Simple Calculation Method Research Articles

A simplified method for theoretical sum frequency generation spectroscopy calculation and interpretation: The "pop model".

Existing methods to compute theoretical spectra are restricted to the use of time-correlation functions evaluated from accurate atomistic molecular dynamics simulations, often at the abinitio level. The molecular interpretation of the computed spectra requires additional steps to deconvolve the spectroscopic contributions from local water and surface structural populations at the interface. The lack of a standard procedure to do this often hampers rationalization. To overcome these challenges, we rewrite the equations for spectra calculation into a sum of partial contributions from interfacial populations, weighted by their abundance at the interface. We show that SFG signatures from each population can be parameterized into a minimum dataset of reference partial spectra. Accurate spectra can then be predicted by just evaluating the statistics of interfacial populations, which can be done even with force field simulations as well as with analytic models. This approach broadens the range of simulation techniques from which theoretical spectra can be calculated, opening toward non-atomistic and Monte Carlo simulation approaches. Most notably, it allows constructing accurate theoretical spectra for interfacial conditions that cannot even be simulated, as we demonstrate for the pH-dependent SFG spectra of silica/water interfaces.

Simplified Calculation Method for the Critical Load Bearing of Market-based Profile Emergency Steel Pier

A novel emergency steel pier, assembled from market-available profiles, has been developed to address the challenges associated with the "regular stockpiling and rapid emergency deployment" of bridge pier repair equipment. These challenges often involve significant labor and financial costs for manufacturing and maintenance. The buckling modes of the columns and pier-girder connections were considered. Using energy methods and plate-shell theory, an analytical formula for the critical load-bearing capacity of the steel pier under emergency conditions was derived. Numerical simulations were conducted for comparison and validation, resulting in an optimized and simplified method for calculating the critical load capacity, which is suitable for engineering applications.The study shows that the critical load-bearing capacity of the emergency steel pier exhibits distinct patterns under the influence of column buckling modes and pier-girder connection methods. In cases where the column is fixed at one end and hinged at the other, or fixed at both ends, the critical load for axisymmetric buckling is affected by factors such as elastic modulus, Poisson’s ratio, height, radius, wall thickness, and the number of buckling waves. When considering non-axisymmetric buckling, the number of circumferential buckling waves becomes an additional factor. A simplified method for calculating the critical load-bearing capacity was developed. The simplified formula depends only on a correction factor, modified buckling stress, the number of columns, and cross-sectional area. This makes it highly practical for emergency engineering applications.

Experimental study on rotary inter-module connections with corrosion-resistant metal materials: Under axial tension

Modular construction is an innovative construction technology that has attracted considerable attention for its pronounced advantages in reducing reliance on on-site labor, speeding up construction, enhancing productivity, and ensuring superior quality. To extend the applicability of modular construction to structures in corrosive environments, such as ocean floating structures for exploring renewable energy, a rotary inter-module connection employing corrosion-resistant metal materials was proposed herein. Six full-scale inter-module connection specimens made of grade S30408 austenitic stainless steel, grade S220503 duplex stainless steel, and grade A96061-T6 aluminum alloy were tested under axial tension. The load-displacement relationships of each specimen were recorded to enable a thorough analysis of the strength, stiffness, and ductility of the tested specimens. As compared to the conventional carbon steel counterparts, the stainless steel specimens showed superior load-bearing capacity with improved ductility, while the aluminum alloy specimens experienced brittle fracture at the bolt shank-bottom plate junction with reduced load-bearing capacity. Three typical failure modes were identified in the experimental study, namely, plastification of the connector and lower corner fitting, plastification of the connector and both corner fittings, and fracture of the bolt. The load-strain relationships of each specimen were also discussed to analyze the load transfer mechanism and structural behavior of the connection. In addition, the applicability and accuracy of the simplified calculation methods based on beam bending theory and Navier solution for rectangular thin plates, respectively, were discussed based on the test results.

Experimental study on progressive collapse behavior of frame structures triggered by impact column removal

In the research field investigating the progressive collapse of building structures, event-dependent collapse processes have gained increasing attention in analytical and numerical studies. Different events could cause varying effects on progressive collapse resistance. The alternate load path could be related to events that could also lead to variations in load actions. However, experimental studies on reinforced concrete (RC) frame structures triggering structural column removal by the low-velocity impact have not been reported. Therefore, this paper performed an initial experimental study employing impact loading as the extreme event to investigate subsequent progressive collapse behavior of structures. Tests were conducted on six RC substructures consisting of a two-span beam and a structural column. Gravity loads were applied to the top of substructures, and a pendulum impact setup was utilized to remove RC columns by low-velocity impact. When the column underwent lateral failures, the downward force exerted by longitudinal steel bars of the column, before they fractured, pulled the two-span beam beyond the compressive arch action (CAA) stage, leading to a collapse process entirely different from their event-independent counterparts. The parametric study based on experimental results indicated that low-elevation impact and increase of column longitudinal bars detrimentally affected the performance of two-span beams resisting progressive collapse, while the increase in concrete strength partially improved the residual bearing capacity after impact column removal (ICR). Based on a dynamic model, a simplified calculation method is proposed for quantifying the downward force.

Design of improved multi-cell L-shaped CFST columns under compression and bending

In recent years, there has been a notable surge in proposals for various forms of special-shaped concrete-filled steel tubular (CFST) columns. Despite various methods developed by researchers for determining the bearing capacity of multi-cell special-shaped CFST columns under different loading conditions, these methods remain lack unified. In this study, FE models were developed to simulate performances of improved multi-cell L-shaped CFST (ML-CFST) column under compression and bending. Parametric analyses have been performed to evaluate impact of various factors, including steel yield strength fy, compressive strength of concrete fcu, steel thickness t, loading direction θ, web height c, and axial load ratio n, on performances of ML-CFST columns. The findings of study indicate that the unidirectional flexural capacity of ML-CFST member exhibits a nearly linear relationship with the variables of t, fy, and c, with a minimal impact observed from fcu on flexural capacity. The width of extended section b, fcu, fy, and t have a certain effect on flexural capacity at any angle, particularly fy, t, and b. While fcu, fy, and t exert some influence on N/Nu-M/Mu correlation curves, their influences are marginal compared to the loading direction, which is the predominant influencing factor. Additionally, Mx0/Mπ/4-My0/M3π/4 curves gradually protrude outward with the increase in n. The effects of t, fy, and fcu on the shape of Mx0/Mπ/4-My0/M3π/4 curve were relatively insignificant. Simplified unidirectional flexural capacity calculation models were proposed based on stress analysis of cross-section under ultimate states. Given that flexural capacities estimated by simplified calculation model are slightly conservative, it is recommended to increase the flexural capacities by 10 %. Furthermore, an elliptical equation was formulated to predict the flexural capacity at any angle, with the predictions being slightly conservative. Based on ultimate equilibrium theory, a simplified calculation method was presented to predict unidirectional eccentric bearing capacities of ML-CFST columns. Through regression analysis, a simplified calculation method expressed as polar coordinate form for biaxial eccentric bearing capacity was established, with calculated values aligning well with FE results.

A Simplified Calculation Method for the Shear Strength of Unsaturated Silt

A Simplified Calculation Method for the Shear Strength of Unsaturated Silt

Calculation and Adjustment of the Activation Temperature of Switchable Heat Pipes Based on Adsorption

Recently, thermal regulators based on adsorption in a heat pipe have been proposed. The advantage of these so-called “switchpipes” over similar approaches is their low on state thermal resistance. In this paper, we propose a methodology to calculate and adjust the activation temperature of such switchpipes. For this purpose, we use a mass balance-based model that considers both the heat transfer properties of the heat pipe itself, which depend on the amount of working fluid, and the adsorption equilibrium of the adsorbent used. This model can be used not only to describe the activation behavior of a given heat pipe but also to optimize the configuration of a heat pipe for specific operating conditions and to select appropriate adsorbents. In this paper, we also propose definitions for basic indicators of the activation properties of the heat pipe, such as the activation temperature and the activation temperature span. Finally, a simplified calculation method is presented that allows the selection of the correct adsorbent among all adsorbents with Type IV and Type V adsorption isotherms.

Application of the new simple weight calculation (SIWEC) method in the case study in the sales channels of agricultural products

In this research is presented a new method for determining the weights of criteria called simple weight calculation (SIWEC) method. The steps of this method are presented in the practical example of determining the importance of criteria for the needs of sales of agricultural products in the Semberija region. During the presentation of this method two methods are elaborated the simple SIWEC method which includes numerical ratings and the fuzzy SIWEC method which includes ratings in the form of linguistic value. In the selected example is presented how to use this method in order to determine the importance of criteria and in both cases the criterion of sales reliability is given the greatest weight. The contribution SIWEC method is reflected in its simplicity, which facilitates decision-making.•The method presented in this research apart from others is that it uses the evaluation of the criteria by decision makers, so the criteria should not be ranked and compared, but simply evaluated.•Unlike similar methods, the presented method uses the adjusted steps of the method for ranking the alternatives, and decision makers are given a different importance in the decision-making.

Calculation Method of New Assembled Corrugated Steel Initial Support Structure of Highway Tunnel

The assembled corrugated steel initial support structure is a new prefabricated structure in highway tunnel engineering, achieving a balance between economy and safety. This study proposes a simplified calculation method and elucidates the mechanical mechanisms of assembled corrugated steel initial support structures. Firstly, the stiffness characteristics of corrugated steel plates were studied based on full-scale tests. A general equivalent stiffness coefficient table was established. Numerical simulations of corrugated steel flange joints were conducted to explore their bending mechanical properties. A two-stage rotational stiffness model for corrugated steel flange joints was proposed. Finally, a plane strain-spring simplified calculation method for the assembled corrugated steel initial support structure was developed, and the monitoring data from the Qipanshan Tunnel validated the correctness and reliability of the proposed method. The results demonstrate that (1) the plane strain-spring simplified model consists of the planar strain equivalent calculation method for corrugated steel plates and the two-line stiffness equivalent spring of the corrugated steel flange joint. The simplified model was validated as effective by monitoring data. (2) Corrugated steel plates exhibit two stages under loading, namely gap elimination and elastic stages. The elastic stage stiffness of corrugated steel plates decreases with increasing ratio of depth to pitch (RDP), positively correlating with plate thickness when the RDP exceeds 0.333 and otherwise negatively correlated. (3) Corrugated steel lining flange joints exhibit distinct elastic and plastic stages in their linear moment–rotation curves under loading.

Experimental and numerical investigations of post-fire behaviour of circular steel tube confined steel-reinforced concrete columns under eccentric loading

Experimental and numerical analysis were conducted to investigate the post-fire behaviour of circular steel tube confined steel reinforced concrete (STCSRC) columns. A total of fifteen circular STCSRC columns, including five stub specimens and ten slender specimens, were tested under eccentric loading after heating following the ISO-834 standard fire curve. The test findings, such as cross-sectional temperature, failure modes, column deformation, residual load-bearing capacity, strains of steel tubes, etc., were all discussed in detail. A sequential thermal-stress coupling finite element (FE) model, including a heat transfer FE model and a mechanical FE model, was then developed using ABAQUS software and verified using the test results. To obtain further numerical data over a wide range of parameters, a parametric analysis was carried out using the established FE models. A simplified calculation method was presented to estimate the residual load-bearing capability of circular STCSRC columns subjected to eccentrical compression after ISO-834 fire exposure.

Axial local bearing behavior of circular reinforced concrete filled steel tube stub columns

In this work, the axial local compression of circular reinforced concrete-filled steel tube (CRCFT) stub columns is studied. Sixteen specimens, including one circular reinforced concrete stub column (CRCC) specimen and fifteen CRCFT specimens, were prepared, considering different variables, such as the local compression area ratio β, sectional steel ratio α, volume stirrup ratio ρv, longitudinal reinforcement ratio ρ, and concrete strength fc. The axial local compression of specimens were experimentally investigated in terms of the damage process, failure mode, load-displacement relationship, ultimate bearing capacity, stiffness, deformation capacity, and strain characteristic. The finite element model of the CRCFT was also developed and validated. The parametric analysis of the local compression area ratio β, sectional steel ratio α, and volume stirrup ratio ρv facilitated the further investigation of the axial local compression behavior of CRCFT. The results showed steel tube buckling and concrete shear failure exhibited by CRCFT specimens. With the increasing local compression area ratio β, the ultimate bearing capacity reduced by 3.6–47.9 %, whereas the local compression strength improvement coefficient βcl increased by 11.8–273.9 %. With the increase in section steel ratio α and volume stirrup ratio ρv, the ultimate bearing capacity, stiffness, and deformation capacity were improved. Longitudinal reinforcement ratio ρ and the concrete strength fc also influenced the stiffness of CRCFT specimens. A simplified calculation method for the ultimate bearing capacity of CRCFT specimens was also presented.

Method of Average Vertical Earth Pressure for HFCCTs Based on Differential Settlement

AbstractThis paper presents a modified and simplified calculation method, taking into account the differential settlement between the soil columns surrounding the cut-and-cover. High-filled cut-and-cover tunnels (HFCCT) are usually subjected to high earth pressures above the top of the CCT due to an ultra-high backfill. However, the estimation methods for earth pressure above the top of CCT are ambiguous. Through the theoretical analysis of the average vertical earth pressure (AEP) at the top of the CCT, it is found that an additional earth pressure above the top of the overburden pressure is induced, and the magnitude is related to the differential settlement between interior and exterior soil columns. Thus, through a combined theoretical derivation and numerical analysis, a modified formula is proposed. The results show that the vertical earth pressure increment above the top of CCT can be linearly correlated to the differential settlement. In addition, the correlation needs to be calibrated by considering several effects on sites, such as slope angle, groove-width ratios, cross-sectional shape, and the type of backfill. The change in influencing factors has no effect on the function type of the p−δ fitting curve, but it will affect the coefficient k.

The hydrodynamic pressure analysis and simplified calculation method of added mass of oscillating horizontal cylinder in finite water depth

Based on the potential flow theory, the hydrodynamic pressure governing equation of an incompressible and ideal fluid acting on a single oscillating horizontal cylinder in finite water depth is derived, solved using the variable separation method. Analytical solutions for the hydrodynamic pressure of the oscillating horizontal cylinder in both sway and heave directions are established via the multipole expansion method and verified against numerical solutions. Using these analytical solutions, the hydrodynamic pressure distributions of the horizontal cylinder under sway and heave motions, varying with dimensionless parameters immersion ratio H (H=h0/h) and diameter-depth ratio L (L=2a/h), are studied. It is found that at the distance of the cylinder from the free surface and seabed is the key factor influencing hydrodynamic pressure distribution. Additionally, the added mass was calculated through integration of hydrodynamic pressure, and the variation of added mass coefficients with L‾ (L‾=2a/h0) and H‾(H‾=2a/(h−h0)) is analyzed. It is observed that, in both sway and heave motions, added mass coefficients increase with decreasing L‾ and increasing H‾. Simplified calculation formulas for added mass coefficients of the horizontal cylinder under sway and heave motions are developed using a two-step fitting method. Finally, errors in calculating the added mass coefficients are compared between the simplified calculation formulas and the analytical solution, showing errors of less than 5%, indicating high accuracy of the proposed simplified calculation formulas for added mass coefficients.

Investigation of structural and optical properties of TM-doped CuO NPs: Correlation with their photocatalytic efficiency in sunlight-induced pollutant degradation

The presence of non-biodegradable, toxic, and harmful organic pollutants in various environmental mediums poses significant threats to ecosystems and human health. This study investigates the impact of transition metal (TM) doping on the photocatalytic performance of copper oxide nanoparticles (CuO NPs) in degrading methylene blue (MB) dye under sunlight irradiation. CuO NPs are synthesized using the co-precipitation method. X-ray diffraction (XRD) analysis revealed a monoclinic structure with space group C2/c for undoped and TM–doped CuONPs, with crystalline sizes ranging from 13 nm for undoped to 36 nm for Zn-doped CuO. Based on UV–Visible Spectroscopy data, the band gap energies and the nature of electronic band transitions are determined using a new simplified calculation method. Accordingly, direct band gap energy exhibits a slight red-shift as a result of doping with Ni, Mn or Fe, from 1.427 eV for undoped to 1.402 eV for Fe-doped CuO. While Co or Zn doping, induces a trivial blue-shift to 1.468 eV and 1.434 eV respectively. The CuO particles show a heterogenous distribution size and shape. The mean grain size raised from 34.3 nm for undoped to about 100 nm for TM-doped CuONPS, excluding the Co-doped CuO for which the mean grain size reached 154.532 nm with highest standard deviation heterogeneity of 125.737 nm. Furthermore, photocatalytic experiments demonstrated that TM-doping significantly enhanced the degradation rate of MB dye under sunlight irradiation. Co-doped CuO is the most efficient catalyst. This makes TM-doping a promising pathway for the use of CuO NPs in wastewater decontamination applications.

Branching ratio in the photodissociation of (C6H5NH2)+-H2O–H218O

Molecular systems including clusters often manifest multiple photodissociation pathways upon absorption of photon energy enough to break down chemical bonds. This certainly raises fundamental questions to chemists: which pathway will be most favored and how can we predict it with precision? To address these issues, we had previously introduced a rather crude but highly simplified and straightforward calculation method, Rice-Ramsperger-Kassel-Marcus (RRKM) calculation method complemented by the concept of extreme loose transition state (eLTS). This approach has proven effective in estimating branching ratios in photodissociation of C6H4BrCl+. Here, we have extended this method to interpret results in IR photodissociation of (C6H5NH2)+-H2O–H218O for further evaluation and refinement of this method. We compared branching ratios derived from RRKM-eLTS with those obtained via phase-space theory (PST) to find that our calculation results through RRKM-eLTS were quite in line with the experimental data while those from PST calculation fluctuated significantly depending on the calculation levels and basis sets. This indicates that RRKM-eLTS model not only aligns well with experimental observations giving insights into the relevant rate constants but also intuitively explains these results. We, hereby, suggest that RRKM-eLTS model is a robust and user-friendly method for computing branching ratios, with possible applications to other molecular systems.

Simplified calculation method of non-Gaussian wind pressure peak factor for large-span spatial roof structures

Based on the wind tunnel test data of a long-span spatial roof structure, the correlation between higher-order statistics and peak factors was obtained according to the time and frequency domain characteristics of wind pressure-time history, as well as the coincidence condition between wind pressure power spectra of measurement points and wind speed power spectra. A simplified peak factor calculation formula was proposed based on the moment-based Hermite polynomial model. The Gaussian part of the peak factor was calculated through the wind speed spectrum based on the zero-crossing theory, and the parameters related to higher-order statistics were considered as the non-Gaussian part of the peak factor. The simplified method was verified through the instantaneous extreme value method based on a coal shed structure with available long-term wind pressure-time history. It revealed that the results of the proposed simplified method correlate well with that of the instantaneous extreme value method, indicating its accuracy and potential value for engineering practice.

Method for calculating the bearing capacities of caisson foundations considering the effects of caisson construction

Theoretical analysis of the effects of caisson on the bearing capacities of large caisson foundations was performed, with the slip line simplified as a polyline. Based on the limit balance of forces in active zone, transition zone and passive zone, a simplified bearing capacity algorithm for caisson shaft wall or partition wall with no buried depth and no excavation is established. The effects of caisson excavation on the caisson foundation bearing capacity were examined, and a theoretical formula for estimating the caisson shaft wall or partition wall bearing capacity considering the effects of the angle and depth of excavation was derived. At the same time, the influence of soil weight and the extension of soil slip line from the bottom of the foundation to the surface on the bearing capacity of the foundation is analyzed when there is a certain buried depth between the shaft wall and the partition wall, and a formula for calculating the bearing capacities of buried caisson foundations was proposed. According to the calculation method of caisson shaft wall or partition wall proposed in this paper under the condition of no buried depth and no excavation, combined with the world’s largest north anchor caisson project of Wufengshan Yangtze River Bridge, the plate loading test and inversion analysis are carried out. The results of the test and the simplified calculation method of foundation bearing capacity are in good agreement, and the error of the inversion value and the theoretical calculation value are within 5%. For the theoretical calculation method of foundation bearing capacity considering foundation excavation and buried depth, experiments, inversion analysis or numerical simulation will be carried out to verify the accuracy of the calculation method.

Sag and Tension Calculations for High-Voltage Overhead Line Conductors

Overhead lines are used to transmit electricity from where it is generated to the receiving stations. The correct design of an overhead line affects public safety, because it should ensure the required clearances between conductors and the ground and objects located in the space under the overhead line. The temperature of conductors in overhead lines depends on the load current and weather conditions, and affects the sag and tension of the conductors. Calculations of sags and tensions of overhead conductors can be performed using simplified calculation methods that do not consider insulator sets. In some situations, this approach may cause calculation errors. This article discusses algorithms for calculating overhead conductor tensions and sags in the tensioning sections of high-voltage overhead lines, accounting for and excluding insulator sets. The analysis is carried out for different lengths of tensioning sections and various thermal and mechanical states of the conductors.

A method for predicting deformation field of deep foundation pit considering spatial effect

Urban underground spaces have experienced significant development and utilization due to the rapid progress of urban construction and continuous advancements in construction technology. The number of foundation-pit projects immediately adjacent to buildings, structures, and pipelines has been increasing. Ensuring the safety of construction and surrounding facilities, it is essential to predict deformation caused by foundation pit excavations. In this study, a simple calculation method was proposed for predicting deformation of an envelope structure and surface settlement caused by deep foundation excavation with spatial effects. Firstly, the principle of minimum potential energy was applied and the lateral displacement equation of the envelope structure was derived, considering spatial deformation effects. Secondly, based on linear elasticity theory, a surface settlement expression was formulated utilizing the plane strain boundary. Finally, the stratigraphic loss method was used to establish a connection between horizontal envelope deformation and surface settlement, allowing for calculations of surface settlement at any position behind the envelope structure. The effectiveness and practicability of the proposed method were demonstrated by comparison of two existing foundation-pit engineering examples.

Experimental study on the flexural performance of FRP grid-reinforced ultra-high-performance concrete I-beams with different steel fiber contents

To adapt to harsh engineering environments, the use of structural components with fiber-reinforced polymer (FRP) grid-reinforced ultra-high-performance concrete (UHPC) is considered a new development trend. Twelve FRP grid-reinforced UHPC I-beams are fabricated to investigate the effects of the thicknesses of FRP grids (0 mm, 1 mm, 3 mm, and 5 mm) and the steel fiber contents of UHPC (0%, 1%, and 2%) on their flexural performance. Four-point bending tests are conducted to obtain the failure modes, load-deflection characteristics, and strain responses of each testing beam, and a simplified calculation method for cracking loading and flexural bearing capacity is proposed. The results reveal that the increase in FRP grid thickness, the ultimate load bearing capacity of FRP grid-reinforced UHPC structural beams increases and the ductility also can be enhanced. The presence of steel fiber effectively inhibits the cracking and increases the first cracking load of the beam during the test process, although its influence on the ultimate bearing capacity is limited. Besides, until to the cracking stage, there is no noticeable change in the tensile strain of the FRP grids as the applied load increases. It has been used to simplify theoretical calculations, which shows good agreement with the experimental results.