Simplified Calculation Formula Research Articles

Experimental investigation of bond behavior with lap splice for CFRP-steel composite bars in coral sea-sand aggregate seawater concrete

The pull-out tests on a total of 81 lap-spliced specimens in 27 groups were conducted to investigate the lap-spliced behavior and the appropriate splice length for CFRP-steel composite bars (C-FSCB) in coral sea-sand aggregate seawater concrete (CSSC). The test variables included the C-FSCB diameter (dc), splice length, concrete cover thickness, concrete strength, lap spacing, stirrup ratio, and materials type. Then, the influence of various test variables on the lap-spliced behavior of C-FSCB in CSSC was analyzed. The results showed that when the splice length was less than 17dc, the specimens exhibited pull-out and concrete splitting failure, while C-FSCB fracture failure occurred when the splice length exceeded 17dc. Severe shear damage was observed on the C-FSCB surface in the case of pull-out and concrete splitting failure. When the splice length was less than 14dc, the bond strength of the specimens was approximately 7.2 MPa. As the splice length increased beyond 14dc, the bond strength gradually decreased. After the cover thickness was greater than 4dc or the compressive strength of CSSC was greater than 30 MPa, the variation in bond strength of the specimens can be negligible. Increasing the stirrup ratio led to an increase in bond strength and a significant reduction in crack width. Compared to specimens with steel bars, the bond strength reduction for specimens with C-FSCB exceeded 25%. Based on the test results, calculation formulas for the bond strength and splice length of C-FSCB in CSSC were established. Furthermore, referring to the approach in the Chinese code GB 50010–2010, a simplified calculation formula for splice length was proposed.

Fourier–Gegenbauer pseudospectral method for solving periodic fractional optimal control problems

This paper introduces a new, highly accurate model for periodic fractional optimal control problems (PFOCPs) based on Riemann–Liouville and Caputo fractional derivatives (FDs) with sliding fixed memory lengths. This new model enables periodic solutions in fractional-order control models by preserving the periodicity of the fractional derivatives. Additionally, we develop a novel numerical solution method based on Fourier and Gegenbauer pseudospectral approaches. Our method simplifies PFOCPs into constrained nonlinear programming problems (NLPs), readily solvable by standard NLP solvers. Some key innovations of this study include: (i) The derivation of a simplified FD calculation formula to transform periodic FD calculations into evaluations of trigonometric Lagrange interpolating polynomial integrals, efficiently computed using Gegenbauer quadratures. (ii) The introduction of the αth-order fractional integration matrix based on Fourier and Gegenbauer pseudospectral approximations, which proves to be highly effective for computing periodic FDs. A priori error analysis is provided to predict the accuracy of the Fourier–Gegenbauer-based FD approximations. Benchmark PFOCP results validate the performance of the proposed pseudospectral method.

Eccentric compression capacity of bolt-welded joints in concrete-encased CFST

The new bolt-welded joint in concrete-encased Concrete-Filled Steel Tube (CFST) without cutting flange demonstrates great mechanical properties and durability, which is also easily constructed at high altitudes or in long-span arch bridges. It is crucial to study the mechanical properties of composite member made of the bolt-welded joint and outer concrete. In this study, a parametric analysis on bearing behavior of bolt-welded joints in concreted-encased CFST under eccentric compression was explored, based on experiments and a validated finite element model. Furthermore, a simplified calculation formula for the eccentric bearing capacity of the bolt-welded joint in concreted-encased CFST was proposed. The results indicated that the bearing capacity increased with the increase of steel tube strength, core concrete strength, reinforcement strength, outer concrete strength, steel ratio, and reinforcement ratio. Increasing the steel ratio and the steel tube diameter-section ratio can enhance the ductility of the member. A rise in stirrup spacing had a detrimental impact on both bearing capacity and ductility. An excessive amount of eccentricity diminished the bearing capacity of the member and alter its failure mode. The proposed simplified calculation formula for eccentric bearing capacity was in strong agreement with both experimental and numerical results.

Practical Formulae for Estimating Cable Tension with Unknown Rotational Restraints by the Frequency Method

To calculate the tension in cables with different boundary conditions, the relationship between cables with fixed–fixed and hinged–hinged boundary conditions in terms of the frequency was determined according to frequency characteristic equations of cables with the two boundary conditions. In this way, a simple calculation formula for tension with fixed–fixed boundary conditions was deduced. Similarly, a calculation formula for the tension in cables with a fixed–hinged boundary condition was proposed using the method. Results show that the proposed formulae, with high computational accuracy and wide ranges of application, can be used to calculate the cable tension under a dimensionless parameter (ξ) not lower than 6.9, so it is convenient to apply the formulae to calculate tension in practice. Meanwhile, changes in the frequency ratios of cables with different boundary conditions than those with a hinged–hinged boundary condition were analyzed. Results show that when ξ is not lower than 25, the frequency ratios of cables of various orders tend to be the same. The boundary coefficient(λ) was introduced. Given the cable stiffness, the tension and boundary coefficient(λ) can be calculated through linear regression. The method considers influences of unknown rotational end-restraints of cables and accurately calculates the cable tension. By using simulation examples and engineering examples, the method was verified to be accurate in calculating the cable tension, thus providing a novel, practical method for estimating tension in cables, booms, and anchor-span strands of suspension bridges.

Study on radon release behaviors of the tubular flow-through radon source with natural radium-bearing materials

To obtain a radon source that is easy to access natural radium-bearing raw material and does not require the approval of relevant departments, the tubular flow-through radon source using radium-bearing ore as the radon-generating material was designed. Based on the theories of radon diffusion-convection migration in porous media, the simplified calculation formula and numerical calculation models of radon activity concentration at the outlet of the tubular flow-through radon source were established, and the radon release rules of the tubular flow-through radon source were studied using a combination of simplified calculation formulas, numerical simulations, and experiments, respectively. The results show that (1) the radon activity concentration at the outlet of the tubular flow-through radon source was dominated by mass (or the volume) of the natural radium-bearing raw material, free radon production rate, and gas flow rate. (2) When the range of radon activity concentration at the outlet is 260–1308 Bq m-3, the relative deviation of the three methods is less than 2.62%. (3) The simplified calculation formula and numerical simulation method proposed in this paper can provide a reference for the design and control of the radon activity concentration of a tubular flow-through radon source.

Linear modeling analysis of the heat balance of the transmission line in high frequency critical ice melting state

Abstract The icing of transmission lines can cause many problems such as increased line load, unbalanced tension, and galloping, posing a serious threat to the reliable operation of the power system. Therefore, linear modeling analysis of the heat balance under a high-frequency critical ice melting state of transmission lines is studied. The thermal conduction states of melting, heating, twisting, rotating melting, and ice layer detachment of ice melting conductors are analyzed. Based on the heat conduction process of thermal melting of ice on transmission lines, a simplified calculation formula for thermal melting ice time is derived to calculate times for heating, ice layer torsion, and air gap increase. At the same time, based on the law of conservation of energy, thermodynamic boundary conditions for iced conductors were established and corresponding physical models were constructed. Based on this model, we conduct a linear modeling of the heat balance in the melting state in order to provide a more accurate prediction of temperature distribution. The experimental results show that there is a negative correlation between environmental temperature and critical melting current, and the melting time decreases with the increase of environmental temperature.

Experimental and theoretical investigation on residual bearing capacity of CFDST-T joints after lateral impact

This study investigates the residual performance of concrete-filled double-skin steel tubular (CFDST) T-joints after lateral impact. One hollow T-joint and five CFDST-T joints with various steel tube thickness and hollow rate were first tested by a pendulum machine. The axial compression test was subsequently performed to explore the residual performance in terms of failure mode, residual bearing capacity, ductility, energy dissipation, and strain evolution. Results indicated that the failure modes of the CFDST-T joint and hollow T-joint were characterized by global bending and severe local indentation, respectively. Besides, the CFDST-T joints exhibited the strongest residual bearing capacity with a hollow rate of 0.52 and the greatest ductility of 0.63. Moreover, increasing the outer tube thickness improved the residual bearing capacity and simultaneously reduced the ductility coefficient while the inner tube exerted little effect on residual performance. Simplified calculation formulas were finally derived to predict the impact residual deflection and residual bearing capacity of the CFDST-T joint based on parametric analysis. This study will provide a reference for future research to contribute to the design of more reasonable CFDST-T joints and promote their application.

Generalized Gibbons-Werner method for stationary spacetimes

The Gibbons-Werner (GW) method is a powerful approach in studying the gravitational deflection of particles moving in curved spacetimes. The application of the Gauss-Bonnet theorem (GBT) to integral regions constructed in a two-dimensional manifold enables the deflection angle to be expressed and calculated from the perspective of geometry. However, different techniques are required for different scenarios in the practical implementation which leads to different GW methods. For the GW method for stationary axially symmetric (SAS) spacetimes, we identify two problems: (a) the integral region is generally infinite, which is ill-defined for some asymptotically nonflat spacetimes whose metric possesses singular behavior, and (b) the intricate double and single integrals bring about complicated calculation, especially for highly accurate results and complex spacetimes. To address these issues, a generalized GW method is proposed in which the infinite region is replaced by a flexible region to avoid the singularity, and a simplified formula involving only a single integral of a simple integrand is derived by discovering a significant relationship between the integrals in conventional methods. Our method provides a comprehensive framework for describing the GW method for various scenarios. Additionally, the generalized GW method and simplified calculation formula are applied to three different kinds of spacetimes — Kerr spacetime, Kerr-like black hole in bumblebee gravity, and rotating solution in conformal Weyl gravity. The first two cases have been previously computed by other researchers, affirming the effectiveness and superiority of our approach. Remarkably, the third case is newly examined, yielding a innovative result for the first time.

Определение границ геологических слоёв методом миграции в обратном времени

The article is devoted to solving an important practical problem - determining the structure of the subsurface space of the geological environment based on surface seismic data. Thanks to the registration of seismic waves reflected from the boundaries of geological layers, it is possible to delineate hydrocarbon deposits, which makes it possible to effectively plan a field development scheme. Optimizing the production process makes it possible to make it profitable, including when developing unconventional hydrocarbon deposits. The paper discusses the technology of constructing a migration image using the reverse time migration method. In the general case, an analytical derivation of the calculation formulas was carried out. For the practically significant case of an acoustic environment, simplified calculation formulas are explicitly written out and implemented in the form of a software algorithm. The issue of improving the quality of the migration image without significantly increasing the computational complexity of the problem is discussed separately. The authors demonstrated the performance of this approach using the widely used Marmousi geological model.

Experimental investigation of CFRP-confined partially encased composite columns under axial compression

The use of fiber reinforced polymer (FRP) confinement techniques to repair partially encased composite (PEC) columns can prevent outward local buckling and corrosive damage in their flange plates. This study investigated the effects of three different carbon FRP (CFRP) strengthening schemes (including hoop, longitudinal, and bidirectional combined bonding of CFRP) on the axial compressive behavior of PEC columns with varying slenderness ratios. Fifteen specimens were tested to analyze their failure modes, bearing capacities, load-deflection responses, and load-strain responses. The results show that CFRP hoop wraps effectively enhance the strength of short columns. Longitudinal bonding of CFRP significantly improves the flexural stiffness of slender columns. Optimal load-bearing capacity enhancement can be achieved through the synergistic effect of bidirectional combined bonding of CFRP. A simplified calculation formula for the axial load bearing capacity of CFRP-confined PEC columns was also proposed, which shows a good agreement with the experimental results.

Mechanical behavior of GFRP-recycled concrete-steel multitube concrete columns under axial compression

This paper proposed a novel GFRP-recycled concrete-steel multitube concrete column (RA-MTCC), which consisted of an external circular GFRP tube, a group of small internal steel tubes in a circular array, and recycled aggregate concrete filling for all the space inside of these tubes. The mechanical behavior of eleven specimens were investigated under uniaxial compressive test considering parameters of the GFRP tube thickness, the configurations of internal steel tubes, the strength and the replacement ratio of recycled coarse aggregates (RCAs). Test results indicated that: (1) the replacement ratio of RCAs had no significant impact on the failure mode and ultimate load bearing capacity but noticeable adverse effect on the stiffness of RA-MTCCs; (2) the small internal steel tube could significantly increase the ultimate load bearing capacity and stiffness of RA-MTCCs, with a maximum enhancement of 82% and 114%, respectively; (3) specimens with GFRP outside exhibited excellent ductility behavior due to the effective confinement provided by GFRP jacket and steel tubes. An analytical model considering the replacement ratio of RCAs was proposed and verified with the present test results. The predicted results showed that the proposed model could accurately predict the full range stress–strain response of RA-MTCCs. Finally, based on the proposed analytical model, a simplified calculation formula for the ultimate bearing capacity of RA-MTCC was proposed.

Ferromagnetism of concrete

Studying the intrinsic properties of concrete is essential for addressing various aspects of concrete structure design, material selection, and sustainability. In this study, a suspended strong magnetic torsion balance device was designed and constructed to investigate the ferromagnetic properties of concrete specimens and their constituent materials. It was found that sand and cement generally exhibit ferromagnetic properties, while aggregates do not possess ferromagnetic properties. Analysis using powder X-ray diffraction (XRD) and chemical experiments confirmed that the ferromagnetic material in sand and cement is elemental iron. A simplified calculation formula for the magnetic force between concrete specimens and an external magnetic field was derived. Three sets of specimens were designed and fabricated for experimental exploration of ferromagnetic properties and magnetic force measurements. The experimental results demonstrate that plain concrete possesses measurable ferromagnetic properties. The magnetic force of concrete initially experiences a rapid decay followed by a gradual leveling off as the distance (from the magnetic field source to the concrete surface) increases. The decay rate approximately follows a fourth-power relationship with distance. Under a loading condition with an applied magnetic field intensity of 0.2 T, the optimal measurement range for ferromagnetic force in concrete is between 0.02 m and 0.05 m.

Investigation on the Ductility Capacity of Concrete Columns with High Strength Steel Reinforcement under Eccentric Loading.

Ductility-based structural design is currently the mainstream method. In order to analyze the ductility performance of concrete columns with high-strength steel reinforcements under eccentric compression, corresponding experimental studies have been performed. Numerical models were established, and their reliability was verified. Based on the numerical models, the parameter analysis was carried out, where eccentricity, concrete strength, and reinforcement ratio were considered to systematically discuss the ductility of the concrete column section with high-strength steel reinforcement. The results show that the ductility of the section under eccentric compression increases with the strength of the concrete and eccentricity, and decreases with the reinforcement ratio. Finally, a simplified calculation formula capable of quantitatively evaluating the section ductility was proposed.

Stiffness evaluation of UHPC-filled socket column-foundation joints: Numerical investigation and analytical model

Socket connections are widely used to connect precast columns to the foundation and the initial stiffness of the socket joints is of great significance for seismic design. The connection efficiency of precast socket column has an important influence on its initial stiffness. Therefore, based on the previous experiment research on socket column by authors’ team, a finite element model (FEM) of ultra-high performance concrete (UHPC)-filled socket precast bridge column-foundation joints was established and verified by the local damages, failure mode and hysteresis curves. The key parameters that influencing the initial stiffness of socket joints were studied by numerical analysis, and a simplified calculation formula of initial stiffness was proposed. In addition, based on the theory of elastic foundation beam, an analysis model for predicting the initial stiffness of socket joints considering rotating stiffness of the connection was developed. The theoretical results are verified by the proposed simplified equations and experiments results in the literature. The method presented in this paper can conveniently predict the initial stiffness of RC socket column-foundation joints with reasonable accuracy.

Anti-collapse mechanism and reinforcement methods of composite frame with CFST columns and infill walls

Masonry infill walls serve as building partitions and are generally considered non-structural components. Their weights are considered in progressive collapse analysis, but the resistance of the infill walls is normally ignored in design standards. Based on the reasonable selection of constitutive models, a refined finite element (FE) model for the collapse resistance of concrete-filled steel tubular (CFST) composite frame with infill walls was established by ABAQUS/Explicit. Cohesive elements were inserted between different masonry blocks to simulate the mortar joints. The collapse resistance contribution and reinforcement methods analysis of the CFST frame with infill walls were carried out based on the validated FE models. Results show that the infill walls significantly contribute to resisting vertical load in the initial loading stage, with a maximum contribution of 55.3%. The infill walls, which are treated as the equivalent compressive struts, change the load-resisting path and effectively improve the load redistribution ability of the frame. The V-type oblique arrangement of tie rebars has better tie effect and collapse resistance of the frame than other arrangements. After pasting the CFRP sheet and spraying the ECC material to reinforce infill walls, the peak load can be increased by 25.1% and 22.9% respectively, and the ultimate load can be increased by 96.2% and 74.5% respectively. X-type pasting the CFRP sheet reinforcement has a better collapse resistance than others. Furthermore, based on the simplification of the infill walls as the diagonal struts, the simplified calculation formulas of anti-collapse capacity of CFST frame with infill walls were studied.

On asymptotic distributions of several test statistics for familial relatedness in linear mixed models.

In this study, the asymptotic distributions of the likelihood ratio test (LRT), the restricted likelihood ratio test (RLRT), the F and the sequence kernel association test (SKAT) statistics for testing an additive effect of the expected familial relatedness (FR) in a linear mixed model are examined based on an eigenvalue approach. First, the covariance structure for modeling the FR effect in a LMM is presented. Then, the multiplicity of eigenvalues for the log-likelihood and restricted log-likelihood is established under a replicate family setting and extended to a more general replicate family setting (GRFS) as well. After that, the asymptotic null distributions of LRT, RLRT, F and SKAT statistics under GRFS are derived. The asymptotic null distribution of SKAT for testing genetic rare variants is also constructed. In addition, a simple formula for sample size calculation is provided based on the restricted maximum likelihood estimate of the effect size for the expected FR. Finally, a power comparison of these test statistics on hypothesis test of the expected FR effect is made via simulation. The four test statistics are also applied to a data set from the UK Biobank.

Theoretical Model for the Analysis of Rotational Behavior of Penetrated Mortise-Tenon Joints in Traditional Timber Structures

ABSTRACT Penetrated mortise-tenon joints (PMJs) are typical wood-to-wood connections commonly used in traditional Chinese timber structures. They play a crucial role in the structural behavior of timber constructions. This study derived a method of theoretical estimation for the rotational behavior of PMJs, which is unique and more comprehensive in that it takes both movement of the rotation center and bending deformation of the tenon into consideration. In addition, it experimentally and numerically validated the theoretical model, and quantitatively analyzed the position changes of the rotation center and the effect of the bending deformation. On this base, simplified calculation formulas are proposed for the prediction of equivalent elastic stiffness and peak moment of PMJs, and then applied for the calculation of the lateral stiffness of timber frames. As a result, the predicted lateral stiffness shows good agreement with test results, demonstrating the validity of the estimation method derived and its applicability to the structural analysis. The results of this study show that the rotation center of the tenon is not stationary, and its moving range in the horizontal direction is much larger than that in the vertical direction. Another pattern found is that the bending deformation of the smaller tenon counteracts more than 20% of the compressive deformation caused by the rigid-body motion, and therefore must be considered when analyzing the rotational behavior of PMJs.

Analytical study on sandwich shells considering partial degree of composite action

This paper is focused on a new structural type - sandwich shell, which includes inner and outer shells connected by hoop connectors to achieve composite action; and a functional layer in the middle. Considering that the hoop connectors are not completely rigid, there will be limited slip between the inner and outer shells, which will lead to partial Degree of Composite Action (DCA). Due to the existence of the hoop connectors and shear lag effect, the stress distribution along the width direction of the shell is uneven, which can be described by effective width. Considering all these factors, this paper first develops an analytical model for sandwich shells with different configurations of connectors; and uses finite element analysis results to verify the analytical model. Next, a parametric study is conducted using the analytical model to study the effects of material strength, the ratio of the thickness of the functional layer to the thickness of the single layer shell, and the ratio of the arc length to the width of the sandwich shell on the effective width. It is found that DCA can significantly affect the stress and strain distributions of the sandwich shell. The effective width for 100% DCA can be used as a conservative value to represent those of other DCAs. Finally, a simplified calculation formula, which can be used in practical design, is derived based on the effective width for 100% DCA.

Method for measuring voltages in channels of a hemispherical resonator gyroscope with an arbitrary orientation axes

<span>The article deals with issues related to solid wave gyroscopes, which are used as a sensor in inertial navigation systems. The article considers a variant of solving problem, when oscillations of the resonator are excited in directions that coincide with their own axes, oriented a priori is unknown. The main contribution this article is the method is proposed for measuring signal amplitudes in virtual main and quadrature channels, the orientation of which does not coincide with the orientation of the signal pickup electrodes. This is achieved by modeling algorithms for measuring the slope of the resonator's own axes and signal amplitudes in virtual channels are evaluation. In order to verify the adequacy of the proposed models simplified calculation formulas for programming microcontrollers are presented. An estimate of the error due to the use of simplified formulas is made. It is assumed that the use of this method will reduce the requirements for the quality of balancing the resonators of gyroscopes. The findings will be useful for mass production of navigation systems with gyroscopes, which have a small drift and are capable of experiencing large shock linear accelerations, for example, in underground inclined drilling, and in meteorological rockets.</span>

Experimental study on stable bearing capacity of wheel-buckle formwork support frames

To prevent the frequent jamming of straight plugs and disk plates, a novel wheel-buckle joint was introduced and investigated in this study. The destabilization failure mode and stable bearing capacity of the new wheel-buckle formwork support frame were studied through nine full-scale test models. Different influencing factors such as the horizontal scissor brace, vertical scissor brace, spacing of the standing tube, and lift height were considered in these tests. The results indicate that all the models tended to adopt a non-sway buckling mode with a large wave valley, and that the maximum horizontal displacement occurred in the upper-middle part of each model. The stable bearing capacity of each model increased with a decrease in the lift height and spacing of the standing tube. Furthermore, the arrangement of vertical scissor braces could significantly improve the stable bearing capacity of the models. Based on the stability theory, a simplified calculation formula for the stable bearing capacity of the support frame was established. The values calculated through the simplified formula were compared with the values calculated through the JGJ300-2013 code and the test values. It was observed that the formula has sufficient accuracy (average error 13.4 %) in predicting the stable bearing capacity of the support frame, and that the JGJ300-2013 code has sufficient bearing capacity reserve. Notably, the conclusions of this study can serve as a reference for further research on new wheel-buckle formwork support frames.