Serviceability Limit State Research Articles

Comparative Analysis of Reinforced Concrete Structure with Traditional and Decoupled Masonry Infill Under Earthquake

Different types of concrete are invented in the past years, in order to improve it`s behavior for different loading and environmental situations. Among them, fibre reinforced concrete (FRC) is one of the most recently developed concrete types. Design procedures for the FRC elements are included in only a few existing code provisions. Among them, fib Model Code 2010 (MC 2010) provides the biggest amount of necessary information and recommendations in order to design FRC elements. Yet, a lack of the guidelines for the design of elements loaded with different combinations of bending moment and axial force is noticed in the existing code provisions. Therefore, in the scope of this paper, interaction curves for FRC are developed. The interaction curves are developed for both, ultimate limit state (ULS) and serviceability limit state (SLS). Furthermore, example of the use of such interaction curves is given. Comparison in the design of reservoir made of reinforced concrete (RC) and FRC is performed. It is shown that the use of FRC especial benefits design according to SLS, as FRC provides better behaviour regarding crack spacing and crack width of element, while developed interaction curves for SLS significantly decrease the time necessary for such a design.

Analysis of the dynamic behaviour of lightweight floor slabs

Floor slabs are one of the integral load-bearing elements in buildings. When it comes to their serviceability limit state (SLS), one of the key aspects is their dynamic behaviour. In case of residential or administrative buildings, the knowledge of dynamic behaviour of slabs is important in terms of hygiene (psyche) of the user. When speaking of buildings such as medical facilities or laboratories that are using delicate machinery, the knowledge of the dynamic behaviour is important in order to prevent vibration induced damage to given machinery. Therefore, the aim of this paper is to provide a brief overview of standards applicable for assessment of dynamic behaviour, present various methods for calculation of first natural frequency, as well as to present outlines for in-situ measurements, all with special regard to voided slabs.

Análise dinâmica de uma laje aliviada biaxial submetida a ações humanas

Abstract The bi-axial hollow slab is the result of applying a technology that removes concrete from the least useful region and replaces it with hollow plastic spheres. This technique leads to material economy and self-weight saving, without considerable inertial loss, enabling larger and more flexible spans. Consequently, these spans are vulnerable to unwanted vibrations and dynamic acceleration caused by external actions, such as movements produced by human activity. This way, understanding the dynamic behavior of this technology and confronting it with normative limits on the project phase is essential for a good performance in the serviceability limit state, bringing comfort to the user. This paper studies the dynamic behavior of a bi-axial hollow slab submitted to human actions, such as jumping, dancing, clapping, moving the body, and moving and clapping at the same time. For that, this work made a numerical model of the structure and applied dynamic actions to it. The numerical results show that, for most of the actions, normative limits are satisfied, but the slab presents excessive accelerations in the case of jumping and dancing.

Development of load-resistance-factor-design-based prestressed concrete tub girders in Colorado

This paper presents a new tub girder series for Colorado, conforming to the articles of the American Association of State Highway and Transportation Officials’ AASHTO LRFD Bridge Design Specifications. Although the B618 tub girders developed by the Colorado Department of Transportation in the 1990s have been successfully used for decades, the need for an upgrade is essential to satisfy the requirements of contemporary bridge design and construction. After examining the performance of tub girders selected from six transportation agencies in the United States, an optimization algorithm was employed to generate efficient prototype sections. Then, detailed investigations were conducted to examine various practical aspects concerning the serviceability and ultimate limit states of AASHTO LRFD specifications. Parametric analysis with five bridge superstructures that accommodate up to four traffic lanes demonstrated the applicability of the prototype girders. A simplified version of the prototype sections was also delineated for regional precasters. Furthermore, a comparative study was carried out to evaluate the geometric stability and production costs of the prototype, simplified, and existing B618 girders.

Nonlinear semi-numeric analysis and simplified analysis of polymer fiber-reinforced concrete prisms under three-point bending test conditions

This paper presents a semi-numeric nonlinear analysis and a simplified analysis for evaluating the load-displacement behavior of polymer fiber-reinforced concrete elements under three-point bending test conditions. The considered elements were notched and unnotched prisms. The nonlinear semi-numeric analysis was based on the moment-curvature relation, plastic hinge approach, and virtual work method. The simplified analysis assumed multilinear load-displacement behavior of the prisms under three-point bending test conditions. It included four variants for the input tensile strength properties and crack widths considered for the serviceability and ultimate limit state. The notched polymer fiber-reinforced concrete prism three-point bending test results from a prior study were the basis for evaluating the simplified analysis, which was subsequently compared with the nonlinear semi-numeric analysis outcomes from the same investigation. Additionally, the simplified analysis and the nonlinear semi- numeric analysis were used to determine the load-displacement behavior of unnotched polymer fiber-reinforced concrete prisms with heights ranging from 25 mm to 250 mm. The results indicate that the simplified analysis provides a practical and efficient method for estimating the behavior of polymer fiber-reinforced concrete structures under three-point bending test conditions, yielding relatively accurate results with minimal computational effort compared to the more exact nonlinear semi-numeric analysis.

Stress relaxation of concrete beams caused by creep and shrinkage effects

Shrinkage and creep are two important physical properties of concrete material which cause increase of the deformation of the constantly loaded structure over long period of time, the feature known as rheology. Additional deformation of concrete structures at the end of the design working period (most commonly 50 years) caused by these phenomena is circa three times larger than the value of the immediate elastic deformation (or even larger in some cases). Hence, in accordance with the corresponding European standard, these effects should be taken in account while evaluating the serviceability limit state of concrete structures, and if significant, consideration of these phenomena is also needed for the verification of the ultimate limit state. In concrete material, creep occurs at all stress levels, and is dependent on many parameters, as cement class, concrete grade, relative humidity of the environment, surface of the structure in contact with the ambient air (drying surface), and the age of concrete (after casting) at the loading moment. Shrinkage of the concrete is independent on loading. It is caused by decrease of the pore water content in the hardened concrete, and is predominantly dependent on the ambient relative humidity. Relaxation describes stress reduction at a constant material strain, usually in prestressing steel tendons. In this study, the physical experiments of multiple concrete beams over time with respect to rheological processes are described. Each experimental system consists of two C35/45 beams horizontally bounded by a prestressed steel cylinder. Decrease of these pretension forces in cylinders over time have been monitored (stress relaxation). All together time histories of two forces are documented, based on measurements conducted in interior environment of an agricultural building. The experimental time histories of the pretension forces are then compared with the results of the finite element numerical analyses conducted in ANSYS software. Creep and shrinkage effects of the concrete material have been considered based on the corresponding European standard for design of the concrete structures. The time-histories of the forces in prestressed cylinders obtained from the numerical simulations are then compared with the experimental data, and discussed. It is concluded, that the estimation of the force decrease over analysed time with the creep and shrinkage effects considered according to the corresponding European standard appears to be slightly larger than the experimentally measured decrease of the force value, hence the assumption is more conservative.

Calibration and verification of creep parameters for concrete

Concrete is a material which undergoes slow increasing deformation while subjected to persistent mechanical stress. This phenomenon is known as creep. In concrete material, creep occurs at all stress levels. Additional deformation of concrete structures at the end of their design working life caused by creep is usually two to three times of the immediate elastic deformation value, but might be even more in some cases. The value is dependent on many parameters, e.g. concrete grade, cement class, ambient environment relative humidity, geometry of the structure (drying surface of concrete in contact with air) and also the age of concrete at the time of loading. According to corresponding European standard, the effects of creep are evaluated using creep coefficient, and should be considered for verification of serviceability limit states, and if significant, also at ultimate limit states. In order to evaluate the creep effects in geometrically more complex structures, numerical finite element (FEM) analyses might be conducted. In commercially available software ANSYS, there is a library of several implicit creep equations, with several input parameters. These parameters need to be calibrated in order to match the assumptions of the creep effects over time in accordance with the corresponding European standard. In this study, calibration process of European standard concrete C35/45 parameters for selected implicit creep equation from ANSYS library is presented. The parameters are calibrated for two different ambient relative humidity (RH) levels, 78.8% and 90%, each for concrete loaded in 28 days (also 90 days for RH 78.8% and 50 days for RH 90%) after its casting, and suitable for finite element analysis of creep effects within the first year after loading of the concrete structure. The calibration process is split into two parts, analytical one conducted in table processor, where approximate estimations of suitable parameter values are determined. The second part consist of the subsequent optimization process in OptiSLang software, where the optimal parameter values are determined in order to achieve the best match between the time dependent Eurocode standard creep coefficient and the creep coefficient based on the results of one solid element uniaxial compression test in ANSYS finite element software. The obtained parameters are then verified on an analysis of a simply-supported concrete beam modelled of solid 3D finite elements. The values of selected creep equation parameters are summarized in the table, and might be used in the subsequent ongoing research.

Generic and simplified approaches for the structural analysis of precast concrete sandwich panels

This paper presents a comparison between three numerical models developed for the structural analysis of composite precast concrete sandwich panels under lateral loading. The first model is based on a full finite element analysis where “slip” between the layers is obtained from the elastic deformability of the various components. The second model is based on a simplified finite element analysis where the effect of the shear connectors is smeared and modeled through an effective shear stiffness of the insulation layer. The third approach provides closed-form expressions for evaluating the deflection and is based on the classical sandwich beam theory where the shear connectors are considered through the effective stiffness of the insulation, similar to the second model. The structural response obtained from the three models was compared for various panel configurations and good correlation was obtained. A reasonable agreement with test results from the literature was also demonstrated. Therefore, both the simplified finite element model and the classical sandwich beam theory (closed-form solution) are recommended for the elastic structural analysis and for estimating the degree of composite action at the serviceability limit state of precast concrete sandwich panels.

An evaluation of non-linear undrained behaviour in the moderate strain range for fine-grained soils

To select appropriate stress-strain parameters for serviceability limit state calculations, an understanding is needed of the likely variation of stress-strain behaviour within the model displacement mechanism. One approach that may be utilised to investigate variations in stress-strain behaviour is by employing a simple non-linear model (with a small number of physically significant parameters) that simulates experimental measurements of soil stress-strain with reasonable precision. By testing the sensitivity of the model parameters to changes in physical properties that can be expected to be related to them the reliability of different models can be established. Recently, empirical analysis of the published triaxial test database RFG/TXCU-278 identified a significant positive correlation between 50 and OCR for four test modes (CIUC, CIUE, CKUC and CKUE). In this paper, a new experimental dataset from a programme of reconstituted soil tests on Kaolin and Bothkennar Clay is used to investigate the validity of a simple non-linear model.

Geotechnical Preliminary Design of Onshore Wind Turbine Foundations

A simplified geotechnical design procedure for foundations of onshore wind turbines is often beneficial because it can provide the types and sizes of foundations required to perform financial feasibility analysis of a project, and can also be used for preliminary design. This study presents a simplified method for designing onshore gravity-based foundations based on limited required data, namely, loads acting on foundations, data provided by manufacturers, and soil properties. The detailed design issues that may be essential for the final design are also discussed. A flowchart of the design process is also presented to visualize the geotechnical design of such foundations. The required calculation procedures can be easily carried out either through a series of spreadsheets or simple hand calculations. An example problem explaining the design of onshore wind turbine foundations was presented to demonstrate the proposed calculation procedure. The data used for the calculations were obtained from the literature. The proposed flowchart provides a quick way for the preliminary design of foundations of onshore wind turbine foundations. The foundation system obtained from the preliminary geotechnical design was numerically modeled using Plaxis 3D software. The global stability of the foundation system under Ultimate Limit State (ULS) loads and soil pressure developed under the foundation were calculated. The soil pressure beneath the foundation under Serviceability Limit States (SLS) loads and the total settlement and rotation of the foundation were calculated. The results obtained from the Plaxis 3D software and those obtained from the preliminary design were in agreement.

Evaluating Serviceability Limit State in a Long-span Skating Stadium Through Natural Frequency Analysis

This study investigated the application of vibration analysis to ensure user safety and establish an efficient management plan for the future utilization of sports facilities. The first natural frequency of the facility was documented at 3.2 Hz, while the second and third frequencies were measured at 3.56 Hz and 4.22 Hz, respectively. Experts posit that amplification is probable when the natural frequency aligns with the second and third modes. Resonance manifested at 1.8 Hz and 2.1 Hz dynamic activities within the anticipated frequency range, resulting in notable amplitude enhancements. Therefore, Constraining rhythmic actions that may elicit repetitive movements when using sports facilities is imperative to uphold serviceability and safety standards.

Design of precast UHPFRC retaining walls – Experimental and numerical validations

This paper focuses on the design as well as on the experimental and numerical validations of the mechanical behavior of a precast ultra-high performance fibre reinforced concrete (UHPFRC) retaining walls. The design, made in accordance with the Canadian Highway Bridge Design Code ( CSA S6, 2019 ), led to the fabrication of a full-scale UHPFRC retaining wall with 3% fibre content which had dimensions of 3 m in height, 2 m in length, 2 m in width, with two vertical and horizontal stiffeners, and very thin vertical and horizontal panels of 40 and 65 mm, respectively. The experimental tests showed that the UHPFRC retaining wall exceeded by 42% the ultimate limit state (ULS) design factored bending moment and showed a very ductile behavior under flexural loading. At service limit state (SLS), the retaining wall had maximum crack opening between 0.15 and 0.28 mm, and a maximum lateral displacement of 4 mm. The finite-element model developed for the application captured accurately the flexural behavior of the UHPFRC retaining wall and was used later in parametric studies to optimize the design. The retaining wall optimal design includes UHPFRC with 3% fibre content and stiffeners with variable cross-section which allows volume reductions of 73% for concrete and 86% for rebars in comparison to the conventional reinforced concrete design.

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Free Vibrations of Sustainable Laminated Veneer Lumber Slabs

In this paper, the results of dynamic laboratory tests of four laminated veneer lumber (LVL) slabs of different thicknesses, widths, and types were presented. In three of the tested slabs, LVL with all veneers glued lengthwise was used (LVL R). In one LVL slab, a fifth of the veneers were glued crosswise (LVL X). Laminated veneer lumber slabs are engineering wood products with several important performance characteristics, making them a sustainable and preferred solution in civil engineering. To ensure the safe operation of a building with LVL structural elements, it is important to know their dynamic properties. The basic dynamic characteristics of the slabs obtained from experimental tests made it possible to validate the numerical models of the slabs. The slab models were developed in the Abaqus program using the finite element method. The elastic and shear moduli of laminated veneer lumber used in the four slabs were identified through an optimization process in which the error between the analyzed frequencies from the laboratory tests and the numerical analyses was minimized. In the case of slabs that possess the same thickness and are composed of different LVL types, the elastic modulus of LVL R in the longitudinal direction was 1.16 times higher than the elastic modulus of LVL X in the same direction. However, the elastic moduli of LVL R in tangential and radial directions were lower than the elastic moduli of LVL X in the same directions. The above was the result of the fact that the 45 mm LVL X slab had 3 out of 15 veneers glued crosswise. In the case of slabs possessing different thicknesses but the same width and type, the elastic modulus of the thicker panel was 1.13 times higher than that of the thinner panel. After validating the models, the numerical analyses yielded results consistent with the experimental results. The numerical models of the LVL slabs will be used to develop numerical models of composite floors with LVL panels in future research. Such models will allow for the analysis of floor dynamic characteristics and user-generated vibrations, which is required when verifying the serviceability limit state.

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

The object of the study was truss-type rod structures, which were investigated for the purpose of finding the optimal design solution in a mixed (continuous and discrete) space of variables. The parameters of the geometric scheme of the truss, as well as the dimensions of the cross-sections of its elements, were considered as design variables. The stated optimization problem is represented as a nonlinear programming task, in which the objective function and nonlinear constraints of the mathematical model are continuously differentiable functions of the design variables. The system of constraints includes strength and stability inequalities, formulated for the design cross-sections of the rod elements of the structure, which is subject to the effect of the design load combinations of the ultimate limit states. As a part of the system of constraints, the displacement constraints formulated for the specified structural nodes, which is subject to the action of design load combinations of the serviceability limit states, are considered. To solve the stated optimization problem, a method of the objective function gradient on the surface of active constraints was used, with the simultaneous elimination of residuals in the violated restrictions. For design variables, the variation of which must be performed according to a given set of possible discrete values, a discretization procedure for the optimal solution obtained in the continuous space of design variables is proposed. A comparison of the proposed optimization methodology with alternative metaheuristic methods and algorithms reported in the literature was performed. On the considered problem of parametric optimization of a 47-span tower structure, a design solution with a weight of 835,403 kg was obtained, which is 1.53...4.6 % better than the optimal solutions obtained by other authors

Elastic–Plastic Analysis of Rigid Passive Piles in Two-Layered Soils

The paper analyses the behavior of a rigid passive pile embedded in a soil profile consisting of a stable layer underlying an unstable layer subjected to a uniform soil displacement. Pile-soil interaction is considered by modeling the soil by a series of elastic–plastic springs along the pile shaft. The modulus of horizontal subgrade reaction is assumed to linearly increase with depth in the unstable layer and constant in the stable one. The ultimate soil resistance is assumed increasing with depth in both layers. The results of analysis are presented in dimensionless form in terms of shear force developed at the slip surface as a function of the pile embedment into the stable layer and the distribution of soil characteristics over depth. The method allows capturing pile response not only at the soil ultimate state but also at the intermediate states. Specifically, the governing equations for the elastic, elastic–plastic and plastic cases are discussed and, whenever possible, a set of closed-form expressions is provided to estimate the maximum bending moment along the shaft and the pile head deflection, so that for an assigned value of the required stabilizing force both ultimate and serviceability limit state of the pile can be checked. A numerical example is given to illustrate the application of the proposed procedure.

Fire-resistance design of ultimate and serviceability limit states for Q690 high-strength steel plate girders under patch loading

This study numerically investigated the serviceability and ultimate limit states of Q690 high-strength steel (HSS) plate girders exposed to fire under patch loading. A shell element numerical model of the Q690 HSS plate girder was created using Abaqus software, and its accuracy was verified through experimental results. A comprehensive parametric analysis involving 512 numerical models was conducted to examine the effects of elevated temperatures, web aspect ratio, loading length, and web depth-to-thickness ratio. Because of the absence of specific design guidance in EN 1993–1-2 for Q690 HSS plate girders exposed to fire, the accuracy of the resistance model specified in EN 1993–1-5 that was applied to steel plate girders at room temperature was verified by employing the material properties of Q690 HSS at elevated temperature. The verification results revealed that the ultimate resistance of the Q690 HSS plate girder obtained from the resistance model in EN 1993–1-5 was considerably lower than that obtained from the numerical analysis. A modified resistance reduction function that applies to the Q690 HSS plate girder at room temperature was proposed based on the resistance model in EN 1993–1-5. Comparisons indicated that the accuracy of the resistance model in EN 1993–1-5 was improved when applied with the proposed resistance reduction function. Additionally, predictive approaches were introduced to determine the ultimate resistance, effective resistance, and effective stiffness of Q690 HSS plate girders in fire. The comparison with numerical results highlighted that the proposed approaches exhibited high accuracy and provided a sound basis for the engineering design of Q690 HSS plate girders.

An Investigation on the Effect of Watertightness Criteria on the Structural Assessment of Prestressed Concrete Substructures of Floating Wind Turbines

The effect of watertightness criteria on structural assessment was investigated in this study through the design of a semi-submersible floater for a 10 MW wind turbine. A structural assessment was carried out for the ultimate, fatigue, and serviceability limit states, where six cases of combinations of the loading conditions and structural requirements were assumed for the assessment of watertightness. The different assessment conditions for watertightness resulted in different designs of prestressing tension, which also caused differences in the design margins for the ultimate limit states as well as the SN diagram used for the assessment of the fatigue limit states. The maximum stress acting on the member of the floating wind turbine differed by about 7.6 to 16.2% for the 50-year and 1-year environmental conditions. The small difference between the stresses for the two return periods can be attributed to the large component of the wind turbine thrust in the variable loads. When the partial load factor of 1.0 was used, the structural requirement in the prestressing design caused larger differences compared to the return period of the loading conditions in the watertightness assessment. The use of the partial load factor of 0.5 for the prestressing design also caused a large difference in the results of the structural assessment, indicating the necessity of further investigation of the determination of the partial load factor for floating offshore wind turbines.

Design of a 3-storey frame building using engineered bamboo composite (EBC)

This paper reports the design of a 3-storey building using engineered bamboo composite (EBC). The building utilizes balloon type EBC frame and EBC hollow decks as the load-carrying system. Gravity load, wind load, and seismic load were considered in the design. In order to prevent the brittle fracture in EBC beams and columns, a T-shaped steel connector, which was used to join the beams and columns of the frames, was intentionally designed with lower moment resistance compared to the connected beams and columns. Hence the damage of the structure can be confined to the steel connector that enables good ductility for the structure. The performances of the structure under serviceability limit state and the ultimate limit state were evaluated based on the elastic analysis. Inelastic static analysis (pushover) was conducted to assess the structural performance beyond the elastic limit when the building subjected to the rare-encounter earthquake. It was demonstrated that the balloon type EBC frame can be designed with adequate stiffness and strength to meet the requirements of serviceability and load-carrying capacity. It also has good ductility when the lateral seismic load beyond its elastic limit. The design and construction of this building provided a testimony that EBC frame structure is suitable for low-rise building in seismic region, and it also has the advantages of quick erection on site and good economy.

Mechanical properties of the composite sandwich structures with cold formed profiled steel plate and balsa wood core

Fiber reinforced plastic (FRP) sandwich structure are increasingly used in construction areas recently for its high strength, light weight and corrosion resistance performance. This paper proposed an innovative composite sandwich structure incorporating GFRP skins, a cold formed profiled steel plate and a light weight balsa wood core. The interaction between the different components was connected by stainless steel core rivets. Three-point bending tests were conducted on eleven specimens to investigate the parameters (shear span to depth (a/d) ratio, thickness of cold formed profiled steel plate and spacing of the stainless steel core rivets) effect on the performance (deflection, ultimate load bearing capacity, and failure modes) of the new proposed structure. The test findings indicate that a reduction in ultimate load-bearing capacity ranging from 13% to 41%, accompanied by an escalation in deflection between 1.7 and 13.9 times, as the a/d ratio ranges from 1 to 6. All beams experienced failure at deflections ranging from span/114 to span/50. Specifically, specimens displayed core shear failure for a/d ratios ≤ 4, transitioning to top skin compression failure at an a/d ratio of 6. Compared to specimens without cold formed profiled steel plate reinforcement, the load bearing capacity of the new proposed composite structure at serviceability limit states and ultimate limit states was increased by 68%−194% and 53%−83%, respectively. Moreover, the reinforcement of the stainless steel core rivets can ensure the coordinated working of different components, and the smaller the spacing, the better the working effect. Finally, an analytical model was developed to account for the impact of cold-formed profiled steel plates on specimen stiffness and load-bearing capacity. This model was subsequently validated through experimental results. Both the experimental and theoretical analysis verified the favorable performance of the proposed new composite structure.