile elements according to capacity design equal to 1.7 is recommended.

Evaluating the Structural Integrity of Cellular Steel Beams with Web Enhancements

Abstract This study investigates the analytical approach of web reinforcement techniques, including high-strength concrete and laced reinforcement, to enrich improvement for the structural behavior of these beams. The analysis compares an unmodified cellular beam (LB1) with a web-reinforced beam (LB2), including the improvements in load-carrying capacity. The study considers the effects of reinforcement on critical design limit states, such as flexural strength, Vierendeel bending, web post-buckling, and shear resistance. The outcomes reveal significant enhancements in LB2’s structural behavior, with over a 100% increase in flexural strength and local axial force capacity and a 165% increase in web post-buckling strength. This research validates the effectiveness of web reinforcement techniques in concentrating on the limitations of cellular beams and maximizing their potential in structural applications.

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.

Forecasting the life cycle of reinforced concrete structures in severe climatic conditions

The article considers the problem of design forecasting of the life cycle of reinforced concrete structures operated in severe climatic conditions using the methodology of limit states. The authors propose to use the reliability index β, conditionally regulated by the norms for design limit states, as a criterion index of the functional suitability of structures. The kinetics of the reliability index β during cyclic freezing and thawing is evaluated by means of multifactor periodic experimental control of strength and deformability indices in frozen and thawed states. Testing was conducted using prismatic (100×100×400 mm) and cubic (100 mm) specimens of the B25 mature concrete (180 days), F270 frost resistance grade. In this case, the parametric failure of an element was identified by the moment when the criterion parameter reached the threshold value. The threshold is extablished (with the required level of reliability) by normative functional models of the limit state, transformed to a form describing the dependence of the concrete resistance parameter on the value of the estimated force and section parameters. Test intervals were determined considering the specificity of concrete frost degradation as a multistage process of structural adaptability, as well as microcrack formation and accumulation. Statistical aspects of resistance parameters were identified from experimental data using the maximum likelihood method and Pearson’s criterion (χ2) in assessing their consistency with the theoretical distribution. Additional transient design situations that consider the thermal-moisture state of the structures are considered. The presented experimental data confirmed the feasibility of the proposed approach.

Contribution to Adjustment of Partial Safety Factors for RC Water Tank Design

Traditionally, the optimisation of civil engineering structures is conducted by a deterministic approach based on global safety factors recommended by the dimensioning codes, such as the Algerian seismic code (RPA) and the Eurocode (EN 1990). These factors are applied to take into account the uncertainties related to the most important parameters of the structure as well as the actions and their effects, and implicitly provide a target level of reliability. The use of these factors aims to introduce a sufficient margin of safety in order to increase the safety of the structure design and to reduce the role of uncertainties on the performance of the optimised structure. In this research, the authors propose to use the semi-probabilistic method in the limit state design of the top ring beam of a Reinforced Concrete (RC) water tank placed on the ground for assessing the partial safety factors of both loadings and materials strength. The reliability approach is first conducted using a computer code developed with Matlab© software based on the Monte Carlo simulation method and on the First Order Reliability Method (FORM). Two random variables are considered, i.e. the static live load and the concrete compressive strength, both modelled by normal distribution laws. In the second part of this work, partial safety factors are adjusted in order to achieve the target reliability in a range of performance of the civil engineering structure. This semi-probabilistic approach is applied to a case study of an RC tank of capacity 250 m3 in order to adjust safety factors so as to obtain a compatible probability of failure with the appropriate target value as a function of consequence class. The results of the study conclude that this semi-probabilistic method allows adjusting adequate partial safety factors according to target reliability.

Evaluating Partial Safety Factors for Shear Strength in Bearing Capacity Calculations for Cohesionless Soils

Calculating bearing capacity is critical when designing shallow foundations. Many countries use limit state design (LSD) as the standard method for geotechnical design. The paper aims to develop realistic LSD partial factors for bearing capacity calculations of shallow foundations on cohesionless soils based on full-scale model tests. The experimental setup consisted of a hydraulic jack, concrete footing, sand samples, and pressure cells placed in a cylindrical wall. Fifteen sand samples were tested and classified by gradation and relative density. Settlement curves were plotted for each sample under an increasing load. The measured ultimate bearing stresses were found to be higher than theoretical values calculated using traditional methods. This indicates that the traditional approach is conservative. The suggested safety factor for the internal friction angle in cohesionless soils (γtan(ϕ)= 1.10) is notably lower than the values specified in Eurocode 7 at 1.25 and the Egyptian code of practice at 1.30. The proposed LSD partial factors allow for more economical designs than traditional factors while maintaining safety. The full-scale model-testing approach is novel and provides realistic factors directly applicable to Egyptian codes. The results are satisfactory and reasonable for the geotechnical design of shallow foundations on cohesionless soils. Doi: 10.28991/CEJ-2024-010-07-015 Full Text: PDF

Prediction of ultimate tensions in mooring lines for a floating offshore wind turbine considering extreme gusts

The design of mooring line parameter for a floating offshore wind turbine (FOWT) should consider the ultimate limit state. Typhoons should be considered as a threatening condition for mooring design, and the characteristics of transient changing wind should be studied. Currently, few extreme value predictions consider gust features, and extreme mooring tensions may be underestimated in practical FOWT design. We conducted the simulations of the 5 MW wind turbine from the National Renewable Energy Laboratory (NREL) in the environmental conditions of extreme gusts, waves, and currents. Extreme gusts were found to cause dramatic increases in mooring tensions under 100-year typhoon conditions. The average conditional exceedance rate (ACER) method is used to predict extreme mooring tensions. The impacts of simulation duration and sample size on the prediction results are then discussed. The results show that in extreme gust conditions, the tail data of the average conditional exceedance rate of mooring tension presents a different extrapolation trend from stable wind conditions. Short-term predicted values in gust conditions are 14–20% larger than those in stable wind conditions. The research shows the necessity of considering threatening gust conditions in the ultimate limit state design of mooring system of FOWT.

Influence of wave spreading on offshore wind turbine design: IEA 15-MW scenario

Offshore ocean waves are directionally spread, whereby the propagation of energy travels in different directions. Despite this multi-directionality, the use of 3-dimensional wave models for loading on fixed offshore wind turbines has been limited. This is partially due to the common assumption that uni-directional sea-states are conservative within a design philosophy. This may not always be true given that in operating conditions the amount of aerodynamic damping in the side-side direction is much lower than the fore-aft direction. This paper aims to address this issue by providing the influence of wave spreading on various offshore wind turbine design scenarios: fatigue, ultimate and service limit state design. This study demonstrates that wave spreading indeed results in more fatigue damage for operating load cases. Despite this, the overall fatigue and ultimate limit state utilisation is still reduced when a wave spreading is adopted.

Design and Analysis of General Hospital Building Using STAAD Pro

Abstract: Structural design is the primary aspect of the civil engineering. The foremost basic in structural engineering is the design of simple basic components and members of a building viz., Beams, Columns and Footings. The principal objective of this project is to analyze and design a general hospital using Staad pro. The design involves manual load calculations, analysis and design of the whole structure using STAAD Pro. The design methods used in STAAD-Pro analysis are Limit State Design conforming to Indian Standard Code of Practice. Structure considered for analysis and design is 21m high hospital building located in the seismic zone III. In this project, we study the effect of various load combinations on the structure by analysing the bending moment diagrams in post processing mode. The project involves detailed drawings of column layout, column detailing and beam detailing

Comparatively Design and Analyze Elevated Rectangular Water Reservoir with and without Bracing for Different Stagging Height

A water tank, like a container that stores liquids, are categorized based on shape studies predict the analysis and design of rectangular as well as circular overhead water tanks through the usage of STADD PRO software. Storage reservoirs, especially overhead tanks, serve the purpose of storing and distributing water to consumers. Water supply planning may not have been adequately done for the recently built Overhead Circular Tank to meet the increasing demands of the expanding urban population. Branched distribution systems could be in several scenarios, including rural irrigation and the distribution of reclaimed water. Time is approaching when the need to conserve and store water becomes so essential. In such moments, it is crucial to develop cost-effective methods for storing and distributing water. The water that is stored in overhead water tanks is strategically placed. The overhead tank is vital as it serves as a common public utility structure. The distribution to nearby areas can be done without the need for pumping!!! The cost efficiency of overhead storage water tanks relies significantly on the quantity of concrete and steel needed for tank construction. As an initial resolution to this issue, it is essential to develop a water storage project based on STAAD principles, famously known as Overhead Water Reservoir. The current study covers the analysis and design of an elevated circular water tank using STAAD.Pro V8i. The design involves manual load calculations and the analysis of the entire structure using STAAD Pro V8i. The method of design used in the STAAD.Pro analysis is Limit State Design; the water tank is being subjected to various loads such as wind load, deadload, self-weight, and hydrostatic load due to water.

Prediction of the fundamental period of infilled RC framed structures considering the maximum inter-story drift at different design limit states

The fundamental period of vibration is a key parameter for the spectral approach to seismic design of structures, as it significantly affects the evaluation of the response spectra values. Even though infill elements can significantly increase a building's lateral stiffness, they are not always considered in the structural design process. This is particularly significant at the damage limitation states considered by the European (Eurocode 8) and Italian (NTC2018) seismic codes, where mostly elastic behaviour is expected. Non-structural elements, in fact, can influence the natural elastic period of buildings, determining spectral accelerations different from those evaluated by the simplified formulas provided by the seismic standards and related guidelines. This research aims to develop novel simplified period-height relationships to estimate the fundamental period of vibration of infilled Reinforced Concrete (RC) framed buildings more accurately at various limit states, as a function of inter-story drift value. To collect information about the fundamental period of structures in different damage conditions, several experimental campaigns involving more than 330 RC framed structures have been considered. Nonlinear numerical analyses have also been performed to integrate the database, especially for the Ultimate Limit State (ULS), considering different number of floors, infill distributions, and geometries. Collected data have been parametrized as a function of the damage level suffered by the considered structures, and different empirical period-height formulations have been defined for each limit state. The proposed relationships have been compared with those found in international, European, and national seismic codes, as well as with simplified formulations in previous literature studies. In particular, the results strongly suggested that the fundamental periods estimated according to the EC8 formulation, overestimates the experimental data, resulting in a potential underestimation of the seismic forces and therefore of damage to non-structural elements. To quantify the differences in spectral acceleration and spectral displacement at all design limit states, some examples have been proposed, considering different Italian seismic zones.

Seismic Fragility Reduction for Base Isolated RC Frame Buildings by Curved Surface Sliding Bearings with Over-Stroke Displacement Capacity

ABSTRACT Recently, experimental studies on failure conditions of buildings equipped with curved surface sliding isolators have shown that when no displacement restraining elements are employed and the concave plates feature a flat rim, the inner slider can run on the edge of the sliding surfaces producing lateral displacement larger than the nominal isolator capacity. The over-stroke displacement capacity reduces the probability of seismic collapse of code-conforming base-isolated buildings for earthquake stronger than the design one. In order to quantify the benefit of the over-stroke displacement capacity of double concave curved surface slider (DCCSS) bearings on the seismic fragility of base isolated buildings, four case studies of six-storey reinforced concrete framed structures, consisting of new constructions and retrofit of existing structures located in high and medium hazard seismic sites, have been investigated in this paper. In all cases, two configurations of the isolation system have been considered, with end-stop displacement or with over-stroke displacement capacity. The seismic performance of the buildings has been investigated by multi-stripe nonlinear time-history analysis. The results of the nonlinear dynamic analysis at the collapse limit state have been compared with nonlinear static analysis in terms of maximum displacement and corresponding base shear. Fragility curves highlight a higher safety margin against collapse for seismic intensities beyond the design limit state of the isolation system with over-stroke capacity.

Variability of coal mine overburden incorporated concrete and its effect on the seismic safety of reinforced concrete building

AbstractImproved utilization of coal mine overburden material (CMOB)‐incorporated concrete in the construction sector can contribute to developing a more sustainable built environment if the results of proven research on the behavior of structures constructed of CMOB‐incorporated concrete are applied. Even though there have only been a few studies on CMOB‐incorporated concrete, no research has been done on how this type of concrete can be used in structures. In particular, researchers have not paid much attention to the fact that the strength properties of CMOB‐incorporated concrete tend to be very variable, even though this variability is needed for a wide range of structural applications (such as limit state design formulation, reliability‐based structural analysis, etc.). For the first time, this research provides quantitative estimates of the variability in compressive‐, flexural‐, and splitting tensile strengths of cured concrete using varying amounts of a CMOB sample as fine aggregate. Taking into account the suggested distribution model, the research also provides a reliability‐based seismic risk assessment of a standard CMOB‐incorporated framed building. The failure probability and dispersion in the drift demand were found to be the same for the frames modeled with CMOB and standard concrete (natural sand); the results demonstrate that CMOB samples can be safely used for earthquake‐resistant constructions.

Research on Design and Analysis of Multi-Story Building by using AutoCAD and STAAD-Pro

“The population of India is the second highest in the world as per the 2022 report” [1]. In order to live well, there is an increasing demand for adequate infrastructure. People are migrating from rural to urban regions. Problems will rise due to the high population in urban areas. Due to a lack of available land for construction in metropolitan areas, high-rise building structures are becoming more necessary to address the population density issue. High-rise structures are in high demand, and their construction must be completed without compromising any of the three criteria of cost, timeliness, and safety. AutoCAD design software enables the production of both 2D and 3D drawings for use in constructing multi-story buildings. This study aims to utilize the software package STAAD-Pro to analyze and design a multi-story building, following the production of 2D and 3D drawings using AutoCAD. STAAD-Pro offers a far quicker method of structural analysis and planning for the likelihood of the fewest faults. The design involves load calculations and analyzing the whole structure by STAAD Pro. “The method used in STAAD Pro analysis is Limit State Design followed by Indian Standard Codes. The loads considered for designing the building are dead loads, live loads, and Wind loads. For analyzing a multi-storied building, one has to consider all the possible loadings and see that the structure is safe against all possible loading conditions” [2]. The aim of this study is to analyze the structural behavior of the building and ensure that it meets the necessary design standards and codes. To remain competitive in the constantly expanding market, it is crucial for structural engineers to optimize their time management. This study highlights the importance of using advanced software tools in the design and analysis of complex structures to ensure their safety and stability.

Finite Element modeling and convergence analysis of a new Biomimetic Branching Structure.

Branching structures are gaining popularity in the field of advanced structures and building design; they offer high performance in terms of strength and lightweight design, along with the flexibility and precision enabled by modern processing technologies like Additive Manufacturing. This paper provides a concise overview of a geometric design procedure for a novel ribbed class of structures which was previously developed by the authors as a biomimetic optimal Micro-architected dome. Hereinafter, linear lattice models are suggested to carry out structural calculations using the finite element method (FEM). The objective is to examine discretization thresholding and strain energy convergence criteria. Results show that convergence is reached for numbers of elements per leg, ranging from 2 to 6, depending on the geometrical configuration of the dome being studied. The strain energy balance also exposes the influence of each internal force on the total mechanical response of the structure, pinpointing bending moment and axial force as the main decisive factors. As a perspective, the study will focus on limit state design calculations and Analysis of how the local geometry influences the overall stability and strength of this new design.