Simple Design Formulas Research Articles

Tensile tests of welded hollow spherical joints reinforced by CFRPs

To improve the tensile strength of welded hollow spherical joints (WHSJs) while maintaining their original structural configuration, a carbon fibre reinforced polymer (CFRP) is proposed in an innovative layered strengthening method. To assess the effect of varying the number of axial and circumferential CFRP layers on tensile properties, axial tensile tests were performed on 12 full-size Q235B WHSJs reinforced with CFRP. The experimental findings revealed that bonding the CFRP layers to the surfaces of the joints substantially increased their tensile strengths. Furthermore, with an increase in the number of layers, the resistance of the reinforced joints improved significantly, showing a proportional increase of 19.85%. The number of layers in the circumferential CFRP at the end anchorage was crucial for enhancing the axial tensile strength. By integrating the resistance equations for welded hollow spheres with those applicable to CFRP, new equations were derived for the resistance of CFRP-reinforced WHSJs. Additionally, the force analysis of circumferential CFRP led to the development of a simplified design formula to determine the optimal number of circumferential CFRP layers.

Axial Compressive Behaviours of Coal Gangue Concrete-Filled Circular Steel Tubular Stub Columns after Chloride Salt Corrosion.

The axial compressive behaviours of coal gangue concrete-filled steel tube (GCFST) columns after chloride salt corrosion were investigated numerically. Numerical modelling was conducted through the static analysis method by finite element (FE) analysis. The failure mechanism, residual strength, and axial load-displacement curves were validated against tests of the coal gangue aggregate concrete-filled steel tube (GCFST) columns at room and natural aggregate concrete-filled steel tube (NCFST) columns after salt corrosion circumstance. According to the analysis on the stress distribution of the steel tube, the stress value of the steel tube decreased as the corrosion rate increased at the same characteristic point. A parametric analysis was carried out to determine the effect of crucial variation on residual strength. It indicated that material strength, the steel ratio, and the corrosion rate made a profound impact on the residual strength from the FE. The residual strength of the columns exposed to chloride salt was in negative correlation with the corrosion rate. The impact on the residual strength of the column was little, obvious by the replacement rate of the coal gangue. A simplified design formula for predicting the ultimate strength of GCFST columns after chloride salt corrosion exposure was proposed.

A Detailed Numerical Model for a New Composite Slim-Floor Slab System.

The paper concerns the numerical modelling of a new slim-floor system with innovative steel-concrete composite beams called "hybrid beams". Hybrid beams consist of a high-strength TT inverted cross-section steel profile and a concrete core made of high-performance concrete and are jointed with prestressed hollow core slabs by infill concrete and tie reinforcement. Such systems are gaining popularity since they allow the integration of the main structural members within the ceiling depth, shorten the execution time, and reduce the use of concrete and steel. A three-dimensional finite element model is proposed with all parts of the system taken into account and detailed geometry reproduction. Advanced constitutive models are adopted for steel and concrete. Special attention is paid to the proper characterisation of interfaces. The new approach to calibration of damaged elastic traction-separation constitutive model for cohesive elements is applied to concrete-to-concrete contact zones. The model is validated with outcomes of experimental field tests and analytical calculations. A satisfactory agreement between different assessment methods is obtained. The model can be used in the development phase of a new construction system, for instance, to plan further experimental campaigns or to calibrate simplified design formulas.

Simplified Design Formula for Tensile Axial Strain of Buried Pipeline Subjected to a Liquefaction-Induced Lateral Landslide

Simplified Design Formula for Tensile Axial Strain of Buried Pipeline Subjected to a Liquefaction-Induced Lateral Landslide

Preliminary design and evaluation method for the seismic isolation layer of a shield tunnel

Theoretical analyses and numerical simulations, proposed to increase the efficiency of tunnel seismic isolation measures, are too complex for solving practical problems. Herein, a simplified design method for a tunnel isolation layer is developed for preliminary calculations of the required physical parameters based on the surrounding rock conditions and seismic isolation performance. The internal force response of a shield tunnel in homogeneous ground before and after the installation of a seismic isolation layer is determined using the proposed method, considering the coupled effect of the isolation layer and surrounding rock by calculating the equivalent elastic modulus. The effectiveness of the derived method is verified using wave function expansion and finite element numerical simulation methods. The results obtained using the simplified design formulae are consistent with those obtained using the wave function expansion method. Furthermore, the effects of the seismic wave frequency, surrounding rock type, elastic modulus, and thickness of the seismic isolation layer on the seismic isolation effect are examined via parametric analysis. The proposed method could be applied to preliminary design and evaluation of seismic isolation layers for shield tunnels with different surrounding rock types.

Simplified optimization of inerter-enabled tuned mass damper for lightweight-oriented seismic response mitigation of long-span domes

Suspending tuned mass dampers (TMDs) from long-span domes has been studied to mitigate seismic responses of long-span domes. However, the strict weight limitations on the suspension mass in conventional tuned mass dampers (TMDs) hinder their widespread adoption. To address this issue, we introduce the inerter-enabled tuned mass damper (IeTMD) that consists of a suspension mass, tuning spring, and a tuned viscous mass damper (TVMD) sub-system into the seismic vibration mitigation of long-span domes. Under the assumption that long-span domes remain within the elastic range and adhere to the small deformation hypothesis, we have proposed simplified design formulae for IeTMDs, guided by the lightweight-based seismic vibration control criterion. Parametric studies are conducted to illustrate the degree to which an IeTMD can improve the performance of the long-span dome when its key parameters change within certain ranges. The effectiveness of the design strategy in exploiting the damping enhancement effect is confirmed. Time history responses of a benchmark long-span dome demonstrate that the IeTMD has high control efficiency, as bi-directional displacements, accelerations, and base shear are significantly reduced. Comparative analyses between the proposed IeTMD and conventional TMD are conducted. Results show that the IeTMD designed by the simplified design formulae can achieve the target control performance with less suspension mass. Furthermore, the frequency analysis shows that the proposed IeTMD contains a wider control frequency band than conventional TMD, illustrating the promising approach for long-span domes.

Machine learning (ML) based models for predicting the ultimate bending moment resistance of high strength steel welded I-section beam under bending

This paper presents an in-depth numerical investigation into the local buckling behaviour and develops advanced machine learning (ML) -based design methods for high strength steel (HSS) welded I-section beams for predicting the ultimate bending moment resistance under bending. Though HSS welded I-sections are commonly used in construction industry, the interaction effect between the flange and web plates as well as the relatively simplified design formulae result in limited accuracy of ultimate bending moment prediction and complex endeavour is involved for sections subject to local buckling. Finite element models are firstly developed and validated against the collected experimental test data, after which an extensive parametric study is carried out covering a larger range of cross-section slenderness and steel grades. Five ML models including Linear regressor (LR), Support vector regressor (SVR), Artificial neural network (ANN), Random forest regressor (RFR) and Boosting algorithm (XGBoost) were subsequently developed based on the test dataset (experimental and numerical data) to train and test the ML models. Though the current design codes of EN 1993-1-12 and AISC 360-16 can generally provide accurate cross-section classifications with appropriate slenderness limits, the ultimate bending moment resistance predictions are overconservative, particularly for slender sections. The developed ML models outperformed the codified design methods with notable improvements and can be employed in predicting the ultimate bending moment resistance of HSS welded I-section beams under bending.

Capacity Spectrum-Based Retrofitting Method and Quick Design for Viscously Damped Structures by Utilizing the Concept of Uniform Damping Ratio

Viscous dampers have proven to be effective in enhancing the seismic performance of existing structures. Despite this, there is still a need for rapid and simplified design methods and formulae for viscous dampers that can take into account the elastic–plastic performance of structures. This study introduces a retrofit design method for existing structures using viscous dampers, based on the concept of uniform damping ratio (UDR), with the aim of fully utilizing each damper. The UDR concept assumes that each damper in the structure provides the same UDR when subjected to seismic excitations of identical intensity. In this method, the first step involves defining the equivalent damping ratio (EDR) of the damper. Then, based on the capacity spectrum of the structure, the response mitigation ratio can be determined, which helps to determine the additional EDR required from the dampers. Once the UDR and additional EDR from the viscous damper have been determined, the parameters of the dampers at each story can be rapidly obtained. To demonstrate the effectiveness of this method, a six-story reinforced concrete frame was utilized as a benchmark structure. A comparison between this UDR-based approach and a traditional design approach was also conducted. The study findings reveal that the UDR concept enables the maximum utilization of energy dissipation capacity of viscous dampers installed in the structure, leading to a more effective and economical design approach.

Numerical modelling of composite steel and concrete double-skin and double-tube square cross-section columns subjected to fire

The fire resistance of composite steel and concrete double-tube and double-skin square cross-section columns has been previously evaluated through experimental tests carried out at the University of Coimbra. The results of these experimental tests were used to calibrate a finite element numerical model. This numerical model allowed a parametric study for developing new simplified fire design formulas for these types of columns. The heat transfer modelling used an implicit analysis where different thermal parameters have been tested. In the mechanical modelling, an explicit analysis was used considering the mechanical properties at high temperatures proposed by different authors for steel and concrete. In the parametric study, the influence of the relative slenderness, loading level and axial and rotational restraining levels in the column's critical and ultimate collapse times were analysed. Columns with slenderness higher than 0.5 showed lower ultimate collapse times than columns with relative slenderness between 0.25 and 0.5, despite the axial and rotational restraining level applied to them. Loading levels above 40% in the columns led to columns' premature ultimate collapse. The increasing axial and rotational restraining level benefited the columns' critical times, however columns showed similar ultimate collapse times when using restraining levels above K1.

Performance analysis and design of circular high‐strength concrete‐filled double‐skin aluminum tubular short columns under axial loading

AbstractThis study investigates the performance and design of high‐strength circular concrete‐filled double‐skin aluminum tubular (CFDAT) columns under axial loading. A new fiber element (FBE) model incorporating a new lateral confinement model is developed that considers the confinement effects and material nonlinearities. A new strength degradation factor is proposed for determining the postpeak behavior of the confined concrete in CFDAT circular columns. Existing experimental results are used to validate the accuracy of the predicted ultimate strength and axial load‐strain () curves of CFDAT columns under axial loading. A comparison of the predictions of the ultimate strength and curves of CFDAT columns using the proposed lateral confinement model is made against the prediction using the three‐dimensional finite element modeling and the existing lateral pressure model of CFDAT columns proposed by other researchers. The performance of the CFDAT columns under axial loading is investigated using a detailed parametric study. The accuracy of existing empirical formulas given in various design standards for conventional concrete‐filled steel tubular columns as well as given by another researcher in predicting the ultimate strength of CFDAT columns is examined. Finally, a simple design formula is proposed and validated against the experimental and numerical results obtained from this study. It is found that the proposed FBE model and the simplified model developed in this study can accurately predict the performance of CFDAT columns under axial loading.

Axial compression performance of concrete filled double skin (SHS outer and CHS inner) steel tubular columns strengthened by CFRP

This paper reports the compressive behavior of concrete-filled double skin steel tubular (CFDST) columns strengthened by CFRP under axial loading. The outer skin was made of square hollow sections (SHS), while the inner skin was made of circular hollow sections (CHS). Twelve CFDST columns strengthened by CFRP and three CFDST columns were tested. The failure mode, load-displacement relationship, axial load-carrying capacity and initial stiffness are given and analyzed. The results showed that the CFDST columns strengthened by CFRP have better mechanical properties than the column without CFRP reinforcement (i.e. the CFDST columns). The CFDST columns strengthened by CFRP eventually failed due to CFRP rupture or buckling of the external steel tube near the end and cracked concrete damage from the outer steel tube. The stiffness and axial load bearing capacity of the column can be improved as the number of CFRP layers increases. A simplified design formula of CFDST columns strengthened by CFRP is proposed, which is in good agreement with the experimental results.

Required number of self‐drilling screws for built‐up column comprising cold‐formed lipped channel sections to ensure flexural buckling as a single unit member

AbstractThis study analyzed the flexural buckling behavior of light‐gauge built‐up compression members joined by self‐drilling screws by using the energy method. A nonconventional mechanical model that simulates the flexural buckling behavior of a built‐up member was proposed, and the contradictions of Bleich's model were described. A simple design formula that directly reflects the parameters of built‐up members was derived based on the proposed model. Furthermore, to ensure flexural buckling as a single unit member, the required stiffening stiffness and number of self‐drilling screws were proposed.

Axial compressive performance of square concrete-encased concrete-filled double-skin steel tube stub columns

This paper explored the axial compressive performance of the concrete-encased concrete-filled double-skin steel tube (CECFDST) column, which comprised inner concentric steel tubes, sandwiched concrete, reinforcement cage and outer concrete. The characteristic stirrup value (λv) and nominal confinement factor (ξ) were chosen as the primary variables to investigate the confinement effects of the CECFDST. Firstly, the failure mode, ultimate strength, axial displacement, and strain responses of 10 specimens were tested and analyzed. The results showed that the combined confinement effects on the behavior of CECFDST were significant. The nominal confinement factor would impact the constraint on the sandwiched concrete and the ultimate strength of the specimens. Increasing the characteristic stirrup value could improve the ductility of the specimens. Secondly, a finite element model (FEM) was established and validated using test results. The full-ranged analysis of the typical FEM was presented, and contact stresses between the steel tube and concrete were quantified. After that, a systematic parametric analysis was conducted to explore the impacts of the primary influential factors related to the confinement effects. At the peak load, the RC component reached the corresponding ultimate strength, and the strength of the CFDST component was in the rising stage. In addition, the influence of contact stress between the RC and CFDST components on the ultimate strength was negligible. The strength reduction index of the square CECFDST stub column was proposed according to the parametric study. Finally, based on the superposition principle, a simplified design method was derived to predict the ultimate strength for the square CECFDST stub column. The simplified design formulas produced satisfactory predictions based on the test and numerical results.

Design formulae for Long-Term responses of continuous Steel-Recycled aggregate concrete composite slabs

The steel-recycled aggregate concrete (RAC) composite slab is a low-carbon structural member with higher constructional efficiency. However, no design method has been established for the serviceability limit state evaluation of such members accounting for long-term effects. The non-uniform shrinkage peculiar to composite slabs significantly deteriorates the long-term responses of slabs, which would be more significant when using RAC. Previous studies only focused on the long-term responses of simply-supported composite slabs using NAC. The investigated responses include member deflection and stress in steel decking. No research attention has been paid to the continuous composite slabs, in which non-uniform shrinkage further induces possible yielding of the negative reinforcement and the limit exceeding of concrete crack width in the negative moment zone. Furthermore, the recycled aggregate influence has not been accounted for in the long-term design of the composite RAC slabs. In this context, this study aims to establish simplified explicit design formulae for the long-term responses of continuous RAC composite slabs accounting for the non-uniform shrinkage effects and the recycled aggregate influence. The target long-term responses include deflection, steel decking stress, negative reinforcement stress, and the concrete crack width in the negative moment zone. The simplified explicit formulae were derived from cross-sectional analysis results with some variables reasonably simplified into constant values based on collected data from real applications. The validation results have shown that the proposed formulae are capable of predicting the long-term responses of continuous RAC composite slabs, with the prediction accuracy similar to the code formulae for reinforced concrete slabs.

Elastic buckling of simply supported bimetallic steel plates

Bimetallic steel plate is a laminated composite one consisting of metallurgically bonded cladding and substrate layers, such as the stainless-clad (SC) or titanium-clad (TC) ones. Due to significant corrosion resistance and cost efficiency, it has gained growing recognition as an alternative to stainless steel plate and is particularly suitable for offshore and marine structures. In this paper, the nominal elastic buckling stress of a bimetallic steel plate is derived by adapting the first-order shear deformation plate theory (FSDT) and compared with the solutions of classical plate theory (CPT). The plates are simply supported and subjected to uniaxial compression; two different types of cladding configurations are considered. The transverse shear stress distributions and shear correction factors are obtained by theoretical analyses. Finite element models of the bimetallic steel plates are developed by MATLAB and ABAQUS to validate the derivation. Parametric studies are then conducted to elucidate the effects of the cladding configuration, clad ratio, elastic modulus ratio and width-to-thickness ratio on the buckling stress. Based on the theoretical analyses, a series of simplified design formulae for the critical buckling stress and design requirements for interface shear strength requirements are proposed for further engineering applications. The research works may provide important bases for understanding and investigating the buckling behaviour of the bimetallic steel structures.

Load-transfer mechanism of distribution beams in giant rectangular concrete-filled steel tubular columns

This study investigates the load-transfer mechanism of a distribution beam and the load-bearing capacity of a huge rectangular concrete-filled steel tubular (RCFST) column through experiments and numerical analyses. Axial compression tests on six giant RCFST columns with a scale factor of 1/5 were conducted. Test results indicated the following: 1) All specimens exhibited excellent ductility and failed by local buckling of the steel tube. The distribution beam experienced shear failure because of the large plastic deformation at both beam ends. 2) The distribution beam effectively improved the ultimate load capacity of the specimen and the concrete core. 3) The yield load of the concrete core was approximately twice the shear capacity of the distribution beam, and its ultimate load capacity was slightly higher than twice the tensile capacity of the distribution beam. Subsequently, corresponding scaled finite element models were established and verified by comparison with the experimental results regarding failure modes, load-bearing capacity, and load–displacement curves. Based on the verified finite element models, numerous parametric analyses were conducted on full-scale RCFST columns, considering different section sizes of steel tubes and distribution beams, as well as layouts of the distribution beam. Based on the experimental and numerical analyses of the load-transfer mechanism of the distribution beam, a simplified design formula for the distribution beam was proposed.

On the uniform torsional rigidity of square concrete-filled steel tubular (CFST) sections

There are a number of scenarios in which structural members experience torsion, including under the direct application of torsional loading, when transverse loading is applied at an eccentricity to the shear centre and as a second order effect arising from lateral torsional instability. To date, the torsional rigidity of concrete-filled steel tubular (CFST) sections has yet to be fully explored; hence a study into the uniform torsional rigidity of square CFST sections is presented herein. First, the strain energy of square CFST sections is formulated, in which the longitudinal warping displacement is assumed to have an undetermined constant. The undetermined constant is then deduced by means of the principle of minimum strain energy, and thus an analytical expression for the uniform torsional rigidity of square CFST sections is obtained. The accuracy of the derived formula is verified against existing theoretical solutions for simplified scenarios, test data and the results of numerical simulations. Finally, the influence of the key parameters in the derived formula for the torsional rigidity of square CFST sections are analysed, and a simplified design formula is presented.

Neural network models for the critical bending moment of uniform and tapered beams

Most design standards require the calculation of the elastic critical bending moment for the design and verification of steel beams. Formulae exists for uniform beams with double or mono-symmetric cross-sections but, for tapered beams, simple design formulae are yet to be developed because of the complexity associated with the non-uniform geometry of these members.This work proposes a neural network model to calculate the critical moment. The model is developed using the Backpropagation and Levenberg–Marquardt algorithms and considering 60549 data samples for training and 8526 samples for validation. The samples are generated by a numerical model using the Finite Element Method (FEM). An innovative methodology to reduce the number of samples necessary to train the model is implemented based on the concept of random sample generation with constrained geometric proportions.The accuracy of the developed model is further illustrated on some particular cases and against the FEM results of other authors. For the uniform beams, the results of the proposed model are compared against those from existing formulae for uniform members showing its improved accuracy.Finally, it is expected that this investigation demonstrates the benefits of the use of neural networks based solutions as fast assessment tools during the search of optimal structural solutions in the early design stages.

Upper-Bound face stability analysis of rectangular shield-driven tunnels in undrained clays

The face stability of rectangular shield-driven tunnels in undrained clays where the undrained shear strength increases linearly with depth is investigated numerically and analytically in this paper. In the framework of the kinematic approach of limit analysis, two new failure mechanisms based on the translational movement of rigid blocks and continuous deformation of soil mass are proposed for collapse and blowout cases. The analytical solutions of the failure mechanisms were compared with those of finite element simulations and the existing approaches in the literature to evaluate their validity and productivity. The critical support pressures obtained from the analytical models are relatively consistent with the results of the numerical simulations for square and wide rectangular tunnels. Simple design formulas were provided for analytical models to compute the limit support pressure for practical use. Finally, parametric studies were performed to explore the impact of different geometrical and geotechnical parameters pertaining to the stability of the tunnel face.

Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers

Transfer functions are often employed to evaluate the vibration characteristics of mechanical and electrical systems. Within a group of transfer functions, some particular ones have the property that swapping the coefficients of the two terms in the equation does not change the properties of the original function. Such functions are said to have a reciprocity property. Mechanical vibratory systems typically have three transfer functions; namely, compliance, mobility, and accelerance. For a single-degree-of-freedom system, the mobility transfer function has the reciprocity property; for a two-degree-of-freedom system, no transfer function has the reciprocity property; and for a three-degree-of-freedom system, one transfer function has the reciprocity property. This paper shows that the presence of transfer functions with the reciprocity property is extremely important for obtaining simple optimal design formulas for dynamic vibration absorbers.