Strength Formula Research Articles

Seismic performance analysis of corrugated-steel-plate composite shear wall based on corner failure

This study investigates the hysteretic performance of corrugated steel plate composite shear walls. Six shear walls were designed for experimental research to analyze the failure process and mode, hysteresis diagrams, backbone curves, energy consumption capacity, and stiffness degradation. The peak loads of SPCSW-1, SPCSW-2, and SPCSW-3 were 688.8 kN, 733.0 kN, and 547.2 kN, respectively, representing increases of 252.8%, 200.4%, and 141.8% (compared with SPSWs: 272.5 kN, 365.7 kN, and 385.8 kN). According to the experimental failure mode, the conventional model was further optimized to achieve corner cracking. The optimization scheme and mechanism analysis of the model were explored. The shear strength formula for a horizontal corrugated steel plate composite shear wall was revised, considering the adverse effect of corner failure, and the shear sharing percentage was determined. The simulation results indicate that the steel type may affect the peak load of the composite shear wall. The energy consumption ratio of the outside concrete, steel plate, and tension column to the pressure column is 13:3:3:1; the ratio is minimally affected by the steel type. The steel skeleton cannot provide full support due to stress concentration after the failure of the concrete corner, which causes adverse conditions. The revised formula was demonstrated to be more accurate for the shear strength calculation of a horizontal corrugated steel plate composite shear wall.

Effect of Sawtooth Angle on Shear Mechanical Behavior of Structural Plane

In order to study the shear characteristics of sawtooth structural planes, shear tests were carried out on structural planes with different sawtooth angles under different normal stresses to study the influence of sawtooth angles on the shear strength of structural planes, and the quantitative relationship between the shear strength parameters and the sawtooth angles of structural planes was obtained. According to the test results, the failure characteristics of the regular sawtooth structure are expounded. The relationship between the shear strength and the angle of the sawtooth structure is analyzed by using More-Coulomb theory, and the empirical formula of the shear strength of the sawtooth structure is given. At the same time, the failure characteristics of the shear plane were obtained by 3D scanning of the shear plane, and the failure law of the structural plane was obtained. The results show that the shear strength of the regular sawtooth structure surface increases with the increase of sawtooth angle, and the failure mode of the structure surface at low angle is climbing slip failure, and the failure mode transitions to climbing shear failure with the increase of sawtooth angle, and the failure mode changes to total shear failure when the sawtooth angle increases further.

Formulation of voids and bubbles as biased sinks to crystalline point defects

In this article, the biased sink behaviour of voids and bubbles to crystalline defects is examined through a properly trained machine learning model. The use of machine learning enables capturing more microstructural details than the conventional analytically-tractable sink strength formulae. With the present machine learning representation, for instance, the sink bias caused by opposite moving tendencies of vacancies against interstitial atoms in hydrostatic pressure fields, is naturally captured. Hence the roles played by several factors, such as the external loads, the number of gas atoms filling a bubble, and bubbles on crystalline interfaces, can be examined systematically. The findings here are shown good accordance with a spectrum of experimental/theoretical results related to sink bias concerning the loading conditions and grain boundaries on void/bubble growth. The present studies are thus expected to offer certain insights to controlling radiation-induced growth of bubbles by a mechanical means.

Research on strength distribution of natural pumice concrete based on precast porosity

In this study, the rubber natural pumice concrete was taken as the research object, and the orthogonal test method was employed to design the experiment, the rubber particles were added to the concrete as precast pores to test the actual porosity, compressive strength and splitting tensile strength of the natural pumice concrete under different precast porosities. According to the change rule, the actual porosity, compressive strength and split tensile strength distribution were respectively fitted. The results show that there is a good correlation between the actual porosity of natural pumice concrete and the precast porosity, and then the empirical formula of rubber particle content and concrete strength is established, which provides a certain theoretical reference for the research on the porosity of natural pumice concrete.

Strength Model of Unsaturated Clays with Adsorptive Effects

The interactions between liquid phase and solid matrix in unsaturated clays can be divided into capillary effects and physicochemical effects according to their formation mechanism. The physicochemical effects (that is, the adsorption effects) become significant at low saturation degrees. However, current strength models for unsaturated soils almost are established on the basis of capillary mechanism, and the contribution of adsorption effects to soil strength is neglected. A binary-medium shear strength model is firstly proposed, involving the capillary and adsorption effects. The unsaturated clay is assumed to consist of two ideal parts, i.e., the ideal capillarity part and the ideal adsorption part, and then the corresponding ideal strength formulas are established. Furthermore, a participation function is used to reflect the degrees of capillary effects and adsorption effects. Finally, predictions are performed on the shear strength of unsaturated clays. After comparing predicted results and exiting test results, it is shown that the proposed model can well describe the strength of unsaturated clays.

Finite element modelling of interlocking stabilized laterite soil block walls

This study sought to use the stress–strain relationship of interlocking stabilized soil block (ISSB) masonry to model its behaviour and develop empirical formulae to aid in predicting its compressive strength. A finite element (FE) analysis adopting the Rankine failure criterion was performed using Abaqus software to simulate the deformability behaviour of the wall which was validated through experimental tests. The compressive strength, modulus of elasticity and density of ISSB defined in the FE model were determined by performing laboratory tests on laterite soil blocks stabilized with pozzolanic cement, hydrated lime and rice husk ash. Conversely, the predictive empirical formulae for the compressive strength of the ISSB masonry was developed by performing statistical multiple regression analysis. In addition to the mechanical properties of masonry, the FE simulation results indicated that the deformability behaviour of ISSB masonry is influenced by the type of stabilizer used on the target material. This dictated the stress distribution and vertical displacement on the masonry. A diagonally stepped failure mode was experienced in more brittle masonry while cone failure mode was observed in less brittle masonry assemblage.

Estimation of ultimate strength of ring-stiffened cylindrical shells under external pressure with local shell buckling or torsional buckling of stiffeners

This study discusses the ultimate strength and collapse behavior of ring-stiffened cylindrical shells under external pressure with local shell buckling or torsional buckling of stiffeners. In past studies, the effect of initial deflection shape on the ultimate strength has not been completely elucidated. Additionally, a clarification of the collapse behavior and theoretical formulation based on it has not yet been reached. Therefore, in this study, the influence of the initial deflection shape is investigated using eigenmodes obtained from the elastic buckling eigenvalue analysis and the hungry-horse mode described by a simple equation. Then, the ultimate strength analyses of 432 models of ring-stiffened cylindrical shells with various dimensions are carried out using the nonlinear finite element method. From the analysis, the collapse modes are classified into five categories, namely, the shell buckling (SB) collapse (localized mode SB-1 and uniform deformation mode SB-2), the torsional buckling (TB) collapse (localized mode TB-1 and uniform deformation mode TB-2), and the combined shell-torsional buckling collapse. A new slenderness ratio is proposed using the formula for strength when the circumferential stress reaches yield stress, and the formula for the elastic buckling strength developed previously by the authors. Then, theoretical formulas for the ultimate strength are developed using the slenderness ratio, which can rationally estimate the strength.

Punching fracture mechanism and strength formula of early-age shotcrete

In tunnel construction, shotcrete is sprayed on excavated surfaces to strengthen the walls and prevent rocks from falling off the tunnel face. Soon after, workers enter the face to erect the steel arch support. However, before entering, they must know the maximum rock size supported by the early-age shotcrete. This study aims to reveal the resistance and fracture mechanism of early-age shotcrete when a rock exfoliated from the tunnel face punches through shotcrete. To this end, we developed a novel experimental apparatus in which the strength deformation characteristics of shotcrete were evaluated through a laser scanner by punching a disc rock against the shotcrete on the substrate rock. The punching experiment was simulated, and the fracture mechanism was revealed using the discrete element method. The stress state of shotcrete sequentially reached the tensile failure criterion at the elements adjacent to the edge of the loaded zone. The elements of shotcrete progressively failed at the fracture process zone with punching. Finally, the punching strength of early-age shotcrete was formulated based on its fracture mechanism.

Seismic performance of a square HSS column to H-section beam bolted connection with double cover plate

This study presents six pseudostatic tests on square hollow section steel (HSS) column to H-section beam bolted connections with double cover plates. The failure modes, load–displacement hysteresis curves, and backbone curves of the joints were obtained, as were the energy-dissipating capacity, stiffness, and strength. The seismic energy of the connections is dissipated by slip between the contact surfaces and plastic deformation of the beam, clamp plates and bolt holes. The joints have good rotation capacity, energy-dissipation capacity, and reasonable strength and stiffness. The connections are rigid used in bracing frame and unbracing frame before slip and semirigid for both after slip. They are full-strength in terms of strength classification. Before the interstory drift reaches 0.05, no obvious inelastic deformation occurs, indicating that the connections can be easily repaired by repositioning the connection and retightening the bolts after a severe earthquake because the interstory drift will be much less than 0.05 during a severe earthquake. A finite-element model (FEM) was established and validated through a comparison of the finite element analysis (FEA) and test results, and the bolt tension, stress distribution of the beam, and rotation of the column flange splicing connection were obtained from the FEA results. The tension of the bolt in the beam web decreased slightly, while the tension of the bolt in the beam flange decreased to 60–70% of the original pre-tension when the interstory drift reached 0.06. The column flange splice connection is rigid. Simplified formulas for joint strength were deduced and validated by testing and FEA.

Estimation of tensile strength and moduli of a tension compression bi modular rock

The Brazilian test has been widely used to determine the indirect tensile strength of rock, concrete and other brittle materials. The basic assumption for the calculation formula of Brazilian tensile strength is that the elastic moduli of rock are the same both in tension and compression. However, the fact is that the elastic moduli in tension and compression of most rocks are different. Thus, the formula of Brazilian tensile strength under the assumption of isotropy is unreasonable. In the present study, we conducted Brazilian tests on flat disk-shaped rock specimens and attached strain gauges at the center of the disc to measure the strains of rock. A tension-compression bi-modular model is proposed to interpret the data of the Brazilian test. The relations between the principal strains, principal stresses and the ratio of the compressive modulus to tensile modulus at the disc center are established. Thus, the tensile and compressive moduli as well as the correct tensile strength can be estimated simultaneously by the new formulas. It is found that the tensile and compressive moduli obtained using these formulas were in well agreement with the values obtained from the direct tension and compression tests. The formulas deduced from the Brazilian test based on the assumption of isotropy overestimated the tensile strength and tensile modulus and underestimated the compressive modulus. This work provides a new methodology to estimate tensile strength and moduli of rock simultaneously considering tension-compression bi-modularity.

A review of the role of underground measurements in the historical development of rock engineering in South Africa

SYNOPSIS This paper describes some important aspects associated with historical underground measurements in South African gold and coal mines. Deformation measurements were used to confirm the use of elastic theory to simulate the rock mass behaviour in the Witwatersrand gold mines in the 1960s. Although a prominent time-dependent component of stope closure was measured as early as the 1930s, it was ignored owing to the benefit of adopting elastic theory. Neglecting the time-dependent response of the rock for many decades resulted in important aspects such as the effect of mining rate, the effect of advance per blast, and the need for enhanced design criteria not being explored. Recent work is only now starting to address this gap in knowledge. In-situ measurements of large coal specimens in the 1960s and 1970s indicated that a linear formula may possibly be a better approximation of coal pillar strengths. This alternative formulation was never adopted, however, as the power law strength formula was already deeply entrenched in the industry at that stage. In spite of these apparent failures to continuously generate and adopt new knowledge, a key lesson learnt is that major advances in rock mechanics will not be possible without careful monitoring of the rock mass behaviour in experimental sites. Areas requiring further research, such as pillar strength formulae for the Bushveld Complex and enhanced design criteria for the gold mines, can only be developed using extensive underground monitoring programmes. Keywords: rock engineering, underground monitoring, elastic theory, time-dependence, pillar strength.

Study on calculation method of stability for embedded penstocks with stiffener ring under external pressure

A three-dimensional FEM(finite element model)is established, including penstocks with initial defect (ovality), backfill concrete, drainage cushion and surrounding rock. The nonlinear static calculation of the model is carried out. The stability of penstocks with backfill concrete, drainage cushion and surrounding rock under external pressure is studied. The sensibility of the embedded penstocks to initial defect, initial gap and elastic modulus of drainage cushion is analyzed. The results of finite element method, Jacobsen method and strength formula in SL281 are compared and analyzed. The results indicate that the FEM of penstocks, backfill concrete and surrounding rock with initial defects is easy to converge by nonlinear calculation; the ovality and gap have little influence on the critical external pressure of the embedded penstocks with stiffener ring, while the drainage cushion has a certain influence on the critical external pressure; the critical external pressure calculated by SL281 is low and safe; compared with Jacobsen method, the critical external pressure of the finite element method is increased by about 14%; for the embedded penstocks with drainage cushion, the finite element method can be used to calculate the influence of the drainage cushion on the critical external pressure, and the appropriate reduction factor can be obtained, and then the Jacobsen result can be modified by the reduction factor.

A method for determining unsaturated strength parameters in stability analysis of loess slope

In recent years, with the rapid development of social economy and progress of human activities in loess area, the Loess Plateau become one of the areas with the most serious soil erosion and the most frequent occurrence of geological disasters in the world. Landslide, collapse, debris flow and ground subsidence are common geological disasters in the Loess Plateau, resulting in a more fragile ecological environment. Therefore, it is very important to accurately predict the stability of loess slope for engineering safety and ecological protection in loess region. But loess is a typical unsaturated soil. the formula of unsaturated strength is seldom used in practical applications. The reason is that the matric suction is difficult to measure. And it cannot be applied in engineering practice. In this paper, based on unsaturated soil shear strength formula of Fredlund, the direct shear test under different moisture content is conducted with the samples of Q1 loess. The effective cohesion and the effective internal friction angle are obtained. Through the matric suction test, the soil-water characteristic curve is plotted. Combined cohesion and matric suction, the strength parameters of unsaturated loess in formula of Fredlund can be informed.

Undue Hardness/Modulus Ratio Claims instead of Physical Penetration Resistance and Applications with Mollusk Shells

The Nanoindentation is a precise technique for the elucidation of mechanical properties. But such elucidation requires physically based interpretation of the loading curves that is widely still not practiced. The use of indentation hardness H and indentation modulus Er is unphysical and cannot detect the most important phase-transitions under load that very often occur. The claim that H versus E plots relate linearly for all different materials is neither empirically found nor correctly deduced. It is most dangerous by producing incorrect materials properties and misleading. The use of H/E (that is also called “elasticity index”) in complicated formulas for brittle parameter, yield strength, toughness, and so-called “true hardness” is also in error. The use of H/E cannot reveal the true qualities of materials without considering phase-transitions under load that require the correct exponent 3/2 on h for the loading curves (instead of disproved 2). This is exemplified with the physical data of different mollusk shells that experience phase-transitions, a new bionics model, and different contributions for their strengthening. The data are compared to the ones of aragonite and calcite and vaterite.

Strength Prediction Formula of Eco-Concrete Based on Cementitious Paste Strength and Aggregate Size

In order to better understand the performance of eco-concrete, this experiment selected three kinds of waterbinder ratio and 4 kinds of aggregates to prepare eco-concrete, and studied the prediction formula of its compressive strength. The results showed that when the aggregate size is fixed, the compressive strength of eco-concrete decreases with the increase of porosity and the decline of cementitious paste strength; the connectivity porosity of eco-concrete is generally about 5% lower than the total porosity, so the total porosity is more suitable to express the strength formula of eco-concrete. The coefficient in the eco-concrete strength formula are mainly affected by the strength of the cementitious paste and the aggregate size. When the target porosity is fixed, the larger the aggregate size, the higher the compressive strength of eco-concrete. When the workability of cementitious paste is constant, the actual porosity of eco-concrete can be expressed by target porosity and paste strength, and the strength prediction formula of eco-concrete expressed by paste strength, aggregate particle size and target porosity shows a good applicability, and has certain reference significance for the practical engineering application of eco-concrete in the future.

Research on the Three‐Dimensional Power Frequency Electric Field Measurement System

It is of great significance to accurately provide electric field information for electric power operators and electric power inspection equipment to ensure the safety of live working robots and electric power workers. In this paper, the principle of parallel plate charge induction is used to detect electric field signals and the influence of the inherent capacitance of the parallel plate on the back‐end circuit is considered. An equipotential ring is used as the structure of the sensing unit to eliminate the uncertainty generated by the edge electric field. The parameters of the sensor probe are determined by the principle of differential‐integration, and its structure is analyzed and designed. The consistency of the designed sensor probe was analyzed, and the results show that the consistency of the sensor is better. We have measured the sensitivity coefficients of the six probes, and the average absolute deviation reached 0.031556. The fits were all above 0.9995. In addition, a three‐dimensional power frequency electric field measurement system that is easy to manufacture is designed using the hexahedral structure, which solves the problem of inaccurate electric field measurement caused by the parallel plate probe and the field source being not perpendicular, and the combined field strength formula of nonuniform electric field was obtained. In the laboratory environment, the three‐dimensional power frequency electric field measurement system produced in this paper is compared with the electric field simulated by an electric field simulation tool. The test results show that the deviation between the measurement system and simulation is within ±0.55%, the measurement range is 1 kV/m–200 kV/m, the resolution is ≥1 V/m, and the maximum electric field can be measured at 200 kV/m. The nonlinear error is 2.15%, and the sensitivity coefficient is 19.10 mV/(kV · m−1), which meets the measurement requirements of the power frequency electric field and can be applied to the actual power frequency electric field measurement.

Structural Analysis of Yoke Part in Design of Driveshaft

Driveshaft used for transmitting torque and rotation, is one of the most important components in motor vehicles. It is required to connect the other components of the drivetrain such as transmission and differential to each other. Basically, comprises of one or more universal joints, yoke parts, splined parts and sometime center support bearing. Each compo-nent on it performs different functions such as angular and axial move-ment. Every component on driveshaft are subjected to torsion and shear stress. Thus, in the design and analysis processes each component should be sufficiently strong against to these all. In this study, numerical and an-alytical methods to design the weld yoke, were investigated and com-pared with each other. In the numerical studies finite element analysis (FEA) implemented by using two different loading conditions, force cou-ple and moment. And the strength formulas were used in the scope of an-alytical method. As a result of the study, the stress on critical section ob-tained from FEA, supports the results from analytical method. Thus, ana-lytical method can be used for the weld yoke design and the FEA can be implemented by using any of force couple or moment as loading type.

A new formula of punching shear strength for fiber reinforced polymer (FRP) or steel reinforced two-way concrete slabs

This study is to propose a new punching shear strength formula for either FRP or steel reinforced two-way concrete slabs based on deterministic and probabilistic methods. Former is to employ the test to prediction ratio and latter is newly suggested approach that can guarantee more reliable prediction considering the significant uncertainties to minimize the possibility of over-estimating punching shear strength. For comparative study, the selected test results and the previous formulas are employed. The proposed new formula exhibits the most accurate test to prediction ratio among the existing formulas. Furthermore, it renders the lowest probability of exceedance that the predicted punching shear strength exceeds the nominal punching shear strength. The proposed new formula can minimize the probability of over-estimating the punching shear strength. Consequently, it can lead to enhance the accuracy, safety and reliability of punching shear strength design of either FRP or steel reinforced two-way concrete slabs.

Flexural buckling behavior of corroded hot-rolled H-section steel beams

This paper mainly investigates the flexural buckling behavior of corroded hot-rolled H-section steel beams under four-point bending. A total 43 observations comprising of five experiments and thirty-eight numerical analysis results were reported to investigate the corrosion types, degrees and locations on the initial imperfections, failure modes and the flexural buckling behavior of steel beam. Based on the analysis, a recommended formula of the flexural buckling strength of corroded steel beams is derived using the direct strength method. The results show that the tested specimens fail with the local buckling of upper flange and web near the mid-span, but the failure positions and the buckling half-wavelength are different with corrosion degrees. The results also show that the yield load, buckling load and ultimate load of tested specimens decrease with the corrosion degrees increasing. When the corrosion ratio reaches 16.88%, the yield load decreases at a ratio of 21.4%, the critical buckling load decreases by 33.2%, the ultimate load after buckling decreases at a ratio of 28.3%, and the ductility coefficient decreases by 59.4%. Finally, the comparison between predicted and actual flexural strength indicates that the proposed formula can calculate the flexural buckling capacity of corroded H-section steel beams with varying degrees of corrosion.

Experimental study on granite acoustic emission and micro-fracture behavior with combined compression and shear loading: phenomenon and mechanism

One element that is essential to consider in underground mining engineering applications is the possibility of pillar failure, which can result in deadly geological disasters, including earthquakes and surface subsidence. Pillars are commonly present under an inclined state and are significantly dependent upon combined compression and shear loading. However, many scholars regard the pure uniaxial compression strength (UCS) of rock as the main evaluation index of pillar strength, which is inconsistent with the field practice. Hence, the present study developed a novel combined compression and shear test (C-CAST) system, which was applied in the investigative acoustic emission (AE) experiments to characterize the failure mechanism and micro-fracture behavior of granite specimens at different inclination angles. The experimental results presented the exponential decrease of UCS of inclined specimens with increase in the shear stress component. Changes in the inclination angle with a range of 0°–10° produced a splitting-shear failure fracture mode from the initial splitting failure. In comparison, an increase in the inclination angle from 10° to 20° produced a single shear failure fracture mode from the initial combined splitting-shear failure. The specimens exhibited nonlinearly reduced microcrack initiation (CI) and damage (CD) thresholds following an increase in the inclination angle, suggesting the dependence of the microcrack initiation and propagation on the shear stress component. The ratio of CI and CD thresholds to inclined UCS varies within a certain range, indicating that the ratio may be an inherent property of granite specimens and is not affected by external load conditions. Additionally, the rock fracture behavior was largely dependent upon the mechanism of shear stress component, as validated by the microcrack initiation and growth. Finally, a modified empirical formula for pillar strength is proposed to investigate the actual strength of inclined pillar. Results of a case study show that the modified formula can be better used to evaluate the stability of inclined pillars.