Empirical Design Equations Research Articles

Mechanics-based machine learning for failure classification of load-bearing walls

This paper presents novel methodologies that combine analytical mechanics with artificial intelligence to classify the failure mode of reinforced concrete walls under lateral loading. The adequacy of existing approaches is examined, including design equations and established machine learning algorithms, against experimental datasets consisting of 330 specimens. Findings indicate that the machine learning algorithms outperform the empirical design equations in terms of failure mode classification; however, the former lacks physical interpretability. To address this limitation, a new concept is proposed by integrating analytical and computational platforms for identifying attributes that dominate the failure characteristics of the walls. Non-dimensional features are derived and substituted into the machine learning algorithms. The aspect ratio of the walls and the amount of vertical rebars in boundary elements are found to be salient factors when categorizing failure modes, followed by the amount of horizontal rebars in the web. Through the application of decision boundaries stemming from the mechanics-based machine learning protocol, design recommendations are suggested to effectively classify the failure mode of load-bearing walls.

Effect of thermal modification on the ballistic performance of coastal western hemlock Cross-laminated Timber (CLT)

To test and understand the potential for integration of thermally modified coastal western hemlock CLT systems in military applications, 109 ballistic experiments were conducted at the United States Army Engineer Research Development Center's Fragmentation Simulation Facility. For a range of CLT thicknesses, the depth of penetration and residual velocities were recorded for different striking velocities utilizing a 0.50 caliber steel sphere projectile. This information was used to compare and add to the existing ballistics data for CLT, investigate the effects of thermal modification on high strain rate loading of wood, assess physics-based empirical design equations used by the Unified Facilities Criteria, and evaluate energy absorbing behavior at a range of thicknesses and striking velocities.The experimental results showed that thermal modification does not significantly alter the full and partial penetration performance of coastal western hemlock CLT. However, the mechanism of fracture along the path of the projectile differed, which indicates that the model parameters used in the UFC design equation (density, hardness, and projectile properties) may not fully encompass the ballistic failure mechanisms of CLT.

Behaviour and design of monotonically loaded reinforced concrete external beam-column joints

This paper describes an experimental investigation into the influence of beam reinforcement detailing, column axial load and shear reinforcement on the joint shear strength of reinforced concrete external beam-column connections. A series of twelve external beam-column joint specimens were tested in three groups of four specimens. Series 1 investigated the influence of beam reinforcement anchorage type and bend radius. Series 2 studied the influence of column axial load on joint shear strength while series 3 studied the influence of intermediate column bars and joint shear reinforcement. The paper presents the experimental results and describes the influence of the considered variables on joint shear strength. Three existing empirical design equations for external beam-column are evaluated using data from this program and previously tested beam-column joint specimens. Finally, design recommendations are made.

Undrained basal stability of braced circular excavations in anisotropic and non-homogeneous clays

This paper introduces the plastic stability solutions of braced circular excavations in anisotropic and non–homogeneous clays. Using the framework of Finite Element Limit Analysis (FELA) under axisymmetric conditions, the upper bound (UB) and lower bound (LB) solutions of the stability of excavations can be obtained. The clay is set to be anisotropic, where the Anisotropic Undrained Shear (AUS) model is used as a failure criterion of the surrounding soil. The results of this study are the proposed stability number which is the normalized parameter of the maximum unit weight and the anisotropic undrained shear strength of clay. Four dimensionless parameters are considered in the study: the anisotropic strength ratio, the depth–radius ratio, the depth–embedment ratio, and the strength gradient ratio. The impact of all considered dimensionless parameters on the results of the FELA solutions is examined. A machine learning regression approach, Multivariate Adaptive Regression Splines (MARS), is employed to develop an empirical design equation to predict the stability number of braced circular excavations in anisotropic and non–homogeneous clays. The proposed MARS equation can be a useful and reliable equation to estimate the basal stability of this excavation problem in practice.

Reliability-based design shear resistance of headed studs in solid slabs predicted by machine learning models

The economical and reliable design of steel-concrete composite structures relies on accurate predictions of the resistance of headed studs transferring the longitudinal shear forces between the two materials. The existing mechanics-based or empirical design equations do not always produce accurate and safe predictions of the stud shear resistance. This study presents the evaluation of nine machine learning (ML) algorithms and the development of optimized ML models for predicting the stud resistance. The ML models were trained and tested using databases of push-out test results for studs in both normal weight and lightweight concrete. The reliability of ML model predictions was evaluated in accordance with European and US design practices. Reduction coefficients required for the ML models to satisfy the Eurocode reliability requirements for the design shear resistance were determined. Resistance factors used in US design practice were also obtained. The developed ML models were interpreted using the SHapley Additive exPlanations (SHAP) method. Predictions by the ML models were compared with those by the existing descriptive equations, which demonstrated a higher accuracy for the ML models. A web application that conveniently provides predictions of the nominal and design stud shear resistances by the developed ML models in accordance with both European and US design practices was created and deployed to the cloud.

Quantifying the Benefits of Geosynthetics Reinforcement in Flexible Pavement Design Using Cyclic Plate Load Testing

Development of pavement design over the past decades has focused on moving from empirical design equations to more powerful and adaptive design schemes. The AASHTO mechanistic–empirical pavement design guide (MEPDG) has been developed to model pavement structure and predict its service life more accurately. Although MEPDG has been widely implemented to design conventional pavement, it is not yet capable of predicting the service life of pavement reinforced with geosynthetics. Given the above concerns, seven full-scale test sections that were constructed at Louisiana Transportation Research Center-Pavement Research Facility (LTRC-PRF) were devoted to a structural experiment to investigate the performance of geosynthetic reinforced pavements. The benefits of using geosynthetics to enhance the performance of pavements constructed over soft subgrades was evaluated using cyclic plate load testing. Cyclic load at a frequency of 0.77 Hz was applied through a 305 mm diameter steel plate. The test results clearly show the benefits of geosynthetics in significantly reducing pavement rutting. The test section with double geosynthetic layers performed better than the other six sections studied. After eliminating the effect of variations in construction, the benefits of geosynthetic reinforcement are quantified within the context of the AASHTOWare Pavement ME Design Guide. The developed design procedure is capable of quantifying the contribution of geosynthetics in pavements to base reinforcement as well as subgrade stabilization. A design methodology is proposed that falls within the context of MEPDG.

Prediction of Uplift Capacity of Cylindrical Caissons in Anisotropic and Inhomogeneous Clays Using Multivariate Adaptive Regression Splines

The uplift capacity factor of cylindrical suction caisson in anisotropic and inhomogeneous clays considering the adhesion factor at the interface is investigated in this paper. The finite element limit analysis based on lower bound and upper bound analyses is used for analyzing purposes. The anisotropic undrained shear model is employed to describe the anisotropic and inhomogeneous clay. The impact of these dimensionless parameters on the ratio of inhomogeneity or strength gradient ratio, the adhesion factor, the ratio of depth over diameter, and the ratio of anisotropic undrained shear strengths on the uplift resistance and the collapse mechanisms of suction caisson foundations are determined. The multivariate adaptive regression splines technique is employed to access the sensitivity of all considered dimensionless parameters on the uplift capacity factor and to propose an empirical design equation as an effective tool for predicting the uplift capacity factor. The results presented in this paper can be guidance for the preliminary design of suction caissons in anisotropic and non-homogeneous clays that are useful for engineering practitioners.

Large displacement analysis of stiffened plates with parallel ribs under lateral pressure using FE modeling with shell elements

This study provides the load–displacement behavior of stiffened plates with parallel ribs when modeled using shell elements with and without considering the large-displacement effects in comparison with the conventional equivalent beam analysis (EBA) in which such stiffened plates are simplified into an imaginary beam with the geometrical properties of an equivalent built-up cross-section. This study highlights the advantages of FE modeling with shell elements and large-displacement analysis (LDA) over the existing EBA method and then provides a path for using this method in the ultimate limit state (ULS) design of stiffened plates. The stress distributions in the panel plate part of the stiffened plates are presented to demonstrate the significance of considering the large-displacement effects in the analysis. The numerical investigation indicated that the linear beam theory does not correctly presume the true behavior of the stiffened plates and that the corresponding load–displacement estimation does not align with its behavior predicted by the LDA. The results also demonstrate that when shell element modeling is utilized, the internal forces and stresses in the panel plate are calculated correctly, only if the large-displacement effects are considered in the analysis. Finally, a method for estimating the ultimate load capacity of stiffened plates with parallel ribs is provided, based on the large-displacement FE analysis with shell elements, which can be used to establish empirical design equations.

Flexural behavior of rammed earth components reinforced with steel plates based on experimental, numerical, and analytical modeling

During past earthquakes, earthen buildings have collapsed causing significant human, economic and heritage losses. In recent years, the authors proposed a seismic rehabilitation technique used to enhance out-of-plane strength and ductility of earthen buildings. This retrofitting solution consists on adding A36 structural steel plates (6.35-mm-thickness and 101.6-mm-width) on both faces of the earthen walls. This proposal enhances seismic performance of earthen structures while protecting occupant lives and reducing expected damages. In this paper, a comprehensive experimental, analytical and numerical study is conducted to evaluate the influence exerted by the amount of steel plates on the out-of-plane strength in reinforced earthen walls. The experimental program includes tests for rammed earth specimens reinforced with different sizes of steel plates. Experimental results are complemented with finite element simulations and analytical formulations based on partially composite beams with interlayer slip. Despite the high variability involved in the mechanical properties of earthen materials and uncertainty in the interaction between the steel plates and the rammed earth, models used in this study predict out-of-plane strength of reinforced earthen specimens within 15% error. In addition, based on experimental evidence, the authors proposed an empirical design equation to calculate the moment or flexural capacity that could be included in retrofitting provisions.

In-plane lateral load transfer capacity of unreinforced masonry walls considering presence of openings

This study proposes mathematical models for the prediction of the in-plane lateral load capacity of unreinforced masonry (URM) walls considering potential failure modes and the presence of openings. The rocking strength is derived from the elasticity theorem for the compound stress condition under the assumption that rocking begins when the stresses at the extreme tensile fiber reach the tensile resistance capacity of the masonry. For toe crushing strength, the equivalent rectangular stress block specified in federal emergency management agency (FEMA) 273 is considered in the calculation of resultant compressive forces. The sliding and diagonal shear crack strengths are formulated based on the upper-bound theorem of concrete plasticity. The proposed models account for the effects of door or window openings on the failure mode and lateral load capacity of URM walls. The reliability of the proposed models is verified by comparing with test datasets comprising 202 URM walls without opening, 3 walls with door opening, and 4 walls with window opening. The proposed models confirm that URM walls are initially governed by the rocking rotation and subsequently ultimately fail via different mechanisms. It is also found that the empirical design equations specified in FEMA 273 and new zealand society for earthquake engineering (NZSEE) overestimate the rocking strength of URM walls and that their predicted their lateral load capacity significantly deviates from the test data. The proposed model results present comparatively better agreement with the test results. The mean and standard deviation of the ratios between the experimental and predicted results are 0.93 and 0.20, respectively, for URM walls without openings, and 0.92 and 0.14 respectively, for URM walls with openings. The proposed models rationally consider the effect of openings on the transition of the failure modes and the consequent reduction in the lateral load capacity.

Empirical Design Equation for Compression Strength of Lightweight FRP Sandwich Panel Walls

Abstract A new empirical design approach is presented for predicting the compression strength of lightweight fiber-reinforced polymer (FRP) sandwich panel columns. The model is simple enough to use...

Evaluation on the behaviour of screwed CFS joints subjected to combined loading

Cold-formed steel (CFS) structures constructed by screw connections are commonly used in low-rise or mid-rise dwellings. Being a critical role affecting the strength and robustness of the structure, the configuration of joist-to-stud joints should be emphasized. However, the design method given by the existing specifications is incapable of covering screwed CFS joint with complex configuration. Therefore, further investigations are required for revealing the resistance and failure behaviour of CFS joist-to-stud screw joint under varying load modes. In this paper, laboratory tests of screw connections were conducted with the loading cases involving shear, tension, and combined tension and shear. This study concerns the behaviour of each connection in the elastic, plastic and failure stages. Finite element method (FEM) based on bushing connector elements was developed to simulate the performance of the screw connections in the physical experiment. Modelling details are given and a close correlation can be noticed when comparing numerical results against experimental outcomes. Moreover, a series of empirical design equations are proposed to predict the stiffness and resistance of the CFS joints.

Pavement Engineering for Forest Roads

Pavement is an essential component of roads as it carries the traffic and provides the required riding comfort. Considering that numerous forest roads are approaching their end of life, the critical issue is identifying the best rational pavement design methods to reengineer existing and build new pavement structures. The purpose of this contribution was (1) to review the big development lines of pavement systems, (2) to have a critical look at the pavement engineering framework, and (3) to bring selected empirical design equations into a comparable scheme. The study resulted in the following significant findings. First, the Trésaguet and McAdam pavement systems represented the state of the art from the beginning of a formal forest road engineering discipline at the beginning of the 19th century and remained for almost 150 years. Second, the emergence of soil mechanics as a scientific discipline in the 1920s resulted in the optimal grading of aggregates and improvement of soils and aggregates with binders, such as lime, cement, and bitumen. Third, the rational pavement design consists of five essential components: (1) bearing resistance of the subsoil, (2) bearing resistance of the pavement structure, (3) lifecycle traffic volume, (4) uncertainties that amplify deterioration, and (5) the limit state criterion, defining thresholds, above which structural safety and serviceability are no longer met. Fourth, rational, formal pavement design approaches used for forest roads were »downsized« from methodologies developed for high-volume roads, among which the approaches of the American Association of State Highway and Transportation Officials (AASHTO) and US Army Corps of Engineers (USACE) are of primary interest. Fifth, the conversion of the AASHTO '93 and USACE '70 methods into the SI system indicated that both equations are sensitive to soil bearing resistance, measured in California Bearing Ratio (CBR). However, there is a lack of validation for the AASHTO and USACE equations for forest road conditions. Consequently, a factorial observational study to gain a basis for validation should be developed and implemented. Additionally, the conversion of simple soil bearing resistance measures, such as CBR, into the resilient modulus will be improved.

Prediction of axial load capacity of concrete walls with openings restrained on three sides

Currently, the empirical wall design equations given in major codes of practices either offer no guidelines or provide overly conservative predictions of the ultimate axial strength of concrete walls with openings restrained on three sides (TW3S walls with openings). In view of the significant shortcomings, an appropriate design equation is required for such walls. This paper presents a numerical investigation on the behaviour of TW3S walls with openings under eccentric axial loading. A finite element model using the ABAQUS software was employed to undertake parametric studies examining the influence of opening parameters, which consisted of configuration and location, on the axial load capacity of TW3S walls. In total, 101 models were developed and analysed. Having established the relationships between the opening parameters and the ultimate load capacity of TW3S walls, a more encompassing design equation was derived. The reliability of the proposed equation was ascertained through comparisons with available test data.

Effect of concrete strength and tube thickness on the flexural behavior of prestressed rectangular concrete-filled FRP tubes beams

This paper presents the results of an experimental study aimed at evaluating the effect of important design parameters on the flexural behavior of unbonded post-tensioned rectangular concrete-filled fiber-reinforced-polymer (FRP) tubes (CFFTs) beams. Four full-scale beams were constructed and tested to failure in four-point bending over a simply supported span of 3,000 mm. The design parameters are the confinement effect of using FRP tube or steel stirrups, the concrete compressive strength, and the FRP tube thickness. The results showed that reinforced concrete (RC) rectangular CFFT beams prestressed with unbonded steel strands can achieve substantially higher flexural strength, inelastic flexural deformation, ductility, and energy absorption capacity than conventional prestressed RC beam without FRP tube. The ultimate strength, deformation capacity, ductility, and energy absorption were increased by 2.43, 1.89, 1.63 and 3.87 times than the prestressed RC beam. The results also showed that increasing the FRP tube thickness of the prestressed CFFT beams from 6.0 to 7.4 mm has led to the increase of the ultimate capacity, ductility, and energy absorption by 19%, 28% and 18%, respectively. Prestressed CFFT beams with high strength concrete (HSC, 70 MPa) enhanced the initial stiffness before cracking, increased the ultimate flexural moment capacity by 7%, with no significant change in the ultimate deflection, compared to normal strength concrete (NSC, 46 MPa). Based on the results of this study, the effect of increasing the FRP tube thickness is more effective in enhancing the flexural strength and stiffness of the prestressed CFFT beams than increasing the concrete strength. An analytical model based on plane sectional analysis using partially confined and unconfined concrete models as well as an empirical design equation are proposed to predict the flexural moment capacity of the tested beams. The proposed models using partially confined and unconfined concrete models and empirical equation successfully predict the flexural moment capacity with satisfactory accuracy on average of 1.06 ± 0.03, 1.23 ± 0.04 and 1.01 ± 0.08, respectively. It was also found that ignoring concrete confinement would highly underestimate the flexural strength. More investigations, however, are needed to assess the effect of a wide range of key influencing parameters to better model the flexural behavior of prestressed rectangular CFFT beams.

Evaluation of peak side resistance for rock socketed shafts in weak sedimentary rock from an extensive database of published field load tests: a limit state approach

This paper presents analyses of the measured peak side resistance of rock sockets constructed in weak claystone, shale, limestone, siltstone, and sandstone. The peak side resistance is obtained from in situ axial load tests on drilled shafts, anchors, and plugs. The parameters that affect the development of peak side resistance are determined using in situ load test data. It is found that peak side resistance increases with the unconfined compressive strength and deformation modulus of the weak rock, and decreases with the increase in length of the shear surface along the rock socket sidewalls. The increase in socket diameter also slightly decreases the peak side resistance. Additionally, it is found that the initial normal stresses do not significantly affect the measured peak side resistance in the in situ load tests. The in situ load test data are used to develop an empirical design equation for determination of the peak side resistance. The proposed model for peak side resistance and the reliability analysis are used to determine the corresponding resistance factors for use in the load and resistance factor design framework for assessment of the strength limit state.

Optimum design of helical antennas by genetic algorithm

AbstractThe genetic algorithm is employed to obtain optimal designs for helical antennas that, over the frequency range of operation, provide considerably smaller axial ratio, higher gain, and an appreciably wider overall bandwidth than the conventional axial mode helices with the same size. Also, for nearly equal bandwidth and peak directivity, the new design provides a 2 to1 reduction in size. For these helical antennas the pitch angle and radius, which are constant in conventional helices, vary continuously along the length; pitch angle increases while radius decreases. Genetic algorithm is used to determine variations of these parameters such that maximum directivity and minimum axial ratio are simultaneously achieved over the largest frequency range. Radiation properties of optimized helices, including far‐field pattern, axial ratio, and directivity, are examined numerically over a wide range of frequencies. Empirical design equations are provided. A 12‐turn prototype optimized helix is constructed and measured. Comparison of measured and simulated radiation patterns shows excellent agreement.

A compact dual band antenna based on metamaterial-inspired split ring structure and hexagonal complementary split-ring resonator for ISM/WiMAX/WLAN applications

A miniaturized dual-band antenna is proposed for industrial scientific and medical (ISM), worldwide interoperability for microwave access (WiMAX), and wireless local area network (WLAN) applications. The proposed antenna consists of hexagonal complementary split-ring resonator (HCSRR), metamaterial-inspired split-ring structure, and a partial ground plane. The prototype antenna is fed by 50-Ω microstrip feed line, which is printed on a 30 × 30 × 0.8 mm3 FR-4 substrate. HCSRR in the radiating element is used to create a new resonance at 2.4 GHz for achieving dual-band characteristics. A split in the outer hexagonal ring induces a magnetic resonance which leads to improvement of the bandwidth of the antenna. The proposed antenna is fabricated and measured. The measured -10-dB impedance bandwidths are 180 MHz (2.42–2.60 GHz) and 2400 MHz (3.44–5.84 GHz) with a resonance frequency of 2.56 GHz and 4.64 GHz, respectively, which is suitable for ISM, WiMAX, and WLAN applications. Analysis of HCSRR is discussed in detail using empirical design equation with metamaterial property. The prototype antenna has suitable radiation characteristics for all resonance frequencies.

Estimating punching shear capacity of steel fibre reinforced concrete slabs using sequential piecewise multiple linear regression and artificial neural network

Estimating punching shear capacity is an important task in the design of steel fibre reinforced concrete (SFRC) flat slabs. The accuracy of commonly employed empirical design equations can potentially be improved with the use of machine learning. This study relies on a piecewise multiple linear regression (PMLR) and artificial neural network (ANN) approaches to construct a prediction model that can approximate the mapping function between the punching shear capacity of SFRC flat slabs and its influencing factors. Moreover, a sequential algorithm for automatically constructing the PMLR model structure is implemented. The algorithms of gradient descent and Levenberg-Marquardt backpropagation are employed to train the ANN based prediction models. A data set including 140 testing samples with six influencing factors of slab depth, effective depth of the slab, length or radius of the loading pad or column, compressive strength of concrete, the reinforcement ratio, and the fibre volume have been collected from the literature. This data set is then used to train and verify the sequential PMLR (SPMLR) and ANN models. Experimental results show that SPMLR can deliver prediction outcome which is better than those of ANN as well as empirical design equations. Therefore, SPMLR can be a promising alternative to assist structural engineers in the design phase of structures containing SFRC flat slabs.

Numerical study of steel sandwich plates with RPF and VR cores materials under free air blast loads

One of the most important design criteria in military tunnels and armoured doors is to resist the blast loads with minimum structural weight. This can be achieved by using steel sandwich panels. In this paper, the nonlinear behaviour of steel sandwich panels, with different core materials: (1) Hollow (no core material); (2) Rigid Polyurethane Foam (RPF); and (3) Vulcanized Rubber (VR) under free air blast loads, was investigated using detailed 3D nonlinear finite element models in Ansys Autodyn. The accuracy of the finite element model proposed was verified using available experimental test data of a similar steel sandwich panel tested. The results show the developed finite element model can be reliably used to simulate the nonlinear behaviour of the steel sandwich panels under free air blast loads. The verified finite element model was used to examine the different parameters of the steel sandwich panel with different core materials. The result shows that the sandwich panel with RPF core material is more efficient than the VR sandwich panel followed by the Hollow sandwich panels. The average maximum displacement of RPF sandwich panel under different ranges of TNT charge (1 kg to 10 kg at a standoff distance of 1 m) is 49% and 53% less than the VR and Hollow sandwich panels, respectively. Detailed empirical design equations were provided to quantify the maximum deformation of the steel sandwich panels with different core materials and core thickness under a different range of blast loads. The developed equations can be used as a guide for engineer to design steel sandwich panels with RPF and VR core material under a different range of free air blast loads.