Ultimate Limit State Design Research Articles

A simple approach for predicting the ultimate lateral capacity of a rigid pile in sand

Rigid piles are widely used as foundations to resist lateral load. A calculation to confirm that the ultimate lateral geotechnical capacity of such piles is not exceeded is required for ultimate limit-state design. Existing (empirical) approaches employed to predict the lateral capacity of a rigid pile in sand assume the net soil pressure is a function of the vertical effective stress and friction angle. However, difficulties in determining the appropriate friction angle(s) make these approaches less useful for practical purposes. A simple alternative approach correlated with the cone penetration test end resistance (qc) is developed in this paper based on ultimate capacities measured in a new series of tests on rigid piles with diameters of 127, 169, 273 and 457 mm and aspect ratios (L/D) between 1·6 and 12. These test results are combined with additional tests reported in the literature to establish a simple formulation for the ultimate net pressure adjacent to a pile in sand. Explicit design equations are also presented for soil profiles with a constant qc value and where qc increases linearly with depth. The proposed equations are seen to provide good estimates of capacities for rigid piles with a wide range of diameters.

Effects of bedplate flexibility on drivetrain dynamics: Case study of a 10 MW spar type floating wind turbine

This paper deals with the effect of bedplate flexibility on drivetrain dynamics of a 10 MW spar type floating wind turbine. The 10 MW drivetrain bedplate is designed based on extreme design loads and ultimate limit state (ULS) design criteria. A decoupled analysis approach is employed. Global dynamic analysis of the 10 MW floating turbine is firstly conducted using an aero-hydro-servo-elastic code, then the global response is used as input to the drivetrain dynamic analysis. Load effects and fatigue damage of gears and bearings in the rigid and flexible bedplate models in different environmental conditions are compared. In addition, sensitivity of the drivetrain fatigue damage to varying fidelity in the bedplate modelling is studied. The results indicate that the bedplate flexibility would increase the load effects on bearings inside the gearbox, while it would reduce the load effects on the main bearings. Reasonable bedplate modelling fidelity is of great importance, because it could save a great deal of computational costs without loss of the drivetrain dynamic response accuracy. The present work provides a reference for a proper drivetrain design and dynamic analysis in the future, by accounting for bedplate flexibility. • A 10 MW drivetrain bedplate is designed for floating wind turbine based on extreme loads and ULS design criteria. • A high-fidelity drivetrain dynamic model is established and the coupled rotor-drivetrain-bedplate-tower eigenmodes are studied. • Load effects and fatigue damage of drivetrain gears and bearings in the rigid and flexible bedplate models are compared. • Sensitivity of drivetrain fatigue damage to bedplate modelling fidelity is studied.

Testing and initial verification of the world's first metal 3D printed bridge

Wire and arc additive manufacturing (WAAM) is a method of metal 3D printing that is suited to the requirements of the construction industry in terms of scale, speed and cost. Using this technology, a 10.5 m span footbridge, the first of its kind, has been printed. The testing, analysis and initial verification of the bridge and its components are described herein. The experiments performed included advanced geometric analysis, material testing, compressive testing of cross-sections and full-scale load testing of the bridge at various stages throughout and post construction. Parallel finite element modelling of the full bridge and its constituent elements has also been performed as part of the verification. Confirmation that the bridge was able to sustain its full serviceability design load enabled to the bridge to be unveiled to the public, with controlled access, for Dutch Design Week 2018. Further testing under ultimate limit state design loading is planned before the bridge is placed in its final location and fully opened to the public. The project highlights the potential for metal 3D printing in structural engineering, as well as the necessary considerations for design.

Extreme responses and associated uncertainties for a long end-anchored floating bridge

Very-long floating bridges represent an innovative marine structure for crossing wide and deep fjords. During the design of a floating bridge, extreme structural responses at a specified probability of exceedance are required to be properly evaluated for ultimate limit state (ULS) design check. This study addresses the estimation of extreme structural responses due to wind and wave loads and associated uncertainties. An end-anchored floating bridge, about 4600 m, is considered in a case study. The long-term extreme responses are estimated by using a simplified engineering approach, in which the long-term extreme response is approximated by the one-hour short-term extreme responses at a high fractile (90% in this study) for selected short-term sea states. The extreme responses are expressed as μ+κ·σ, where μ and σ are the ensemble mean and standard deviation, and κ is a multiplying factor. Statistical analyses indicate that the structural responses, including axial force, strong and weak axis bending moments of the bridge girder, are close to follow a Gaussian distribution. A simplified analytical method, the Gumbel method and the mean upcrossing rate (MUR) method are employed to estimate the multiplying factor κ and extremes. The κ estimated by these three methods are generally close, varying in the vicinity of 4. The κ and extremes estimated by the simplified method have a much smaller variation than the Gumbel and MUR methods. Statistical uncertainties and model uncertainties in the extreme value prediction are also addressed. Based on the results of 10 sets of 10 1-h ensembles, the mean and coefficient of variation (CoV) of μ,κ,σ and extremes of structural responses of 10 1-h simulations under two selected sea states are evaluated. The CoV of σ is less than 0.045, but the CoV of κ is relatively large, mainly between 3.5×10-2 and 6.5×10-2. The CoV of extremes estimated by the simplified analytical method is fairly small, less than 0.035. While the CoV of extremes estimated by the Gumbel and MUR methods are much larger and can reach 0.137 and 0.158, respectively. In practical design of floating bridge, only a limited number of simulations (e.g. 10 1-h) are conducted to predict the extreme structural responses. This will introduce statistical uncertainties and should be corrected by a factor for a conservative estimate. A simplified procedure to derive the correction factor is presented in this study. For the floating bridge considered with 10 1-h simulations, the correction factor is recommended to be 1.1 when the absolute value of mean μ is smaller than σ, and be 1.2 when the absolute value of mean μ is larger than σ, in order to achieve a 90% conservative estimation of extreme.

Mechanical performance of affordable and eco-efficient ultra-high performance concrete (UHPC) containing recycled tyre steel fibres

This study aims to develop an affordable eco-efficient ultra-high performance concrete (UHPC) using normal mortar, recycled tyre steel cords (RTSC) and recycled tyre steel fibres (RTSF). Twelve UHPC mixes containing either RTSC, RTSF or blends of the two in various ratios are studied for total fibre volumes of 2, 3 and 4%. The effect of short fibres and cleanliness of RTSF on flexural strength of UHPC is examined, and it is shown that rubber and other impurities, as well as fibres with less than 9 mm length, significantly reduce the strength of the UHPC mix. This confirms that cleaning and reducing the amount of short fibres is necessary for improved performance. Although mixes containing RTSF only do not exhibit the same flexural performance of mixes containing RTSC or manufactured fibres, similar strength can be achieved by using hybrids (RTSC and RTSF) or a higher dosage of RTSF. The main strength parameters used in serviceability and ultimate limit state design are experimentally derived and prediction models are proposed. A Material efficiency study of the mixes shows that use of RTSF in UHPC provides significant cost and environmental benefit. Such affordable and robust UHPC mixes can help develop new and more sustainable applications for the construction industry.

The Effect of Targeted Field Investigation on the Reliability of Axially Loaded Piles: A Random Field Approach

This work deals with the effect of targeted field investigation on the reliability of axially loaded piles, aiming at an optimal serviceability and ultimate limit state design. This is done in a Random Finite Element Method (RFEM) framework properly considering sampling in the analysis; the RFEM method combines finite element analysis with the random field theory. In this respect, the freely available program called RPILE1D has been modified by the authors as to consider sampling of both soil and pile properties. In each RFEM realization, failure is considered to have occurred when the calculated shaft resistance of pile considering spatially uniform properties (average of sampled values from the soil and pile random fields) is greater than the respective “actual” one considering spatially random properties for both soil and pile. The necessary numerical demonstration of the proposed methodology is done by considering two sampling strategies: a) sampling from a single point and b) sampling from a domain, both along the pile, whilst the various parameters governing the statistical uncertainty of the problem are examined; 5383 different cases were considered in total. As shown, a targeted field investigation may minimize or even eliminate the statistical error inserted in the design. The error is quantified by the difference in the probability of failure comparing different sampling scenarios. Another main finding is that the optimal horizontal sampling location occurs where the pile is going to be constructed. In addition, it is shown that the benefit of a targeted field investigation is much greater than the benefit gained using characteristic soil property values.

Design and experimental verification of a novel fibre-reinforced polymer sandwich decking system for bridge application

The paper presents the selected research results on the development of a novel fibre-reinforced polymer sandwich decking system dedicated for bridge applications and applied in the first Polish all-composite vehicular bridge. Based on a review of recently implemented similar systems, the novel solution has been proposed and checked according to relevant codes as a part of all-composite bridge design. Due to the novelty of sandwich design, the comprehensive structural testing has been carried out to verify design assumptions as well as to assess its stiffness, strength and safety. In order to find the optimized structural solution of fibre-reinforced polymer deck, the laboratory tests were conducted on several FRP sandwich panels having various core foam density and internal ribs’ fabric architecture. The panels were subjected to three loading schemes to check their response under bending, shear and bearing as well as to examine their structural behaviour up to failure and corresponding failure modes. The stiffness, strength and safety against failure were experimentally determined. In this paper, the test results have been compared to the ultimate and serviceability limit state design criteria formulated in the European guidelines and applied in an actual bridge design.

Analytical Solutions for Ultimate Limit State Design of Thermal Piles

AbstractThis work aimed at providing analytical closed-form solutions for the design of thermal piles. To this end, a model in which a cylindrical pile is attached along the shaft to a series of di...

Design of the out-of-plane strengthening of masonry walls with fabric reinforced cementitious matrix composites

Fabric reinforced cementitious matrix (FRCM) composites, made of high strength textiles externally bonded with inorganic matrices, experimentally proved effective to enhance the capacity of masonry walls. With the aim of fostering the transfer of knowledge from scientific research to engineering practice, this paper proposes an approach for the design of the out-of-plane flexural strengthening of masonry walls by FRCM systems. The mechanical properties of the reinforcement are derived by combining the results of tensile tests on textile specimens and FRCM-to-substrate shear bond tests. An expression for the preliminary design of the reinforcement is proposed, according to a limit analysis approach, based on tensile and bond strength of FRCM. Whereas, for structural assessment, strain compatibility is enforced, and the bending moment capacity of the reinforced wall is based on FRCM stiffness, tensile and bond strains, consistently with existing building codes. An estimate of the out-of-plane displacement capacity is also developed, which is particularly useful in seismic assessment. A wide experimental database is used to validate theoretical relationships, tune calibration coefficients and derive safety factors, in accordance with the design-by-testing framework of Eurocode 0 for ultimate limit state design.

Serviceability limit state design of large concrete structures: Impact on reinforcement amounts and consequences of design code ambiguity

Reinforced concrete is typically designed taking into account the critical load combination in the ultimate limit state (ULS), while further checked in the serviceability limit state (SLS). Experience shows that the SLS control can result in unexpected additional reinforcement amounts. This paper investigates this topic through (i) a case study and (ii) a parametric study. In the case study, different methods are used to check a cross section subject to membrane and plate forces. We found significant variation in the results using different methods, due to the amount of choices pertinent to the methods. The variation in results was found to increase with increasing load complexity. The parametric study shows the amount of additional reinforcement necessary due to crack width requirements compared to ULS design. The crack width requirements in Eurocode 2 is shown to require a relative increase of several hundred percent in reinforcement compared to ULS design, and an absolute increase, as a percentage of the effective concrete area, of 9%. We conclude that there are large discrepancies in subjective understanding of the crack width limitation requirements as well as in interpretation of the code provisions and calculation methods.

Robust design of energy piles using a fuzzy set-based point estimate method

Energy piles have been adopted worldwide as a green foundation technology. The current geotechnical design methods for energy piles — factor-of-safety-based design and reliability-based design — mainly focus on the safety and cost, while design robustness is usually ignored. This paper presents a robust design model for energy piles that is based on the load-transfer method. A fuzzy set-based point estimate method is adopted to quantify the uncertainty in the ultimate limit state design and serviceability limit state design. This robust design approach is intrinsically a multi-objective optimization, in which the optimal design can be determined by simultaneously meeting the requirements for safety, cost and robustness. The proposed robust design approach for energy piles is demonstrated through a case study.

Width Effect of CFRP Strips on the Compressive Behavior of Plain Concrete Cylinders

Several experimental studies have been conducted to investigate the influence of fiber-reinforced polymer on confined columns. Most of these studies examine the effect of some variable parameters such as the spacing between strips, the number of layers, the initial strength of concrete and the degree of confinement. This paper is the result of an experimental study on the behavior of plain concrete cylinders (O160 × 320 mm) reinforced with carbon fiber-reinforced polymer (CFRP) layers. The main purpose of this work is to study the influence of strip width of CFRP composite used for reinforcement. Five series of tests were carried out under a cyclic and progressive axial compression loading to failure. Tests were carried out using a compression machine MCC8 of 3000 kN capacity with automatic data acquisition system. In this investigation, the stress–strain curves were plotted in order to determine the stress–strain relationships and to obtain the behavior of the concrete cylinders. In conclusion, it is evident that this study has shown an optimal configuration and an adequate distribution of CFRP composite materials to minimize the utilization of the latter and thus to use it to its ultimate strength and to carry out the ultimate limit state design as well.

A proposal to modify the moment coefficient in Eurocode 2 for predicting the residual strength of corroded reinforced concrete beams

Ultimate limit state (ULS) criteria are used to design reinforced concrete beams which give a ductile behaviour at failure. This means the resisting moment, Mt, is less than the resisting moment in compression, Mc. Since steel reinforcement is susceptible to corrosion, the ultimate capacity can be seriously affected as the degree of corrosion increases. The impact of corrosion to the main steel reinforcement on the flexural performance of reinforced concrete beams is investigated. Beams measuring 100 mm wide × 150 mm deep with differing levels of under-reinforcement (Mt/Mc ratios) were tested under four-point bending. Although the design code for reinforced concrete beam design has gone through various changes over the years, the fundamentals for design has broadly remained the same in that the beam is designed with an ultimate moment-coefficient (K=M/fcbd2) with sufficient capacity to be able to easily carry the service loads it is exposed to. However, the long term influence of corrosion on the steel reinforcement is not considered at the design stage although a manufacturing factor of safety is applied. The analysis in this paper uses a modified-moment coefficient (Kcorr=Mcorr/fckbd2) based on EC 2 ultimate limit state design guidelines to predict the residual flexural strength of reinforced concrete beams suffering from main steel corrosion. Two grades of concrete (>C35/45 and <C35/45) are considered as used in EC 2 [1]. The results obtained in this investigation show that there is a relationship between the reducing moment-coefficient of corrosion-affected concrete beams and both the degree of under-reinforcement (Mt/Mc) and degree of corrosion to the main steel reinforcement for beams with concrete grades >C35/45. The analysis is then extended to include test data from other researchers to develop a similar simplified empirical analytical expression for beams with concrete grades <C35/45, thereby enabling a prediction of residual strength due to corrosion to be made for any beam size or concrete strength grade.

DESIGN OF BOLTED CONNECTIONS SUBJECT TO TORSION AND SHEAR IN THE ULTIMATE LIMIT STRESS STATE

Steel connections transferring axial and shear forces in addition to bending moment and/or torsional moment are widely used in steel structures. Thus, design of such eccentric connections has become the focal point of any researches. Nonetheless, behavior of eccentric connections subjected to shear forces and torsion in the ultimate limit state is still ambiguous. Most design codes of practice still conservatively use the common elastic analysis for design of the said connections even in the ultimate limit states. Yet, there are some exceptions such as the design method proposed by CAN/CSA-S16-14 which gives tabulated design aid for the ultimate limit state design of these connections based on an empirical equation that is derived for ¾ inch diameter A325 bearing type bolts and A36 steel plates. It was argued that results can also be used with a margin of error for other grade bolts of different sizes and steel of other grades. As such, in this paper, the performance of bolted connection subject to shear and torsion is experimentally investigated. The behavior, failure modes and factors affecting both are scrutinized. Twelve connections subject to shear and torsion with different bolts configurations and diameters are experimentally tested to failure. The accuracy of the currently available design equations proposed is compared to the outcomes of these tests.

Structural Behaviour and Mechanical Properties of Welded Steel I-Girders with Corrugated Webs

Steel I girders with corrugated webs are appropriate alternatives for normal flat-web girders in steel structures since they provide lighter and smaller beam features in steel design. Based on the existing literature, the corrugated web beams (CWBs) provide many advantages for structural applications. In this study, a series of numerical analyses have been performed in order to investigate the structural behaviour of steel I girders with corrugated web profile and to compare their mechanical performance with normal welded beams. Theory of Ultimate Limit State design has been adopted in accordance with AS4100 (Steel structures, Standard Australia, Sydney, 1998) along with considering geometric and material non-linearity in the numerical analyses in SAP2000. Comparing the results of the numerical investigation, merits of using corrugated welded beams (CWBs) over normal welded beams (WBs) have become apparent. Moreover, investigations regarding force–displacement relationship and buckling analysis of the webs were carried out and presented to further validate the advantages of using corrugated web beams. CWBs have been used in some parts of Australia without detailed information about their mechanical properties. Thus, based on the outcomes of this study, CWB table for dimensions and cross sectional properties has been developed and proposed for practical applications.

Probabilistic design model for energy piles considering soil spatial variability

Energy piles are sustainable green foundations. Although several geotechnical design methods have been proposed, no methods have yet been developed to quantify the uncertainty propagation in thermo-mechanical pile-soil interactions. The probabilistic model proposed in this paper, which is based on load-transfer curves, considers the effects of spatial variability for energy pile design. The developed random finite difference method is used to address the effects of vertical spatial variability on the ultimate limit state design and serviceability limit state design. This study points to the necessity of modeling the soil spatial variability in the thermo-mechanical pile-soil interactions in energy piles.

Seismic response modification factor for steel slit panel-frames

In this paper, the overstrength, ductility and response modification factors of moment resistant frame (MRF) with steel vertical slit panel (SSP-MRF) were investigated and determined. For this purpose, buildings with various stories were used. Abaqus software was used to perform the static pushover analysis, linear dynamic analysis, and nonlinear incremental dynamic analysis. In this research, seismic response modification factor has been evaluated for each model structure using pushover analysis, and the tentative value 8.11 has been proposed for the ultimate limit state design method. Some of the results of pushover analysis and nonlinear incremental dynamic analyses were compared. According to this comparison, the response modification factor of 10-story model structure derived from pushover analysis (6.14) was slightly smaller than those obtained from incremental dynamic analyses (7.5).

The effect of realistic curing temperature on the strength and E-modulus of concrete

The strength and E-modulus of concrete are decisive parameters when it comes to ultimate limit state design, serviceability limit state design, and early age crack assessment. The properties of concrete are generally determined in the laboratory under 20 °C isothermal conditions and then used as the basis for calculations under realistic temperature conditions. It is well-known, however, that the curing temperature affects both the rate of property development in concrete and the “final value” of a given property. The current study investigated the effect of a realistic temperature history on the compressive cube strength, the tensile strength, and the tensile E-modulus for two concretes, a reference concrete and a fly ash concrete. Concrete specimens were subjected to either (1) 20 °C isothermal curing conditions, or (2) realistic temperature curing conditions for 14 days and then 20 °C isothermal conditions, until they were tested after 28 and 91 days. Parallel tests performed in a Temperature-Stress Testing Machine were also used to evaluate the results. The reference concrete showed a general reduction in strength and E-modulus when subjected to a realistic curing temperature, whereas the fly ash concrete showed an 11% increase in the 28-day E-modulus when cured under realistic temperature conditions. Furthermore, in both isothermal and realistic curing temperature conditions, the fly ash concrete showed a pronounced property development beyond 28 days, which could not be described by the material model currently used.

Assessment of a standard ULS design procedure for offshore wind turbine sub-structures

Sub-structures of offshore wind turbines are designed according to several design load cases (DLCs) that cover various fatigue (FLS) and ultimate limit states (ULS). The required DLCs are given in the current standards, and are supposed, on the one hand, to cover accurately all significant load conditions to guarantee reliability. On the other hand, they should include only necessary conditions to keep computing times manageable. For ULS conditions, the current work addresses the question whether the current design practice is, firstly, sufficient, and secondly, sensible concerning the computing time by only including necessary DLCs. To address this topic, data of five years of normal operation, simulated using a probabilistic approach, is used to extrapolate 20-year ULS loads (comparable to a probabilistic version of DLC 1.1 for substructures). These ULS values are compared to several deterministic DLCs required by current standards. Results show that probabilistic, extrapolated ULS values are fairly high and exceed standard DLC loads. Hence, the current design practice might not always be conservative. Especially, the benefit of an additional DLC for wave peak periods close to the eigenfrequency of the sub-structure is indicated.

Numerical Modeling and Dynamic Analysis of a Floating Bridge Subjected to Wind, Wave, and Current Loads

Designing reliable and cost-effective floating bridges for wide and deep fjords is very challenging. The floating bridge is subjected to various environmental loads, such as wind, wave, and current loads. All these loads and associated load effects should be properly evaluated for ultimate limit state design check. In this study, the wind-, wave-, and current-induced load effects are comprehensively investigated for an end-anchored curved floating bridge, which was an early concept for crossing the Bjørnafjorden. The considered floating bridge is about 4600 m long and consists of a cable-stayed high bridge part and a pontoon-supported low bridge part. It also has a large number of eigen-modes, which might be excited by the environmental loads. Modeling of wind loads on the bridge girder is first studied, indicating that apart from aerodynamic drag force, aerodynamic lift and moment on the bridge girder should also be considered due to their significant contribution to axial force. Turbulent wind spectrum and spatial coherence play an important role and should also be properly determined. The sway motion, axial force, and strong axis bending moment of the bridge girder are mainly induced by wind loads, while the heave motion, weak axis bending moment, and torsional moment are mainly induced by wave loads. Turbulent wind can cause significant larger low-frequency eigen-mode resonant responses than the second-order difference frequency wave loads. Current loads mainly contribute damping and reduce the variations of sway motion, axial force, and strong axis bending moment.