Secondary Moment Research Articles

Numerical Simulation for Strength and Stability of RC Tapered Columns

This study investigates the strength and stability of Reinforced Concrete (RC) linearly tapered square columns. Evaluating the slenderness ratio of an RC column requires the radius of gyration of its cross-section, which is well-defined for a prismatic column but not for a non-prismatic one. This study primarily investigates the application of the ACI Code formulae to evaluate the slenderness ratio of RC columns with the studied geometry. Validated numerical models, using Abaqus, were employed to perform nonlinear first- and second-order analyses on the investigated columns subjected to eccentric axial loads. The concrete damaged plasticity model was employed to simulate the nonlinear behavior of concrete. The static Riks solver, available in Abaqus, was utilized for nonlinear analyses: first, with an inactivated geometric nonlinearity for a first-order analysis, and second, with an activated geometric nonlinearity to consider the effects of secondary moments (p-δ effects). The findings indicate the reliability of defining the slenderness ratio of an RC linearly tapered column based on the ACI Code formulae, using the average cross-section of the tapered column.

Experimental investigation of External FRP strengthening column against secondary moment of slender effect

The essential design code guidelines for Fiber Reinforced Polymer (FRP) strengthened Reinforced concrete columns are limited to short columns strengthened with FRP wrapping. As a result, they are primarily non-applicable to slender RC columns where there is a significant second-order/slenderness impact. The purpose of the current study was to experimentally recognize how effectively longitudinal carbon panels (CFRP) and basalt fiber-reinforced polymer (BFRP) lateral wrapping can reduce lateral deflection and increase the strength of variable thin square reinforced concrete columns. A total of 8 square RC columns of 120 mm width were performed in three groups, according to the slenderness ratio 22, 29, and 35. The strengthened columns were developed using two distinct strengthening techniques. The first is a longitudinal CFRP laminate with lateral partial BFRP wrapping (EBWGL) plus grooved bonding, and the second is a lateral partial wrapping (EBW) of the BFRP film. The column was tested with 30 mm eccentric compression. In general, the EBWGL reinforcement technique significantly improves the flexural strength of columns. Moreover, it is noteworthy that the EBW method did not considerably reduce the secondary effect as the slenderness ratio increased. The EBGWL has a great reducing effect that gets better as the slenderness ratio gets higher.

Radiogenomics Map-Based Molecular and Imaging Phenotypical Characterization in Localised Prostate Cancer Using Pre-Biopsy Biparametric MR Imaging.

To create a radiogenomics map and evaluate the correlation between molecular and imaging phenotypes in localized prostate cancer (PCa), using radical prostatectomy histopathology as a reference standard. Radiomic features were extracted from T2-weighted (T2WI) and Apparent Diffusion Coefficient (ADC) images of clinically localized PCa patients (n = 15) across different Gleason score-based risk categories. DNA extraction was performed on formalin-fixed, paraffin-embedded (FFPE) samples. Gene expression analysis of androgen receptor expression, apoptosis, and hypoxia was conducted using the Chromosome Analysis Suite (ChAS) application and OSCHIP files. The relationship between gene expression alterations and textural features was assessed using Pearson's correlation analysis. Receiver operating characteristic (ROC) analysis was utilized to evaluate the predictive accuracy of the model. A significant correlation was observed between radiomic texture features and copy number variation (CNV) of genes associated with apoptosis, hypoxia, and androgen receptor (p-value ≤ 0.05). The identified radiomic features, including Sum Entropy ADC, Inverse Difference ADC, Sum Variance T2WI, Entropy T2WI, Difference Variance T2WI, and Angular Secondary Moment T2WI, exhibited potential for predicting cancer grade and biological processes such as apoptosis and hypoxia. Incorporating radiomics and genomics into a prediction model significantly improved the prediction of prostate cancer grade (clinically significant prostate cancer), yielding an AUC of 0.95. Radiomic texture features significantly correlate with genotypes for apoptosis, hypoxia, and androgen receptor expression in localised prostate cancer. Integration of these into the prediction model improved prediction accuracy of clinically significant prostate cancer.

Nonlinear mechanical behavior and stress amplification effect correction of thin plate welded structure considering initial deformation

With the continuous development of light weight of ships, thin plate welded structures are widely used in superstructure of large hull structures and high-speed boats. However, the thin-plate welded structure has a special nonlinear mechanical behavior because of its small stiffness, more complicated welding deformation. The nonlinear mechanical behavior of thin plate welded structure is mainly caused by large slenderness ratio and complex initial buckling deformation, which can be characterized and quantified by defining global deformation angle αG and local deformation angle αL. Because of the welding angle deformation and welding dislocation, there is obvious stress amplification effect at the welding corner, but the traditional stress amplification correction formula is only suitable for thick plate welding structure. Aiming at the nonlinear mechanical behavior and secondary bending moment effect of thin plate welded structure, an analytical model of thin plate welded structure with initial deformation is established by combining theoretical derivation and numerical method. The results show that the additional bending moment effect caused by local welding deformation angle cannot be ignored. Finally, combined with a series of fatigue tests, the additional bending moment caused by bending deformation and angular deformation of typical welded joints is analyzed, and the notch stress field and fatigue strength correction of thin plate welded structures with initial defects are realized.

Laboratory study on bearing capacity of batter rock-socketed pile group under combined loads

The batter rock-socketed pile (BRSP) groups have been gradually introduced in practice to support not only the vertical load caused by overlying infrastructures but also the horizontal loads caused by waves and wind. A series of laboratory model tests were conducted to investigate the bearing capacities of the BRSP groups installed with their batter piles ranging from 0° to 20° under combined vertical and horizontal loads. It is found that the vertical ultimate bearing capacities nonlinearly increase with the increase of the batter angle with its optimum batter angle of 10°. The normalized vertical loads and horizontal ultimate loads are nonlinearly related to their relationship in an ellipse function. The plumb rock-socketed pile groups develop primarily a pair of shear forces and secondary bending moments due to the clockwise rotation under the pure horizontal loads. The BRSP group may fail due to the pile fracture near the pile cap in the form of the plastic hinge or compression failure at the base of the front pile. The corresponding load-displacement curves mostly have no peak or sudden downward trend.

Optimal Attack Energy Allocation Against Remote Estimation in Cyber-Physical Systems

This paper focuses on designing an optimal attack energy allocation strategy to disrupt the performance of remote state estimation with unknown gains for cyber-physical systems (CPSs). To deal with the unknown gains, the Cramér-Rao Bound (CRB) is introduced to obtain a lower bound of the secondary moment of the estimate error. Then, by solving an optimization problem that maximizes the average CRB over a finite time horizon with energy constraint, an optimal attack energy allocation strategy is derived. Compared with the existing works, the rigorous assumption that the attacker has full knowledge of the system is removed, and the computational complexity of solving the optimization problem is significantly reduced. Finally, numerical results validate the presented strategy.

Refined beam finite element model for thin-walled multi-cell box girders considering distortion and secondary distortional moment deformation effect

In this paper, a novel one-dimensional refined beam finite element model (FEM) accounting for non-uniform distortional warping and secondary distortional moment deformation effect (SDMDE) is formulated for the distortional analysis of thin-walled multi-cell box girders with cantilevered flanges. The extra distortional angle is introduced to incorporate SDMDE, and the validity of which is proved through rigorous theoretical derivation. The in-plane and out-plane deformations at any point around the edge of transverse section built upon the distortional center are unified in the same form and described in detail. The governing differential equations in terms of two generalized displacements, distortional angle χ and primary distortional angle curvature Θ, are derived based on the principle of minimum potential energy (MPE) and solved exactly so as to provide non-polynomial shape functions for the establishment of element stiffness matrix and nodal load vector. A series of multi-cell rectangular hollow section (RHS) girders are analyzed and particular extensions are given to single-cell and multi-cell bridge girders with cantilevered flanges. Comparisons to the results generated from corresponding ones provided by pioneering work or shell FEM analyses not only validate the correctness and reliability of the present beam element formulations but also highlight the significance of the inclusion of SDMDE when the cantilevered flanges are arranged.

Analytical solution for seismic response of vertical shaft with primary and secondary linings under SH wave excitation

This paper presents a novel mechanical model for seismic response analysis of vertical shafts. The model is based on elastic foundation beam theory and simplifies the shaft linings as parallel Euler Bernoulli beams. Their interaction is simulated using uniformly distributed springs. The governing differential equation for shaft vibration is derived for SH wave excitation. The seismic input motion is applied to the primary lining by converting the free field displacement into harmonic form. The closed-form solutions for seismic response of both primary and secondary linings are obtained via the transfer function method. The accuracy of analytical solution is validated by comparing with finite element analysis results. Additionally, the impact of foundation stiffness, secondary lining thickness, shaft outer diameter, and relative stiffness between linings on seismic response are investigated in the parametric analysis. The analytical solutions of the seismic response analysis of vertical shafts indicates that the relative stiffness between linings significantly affects the secondary lining's peak bending moment. Furthermore, higher stiffness of the elastic connection layer between the two linings can effectively reduce the peak displacement response of the secondary lining.

Fatigue tests on connections of hollow sections made of high‐strength steel with shape‐optimized gusset plates

AbstractStructures made of hollow sections are often used in the construction of steel bridges, agricultural machinery and trucks. Due to secondary bending moments and local stress concentrations at the connection between brace and chord these joints have a low fatigue strength. In case of high‐strength steels, a decisive fatigue design leads to larger wall thicknesses and dimensions of the hollow sections and thus to uneconomical constructions. In the course of the research project FOSTA P1442 truss joints of hollow sections made of high‐strength steels were reinforced by attached and plugged through gussets plates to increase the fatigue strength by relocating the most critical detail at the weld toe to areas subjected to lower stresses. At the University of Applied Sciences Munich, 35 large‐scale fatigue tests on hollow section K‐joints with differently shaped gusset plates were performed to verify the results of the Finite Element Analysis. In order to verify the applicability of the results to real structures, two trusses with a span width of 6 meters were tested. Based on the data of the experimental tests, a fatigue design recommendation for connections of hollow sections with gusset plates could be developed. Within this paper the set‐up and results of the fatigue tests are summarized.

Numerical and theoretical analysis of normal stress distribution in flanges of I-girders with trapezoidal corrugated webs under uniform bending

I-girders with corrugated webs (IGCWs) are a new type of structure that has been increasingly used in engineering. The normal stress distribution in flanges of IGCWs is quite complicated compared with that of conventional I-girders under in-plane loads. This study numerically and theoretically investigates the normal stress distribution rules and mechanisms in flanges of I-girders with trapezoidal corrugated webs (IGTCWs) under uniform bending in the elastic stage. First, finite element (FE) modelling was developed using ABAQUS software and verified by the available experimental results. Based on the verified FE models, a detailed analysis of the normal stress distribution in flanges of IGTCWs was performed. The results show that the normal stresses are nearly uniformly distributed over the flange in cross-sections with inclined web folds. Normal stresses in cross-sections with parallel web folds are approximately linearly distributed along the flange width, with stresses away from the corrugated web side being much larger than those near it. Its mechanism is explored using a secondary transverse moment theory, which is improved and completed by considering the proposed effective cross-section coefficient and equivalent width coefficient for the action of shear flow. The reliability of this theory was verified through comparison with the normal stress difference and distribution results of the supplementary FE models. Finally, the formulae for calculating the normal stresses in flanges of different cross-sections of IGTCWs under uniform bending are presented. These formulae suggest that secondary normal stresses generated by secondary transverse moments in cross-sections with parallel web folds account for 7% to 13% of the total normal stresses and cannot be ignored in the stress analysis.

Numerical analysis of novel concrete filled K joints with different brace sections

All over the world, truss structures are commonly used in long-span bridge. Since joint is the weakest part of this structure, this paper proposes a novel type in which different brace members are used in the concrete filled box section K-joints. This novel type is designed as rectangular compression brace with the brace width to chord ratio β<0.8 and chord welded tension brace (β=1). That configuration allows to reduce the gap, thus eliminate the secondary moment. Moreover, load transfer and failure modes are not similar to the ordinary. Numerical simulation is the used method of investigation in which validation is carried out through thirty-four models composed of RHS K gap Joint – CFST T Joint – CFST Y Joint – RHS T Integral Joint – CFST K gap Joint. Difference between experiments and Finite Element models are less than 20% thus acceptable. Through the validated numerical simulation model, analysis of suitable boundary conditions and variation of initial stiffness, ultimate strength are presented in accordance with the novel joint parameters. Comparison of the novel joint type to the rectangular hollow section (RHS) and rectangular concrete filled steel tube (RCFST) is carried out in terms of initial stiffness and ultimate strength. Finally, optimization of the novel type of joint is proposed for engineering practice so as to have overview of the strength in practical aspect. Results have shown that most of the proposed types of boundary condition procure the joint deformation while subjected in compression and tension load. Tension brace failure is the typical failure mode of the novel joint in which the chord width, the parameter β are fundamental and directly proportional to the joint initial stiffness and ultimate strength. For β=0.8 and the chord width between 500 and 1000 mm, the initial stiffness can vary from [9944.92kN/mm−19887.31kN/mm]; ultimate strength varies from [29551.76kN−117916.20kN]. Moreover, the novel joint type is stronger than the RHS and the RCFST in both initial stiffness and ultimate strength. That difference is about 3–6% in the initial stiffness and around 10% for the ultimate strength. These demonstrate that the novel type of joint is acceptable in engineering truss bridge with proposition of joint optimization.

Behavior and design of circular concrete columns strengthened with textile-reinforced mortar subjected to eccentric compression

Textile-reinforced mortar (TRM) is a cheaper and eco-friendlier material for the concrete confinement than steel and fiber-reinforced polymer (FRP). The behaviors of plain concrete slender columns with circular cross-section strengthened with TRM under eccentric compression were analyzed both experimentally and analytically in this paper. The test results showed that TRM could effectively inhibit the extension of cracks in columns, and increasing the number of textile layers from one to three led to a 44% increase in ultimate load. Meanwhile, the secondary moment of columns relative to the total moment varied from 20% to 35%, which was positively related to the confinement effectiveness of TRM. Then, a comparison of the behaviors of confined concrete columns under axial load-flexural moment (P-M) loading demonstrated that the confinement provided by TRM was relatively insufficient when compared to steel and FRP, behaving a post-peak softening phase of compressive constitutive curves. However, the textile with high tensile strength improved the stress distribution of cross-section of eccentrically loaded columns, thereby observing a much slower reduction in ultimate load with the increase of the eccentric ratio. Finally, according to a cross-section bearing capacity analysis, the procedure of analytical calculations was proposed to predict the ultimate load of TRM-confined concrete columns at a given eccentric ratio. Furthermore, the proposed analytical calculations provided a parametric study to reveal the correlation between the eccentric ratio and the number of textile layers, and then a simplified regression formula for design purpose was developed. This research highlights the behavior and design of concrete strengthened with TRM under P-M loading, which would give researchers and engineers an insight.

Numerical analysis on the moment redistribution behavior of prestressed continuous beams considering the effect of construction method

The design method for the prestressed continuous beams (PCBs) in the current design codes usually neglects the effect of construction method, which determines the distribution of initial internal forces caused by dead load in the PCBs. To fully investigate the moment redistribution behavior of the PCBs constructed by monolithic casting (MC), simply supported-continuous (SC), and cantilevered-continuous (CC) methods, a simplified but effective numerical analysis method was proposed by combining the modified force method and incremental method, in which the effect of initial internal forces and secondary moment were isolated and discussed. The proposed numerical method was first calibrated by the test results, and then used to predict the mechanical behavior of 27 PCBs during the whole loading process with the parameters of construction method, the effective prestressing stress in the prestressing tendons (fpe), the degree of prestressing (PPR), and the relative neutral axis depth (ξ). Based on the analysis results, it was observed that the initial negative and positive bending moment in the PCBs produced by different construction methods helps improving the moment redistribution ability of the sections with maximum negative and positive bending moment, respectively. Besides, the current design codes generally overestimate and underestimate the ultimate bearing capacity of the simply supported-continuous and cantilevered-continuous PCBs, respectively.

Design of Stealthy Deception Attacks With Partial System Knowledge

This article investigates the design of stealthy deception attacks with the aim of destroying the estimate performance without knowing the filter gain. The residual used to detect attacks is generated by the parity space approach and the Kullback–Leibler divergence is adopted as the metric of stealthiness. We first give the necessary and sufficient condition for the inexistence of the strictly stealthy attack, which does not change the residual and can lead to unbounded estimate error. When the strictly stealthy attack does not exist, a lower bound of the secondary moment of the estimate error is then derived via the posterior Cramér–Rao bound. The zero-mean Gaussian attack that maximizes this lower bound is obtained by solving a convex optimization problem. The proposed method can also be applied to design stealthy attacks with the aim of destroying the control performance. Finally, a numerical example of longitudinal flight control system is illustrated to demonstrate the effectiveness of the proposed attack.

Bending behaviours of load-carrying fillet welds around misaligned hollow structural sections

Misaligned hollow structural section (HSS) chords have gained increasingly application in the tubular joist structures connecting panelised façades. Despite the fillet welds are known to be efficient in connecting the HSS structures, the bending behaviours and fracture characteristics of welded misaligned HSSs have not been clearly understood for their engineering practice. This paper presents the results of an experimental and finite element (FE) modelling study with focus on the combined stress states of the misaligned HSS and the critical weld throat plane in its connecting welds. The configurations for the corner connection and the interior wide connection were compared in terms of their failure modes and load–deflection response. A theoretical analytical approach for predicting the combined stress of the misaligned HSS chord and the fillet weld in the connection subjected to flexural, shear and torsional loading is proposed and shown to achieve a good correlation. Based on the results of validated FE models, the traction stresses of fillet welds with appropriate allowance of the weld eccentricity induced secondary moment are demonstrated to give a better replication of the stress distribution of the critical weld throat plane. Finally, it has been found from a FE parametric analysis that the local stress concentration at the critical weld throat plane can be significantly amplified with increased weld flank angle, decreased HSS chord thickness-to-width ratio, increased misalignment angle of HSS chord or reduced relative weld leg length, in which the last two influential factors notably contribute to the elevation of stress concentration.

Ultimate bearing capacity of composite beams with reinforced web opening under hogging moment: Practical calculation method

An experiment was conducted using an empty belly truss as the mechanical model. Based on the results, the secondary bending moment function was derived according to the plastic stress distribution on the four corner sections of the opening mouth under the limit state. An ultimate bearing capacity calculation method of the web opening composite beam in the hogging bending moment region with reinforcement measures was established. This method considers the shear capacity of the concrete slab above the opening, which more closely approximates actual engineering practice. The results indicated that the shear capacity of the openings in the web hogging bending moment region can be effectively improved by installing stiffeners at the openings. Moreover, the bearing capacity increased with an increase in the area of the reinforcing plate, and the concrete slab significantly contributed to the shear bearing capacity. The theoretical results aligned with the experimental results obtained using the finite part method, and the accuracy and reliability of the proposed method were verified.

Shear behavior of prismatic and nonprismatic beams with trapezoidal steel web corrugations considering secondary internal force induced by external prestressing

This paper analyzes the shear behavior of statically determinate and statically indeterminate nonprismatic and prismatic beams with trapezoidal steel web corrugations (TSWCs) under external prestressing. The results indicate that for nonprismatic beams with TSWCs, the bending moments and axial forces can also induce additional shear stresses, which will lead to a redistribution of shear stresses on the sections. Moreover, for the nonprismatic statically indeterminate beams with TSWCs, the secondary bending moment and secondary axial force also affect the shear stresses distribution of the sections. This finding has not been reported previously. Therefore, it is not accurate to deem that all shear stresses on TSWCs are completely generated by shear force in the existing specifications. Then, the differences of the shear behaviors between prismatic and nonprismatic indeterminate beams with TSWCs under external prestressing are explored. Consequently, a new practical formula is derived for calculating the shear stresses on the TSWCs induced by external prestressing. The formula can be applied to not only statically determinate and statically indeterminate prismatic beam, but also statically determinate and statically indeterminate nonprismatic beams with TSWCs under external prestressing.

Simulation Research on Continuous Concrete Beams Reinforced with External Prestressed CFRP Tendons.

This paper examines the effects of different loading patterns on the static characteristics of continuous concrete beams reinforced with external prestressed carbon fiber-reinforced polymer tendons (EPCFRPT) and qualitatively analyzes the results for two continuous concrete beams: SB-1 under symmetrical loading, and SB-2 under asymmetrical loading. Then, a finite element analysis model is introduced and calibrated by tests conducted at Southeast University and data collected from a literature review. Based on the FEA model, the initial prestress, cross-section area, and eccentricity of CFRP tendons as well as the steel reinforcement configuration were selected by a parametric study. The results indicated that the initial prestress and tendon cross-section area had the most influence on the tendon stress increment and the secondary bending moment of the middle support, while the reinforcement distribution and eccentricity of the tendons had little effect. The secondary bending moment had a linear positive correlation with the stress increment of tendons. These results allow a simplified equation for calculating the external load bending moment amplitude coefficient at ultimate to be proposed.

Shear behavior of single cast-in anchor simulating characteristics of bridge bearing anchor

A bridge bearing anchor transmits various loads of a superstructure to a substructure. Most anchors are generally designed without consideration of characteristics such as concrete pedestal, grout bedding, and anchor socket. This study investigated the shear behavior of anchors in accordance with the edge distance, embedment depth, compressive strength of concrete, and height of the concrete pedestal in order to simulate the practical characteristics of the bridge bearing anchors. The actual shear capacity of the anchor differs from the shear strengths calculated by the ACI 318 and EN 1992-4; especially, the importance of the embedment depth is underestimated in these codes. An increase in the height of the concrete pedestal has a negative effect on the shear capacity because of the stress concentration. The grout is fractured prior to the occurrence of local damages in concrete, resulting in a secondary moment. As a result, the effect of the level arm is observed. An equation, which can predict the relative cracking degree of concrete, is proposed by analyzing the displacement of grout and concrete. High strain occurs in the stirrups close to the anchor, and the behavior of the strain is more influenced by the embedment depth than the edge distance. The comparison of obtained and analytically evaluated failure loads by calculations according to EN 1992-4, Schmid model and Sharma model was conducted to consider the effect of supplementary reinforcement. Finally, the design equation of concrete breakout strength is modified to predict the more precise shear resistance of a bridge bearing anchor.

Seismic behavior of linked column system as a steel lateral force resisting system

In previous research, the seismic behavior of linked column frame (LCF) system as a dual structural steel frame system that Consists of the primary linked column (LC) and the secondary moment frame (MF) systems has been evaluated. In this research, based on the high capacity of the linked column system in lateral load resisting, this system has been used as the only lateral load resisting system in the building frame. Studies have shown that this approach not only eliminates the main disadvantages of the LCF system, but also preserves the ability to repair structures after an earthquake. Therefore, the designed models of the linked column system have been evaluated using nonlinear static pushover analysis, nonlinear dynamic time history analysis, incremental dynamic analysis and endurance time method analysis. In the evaluation of the seismic behavior of the linked column system, design approach, structural stability and collapse mechanism, ductility, the seismic performance factors of response modification coefficient (R), overstrength factor (Ω0) and deflection amplification factor (Cd), the values of interstory drift ratio at the DBE and MCE seismic hazard levels, maximum seismic capacity and fragility curves, permanent displacement after the earthquake and the weight of steel used in the structure have been investigated. Each of the analysis results shows that the linked column system has a suitable seismic behavior against earthquakes. Therefore, in a preliminary evaluation, the linked column system is introduced as a steel lateral load resisting system that provides the ability to repair structures after an earthquake.