Effective Stiffness Coefficients Research Articles

Generation a solution to the equations of elasticity theory for a layered strip basing on the principle of compressed mappings

A systematic presentation of the modified classical semi-inverse SaintVenant method as an iterative one is given on the example of generating a solution to the differential equations of elasticity theory for a long layered strip. The firstorder differential equations of the plane problem are reduced to the dimensionless form and replaced by integral equations with respect to the transverse coordinate, just as it is done in the Picard method of simple iterations. In this case, a small parameter appears in the integral equations before the integral sign as a multiplying factor, which is used to ensure convergence of solutions in accordance with the Banach’s principle of compressed mappings. The equations and elasticity relations are converted to a form that enables to calculate the unknowns consecutively, so that the unknowns being calculated in one equation are the inputs for the next equation, and etc. Fulfillment of the boundary conditions at the long edges leads to ordinary differential equations for slowly and rapidly changing singular components of the solution with sixteen effective stiffness coefficients that are defined by integrals from the given ones as a stepped function of Young's moduli for each layer. Integrating of these ordinary differential equations makes it possible to obtain the formulas for all the required unknowns of the problem, including transverse stresses that are not defined in the classical theory of the beam and solutions of the edge effect type, and to fulfill all the boundary conditions for the elasticity theory problem. The solution of three boundary value problems of the strip elasticity theory is provided such as for a two-layer strip with layers of the same thickness and different thicknesses, and a strip with an arbitrary number of layers. Formulas for all unknowns of the problem are obtained.

Graph neural network for predicting the effective properties of polycrystalline materials: A comprehensive analysis

We develop a polycrystal graph neural network (PGNN) model for predicting the effective properties of polycrystalline materials, using the Li7La3Zr2O12 ceramic as an example. A large-scale dataset with >5000 different three-dimensional polycrystalline microstructures of finite-width grain boundary is generated by Voronoi tessellation and processing of the electron backscatter diffraction images. The effective ion conductivities and elastic stiffness coefficients of these microstructures are calculated by high-throughput physics-based simulations. The optimized PGNN model achieves a low error of <1.4% in predicting all three diagonal components of the effective Li-ion conductivity matrix, outperforming a linear regression model and two baseline convolutional neural network models. Sequential forward selection method is used to quantify the relative importance of selecting individual grain (boundary) features to improving the property prediction accuracy, through which both the critical and unwanted node (edge) feature can be determined. The extrapolation performance of the trained PGNN model is also investigated. The transfer learning performance is evaluated by using the PGNN model pretrained for predicting conductivities to predict the elastic properties of the same set of microstructures.:

Performance of special RC shear walls under lateral cyclic and axial loads

Reinforced concrete (RC) shear walls are common structural elements, although their cyclic behavior under different combinations of axial and lateral loading requires further study. The boundaries of flexural-dominated walls experience the greatest stress and strain; thus, rebar layouts are vital in this area and have significant effects on the cyclic behavior of a wall. In the current study, three full-scale walls were designed and constructed using the ACI318-19 special structural wall criteria with boundary elements placed at each end of the wall. Cyclic testing was performed on RC shear walls for different lateral and axial load combinations. These large-scale tests showed how axial loads affect the seismic performance of special RC shear walls. The seismic parameters of the force–displacement hysteresis curves, concrete strain, rebar strain, dissipated energy and stiffness are presented and discussed. The experimental findings demonstrate the effect of axial loading on the wall deformation capacity, strength capacity and mode of failure. Experimental backbone curves for numerical models of walls as recommended by ASCE41-17 revealed that the ASCE model overestimates the effective stiffness of walls with axial loads of less than 10% fcAg, A four-line model is proposed to estimate the force–deformation relationship. It is demonstrated that the effective stiffness coefficient should be a function of the axial load ratio.

A novel modeling and virtual testing method of hydrogen storage COPV considering stochastic wrinkle defects

Manufacturing imperfections lead to the uncertainty of safe performance of hydrogen storage composite overwrapped pressure vessels (COPVs). The main objective of this research is to clarify the influence of stochastic wrinkles on the mechanical responses of hydrogen storage COPVs subject to the internal pressure. A novel modeling approach of macro-scale COPV introduced with meso-scale wrinkles is investigated for the finite element (FE) analysis. Where the wrinkles are considered as mathematical perturbations in the form of effective stiffness coefficients. Both wrinkle severity and spatial distribution are taking as the stochastic variables to estimate the defect-induced displacement responses. Multiple computations are conducted as virtual tests to obtained the statistical characteristics of displacement responses corresponding to wrinkle distribution variables. Numerical results indicate a more sensitive response characteristic of circumferential displacement under internal pressure. And the wrinkles distributed in dome part shows a more distinctive displacement distortion than that in cylindrical part.

Betonarme Kirişlerin Moment-Eğrilik ve Etkin Kesit Rijitlkleri

In determining the seismic performance of reinforced concrete (RC) structures in national and international earthquake regulations, it is desired to use effective section stiffness of the cracked section in RC structural elements during the design phase. Although the effective section stiffness of the cracked section is not constant, it depends on parameters such as the concrete strength and reinforcement ratio. In this study, RC beam models with different concrete strength, tensile and compression reinforcement ratios were designed to investigate nonlinear moment-curvature relationships and effective stiffness coefficients. Analytically investigated parameters were calculated from TBEC (2018), ACI318 (2014), ASCE/SEI41 (2017), Eurocode2 (2004) and Eurocode8 (2004, 2005) regulations and moment-curvature relationships. The effective section stiffness coefficient obtained from the analyses were compared with the effective section stiffness coefficient given for RC members in different regulations. The results obtained at the end were examined by comparing them according to different parameters and models. For constant concrete strength and tensile reinforcement ratio in RC beams, with increasing compression reinforcement ratio, effective stiffness coefficient values increase. In RC beams with constant compression and tensile strength ratio, effective stiffness coefficient values increase with increasing concrete strength. The compression reinforcement ratio has been proved to be effective on the maximum moment bearing capacity of the RC beams, effective flexural stiffness and effective stiffness coefficient and ductility of the sections.

Free Vibration of Inclined Twisted Cables

This paper is aimed at simulating and investigating the coupled translational and rotational vibrations occurring simultaneously in inclined sagged cables. The three-dimensional behavior of the single-layered six wires strand stiffness results are reduced to effective one-dimensional behavior from the elasticity-based finite element behavior analyses under axial tension and torsional loads. These are directly compared with multiple one-dimensional analytical model results. The effective stiffness coefficients agreed well for the actual lay angle of the cable and at angles below 20 degrees with finite element models where internal contact was not considered. To find the cable natural frequency and corresponding modal shapes the derived primary stiffness and mass matrices are discretized over the inclined sagged cable using a finite element model where the two-node cable element has three translational and three rotational degrees of freedom. The vibration behavior is also studied using extensive experimental tests using the same cable geometry and material used in the numerical calculations. In addition to the physical experiments, the finite element model accuracy was also compared with results from a well-known analytical model available from the literature for horizontal cables, and the influence of the inclination angle variation was also investigated and compared with the computer finite element software ABAQUS for the same purpose. The results found confirm the correctness of the derived formulation, mathematical, and psychical importance of the six-degrees of freedom finite element model developed and the efficiency in evaluating the coupled cable dynamic behavior. It addition, the results highlight the fundamental dynamics of inclined cables and the role of the inclination angle, sag, and weight of the cable.

Seismic dispersion, attenuation and frequency-dependent anisotropy in a fluid-saturated porous periodically layered medium

SUMMARY The White model is generally used to quantify seismic dispersion and attenuation caused by interlayer wave-induced fluid flow. However, this model derives P-wave dispersion and attenuation only in the direction perpendicular to the layer. Thus, in this study, we derive the exact analytical solutions for full effective stiffness coefficients of a fluid-saturated layered porous medium so as to calculate the angle-dependent seismic dispersion and attenuation and frequency-dependent anisotropy. The analytical solution for fluid pressure is derived using Biot's equations of quasi-static poroelasticity. Then, the mean stress or strain is obtained through its relationship with fluid pressure, and the stress–strain value is used to derive the effective stiffness coefficients. This is followed by the calculation of the angle-dependent seismic dispersion and attenuation and frequency-dependent anisotropy. Our results show that the layered medium with alternating gas- and brine-saturated layers having the same matrix is isotropic at all frequencies. However, the layered medium with periodically distributed highly porous, thin layers shows significant frequency-dependent anisotropy. In the case of P wave, the largest magnitudes of dispersion and attenuation are observed in the direction perpendicular to the layer, while those for SV wave occur at the incident angle of around 45°. When our model is compared with the previous models, the low- and high-frequency limits of our model are found to be identical to the poroelastic Backus averaging. In addition, the widely used single relaxation function approximation is found to be a good approximation of our exact solutions. Our proposed model is easy to use and can be applied in the seismic exploration of the layered earth.

Fabrication and mechanical behavior of an all‐composite interlocked triangular honeycomb sandwich structure: Experimental investigation and numerical analysis

AbstractThe interlocked composite honeycomb structures have high specific strength and specific stiffness, convenient processing, and low cost with great application potential in aerospace, marine, construction, and civil fields. In this study, an effective method is proposed for manufacturing an all‐composite interlocked triangular honeycomb (CITH), and the quasi‐static mechanical properties of the honeycomb and the corresponding sandwich structure (CITHSS) are examined. Through experimental tests, the basic mechanical properties of CITH and CITHSS are analyzed. Further, the effective strength and stiffness coefficient of the slotted carbon sheets constituting CITH are measured through tensile experiments. The in‐plane stiffness model of CITH is derived based on the continuous equivalent method. The failure strength models of CITHSS are also established. At the same time, the failure modes under three‐point bending and edge compression loads are predicted. The experimental results reveal that compared with the interlocked Kagome and square honeycomb, the specific strength of CITH is increased by 27.8% and 24.4%, respectively. Further, the specific stiffness is increased by 148.4% and 8.3%, respectively. Compared with aluminum honeycomb sandwich, the compressive and bending specific strengths of CITHSS are increased by more than 46.5% and 15.2%, respectively. The debonding failure and edge effect are found to be the main weakness of CITHSS. Overall, CTIH and CITHSS exhibit excellent mechanical properties and create feasible options for processing complex multifunctional composite honeycombs by interlocking technology.

CFD-Predicted Rotordynamic Characteristics for High-Temperature Water Liquid Seal Considering Tooth Deformation

With the development of high-temperature centrifugal pump, the temperature of the medium in the pump must be higher than the normal water temperature. It is particularly important to study the rotordynamic characteristics of the seal at high temperature due to it being the core component of the rotor system. This paper takes the high temperature water liquid seal as a research object to study its rotordynamic characteristics based on the fluid-solid-thermal coupling, the deformation of seal teeth under thermal and dynamic loads was calculated. Based on the test rig, the leakage flow rate and drag power loss of water liquid seal at 20 °C, 50 °C, and 86 °C temperatures were tested and compared with the CFD (Computational Fluid Dynamics) calculation. Meanwhile, the DEFINE-CG-MOTION and DEFINE-PROFILE control macro were used to establish the rotor whirling equation, the frequency-independent rotordynamic coefficients (K, k, C, c) and frequency-dependent rotordynamic coefficients (Keff,Ceff) were evaluated by transient CFD method. This analysis was done at three different pressure drops (2.08, 4.12, and 8.25 bar) and three rotational speeds (2000, 4000, and 6000 r/min). The results show that with the increase of water temperature, both the leakage flow rate and drag power loss decrease, indicating the 86 °C water seal has a better sealing capacity. From the rotordynamic perspective, with the increase of water temperature, the direct stiffness coefficient decreases, and the effective stiffness coefficient Keff for 20 °C water seal possesses a better stiffness capability than the other two temperature seals. The effective damping coefficient Ceff for 20 °C water seal is larger than the other two temperature seals, which means it is more stable for the rotor system.

Experimental research on the bending performance of locked coil wire rope and Galfan strand

As a key component in prestressed structures, the bending stiffness of a cable significantly affects the dynamic response characteristics, such as vibration control and cable tension measurements using the vibration method. Based on the beam theory, this study reports experimental results on the bending performance of locked coil wire ropes and Galfan strands. Quasi-static bending tests under different end treatments and prestress levels were conducted, using four common specifications of locked coil wire ropes and three specifications of Galfan strands, to infer the effective flexural rigidity and to study the flexural performance of the cables. The results show that the load-deformation curves of unprestressed cables are bilinear, which is similar to that of a simply supported beam. The physical stiffness of the prestressed cables is not obvious. The geometric stiffness produced by the prestress dominates, and the effective stiffness coefficient can exceed 1000. Based on the Papailiou theory and beam theory, a predictive model is proposed for predicting the bending stiffness of cables under high prestress conditions. This model provides a reference for bending stiffness predictions of cables.

Effective flexural stiffness for reinforced concrete shear walls having confined boundary elements

In the design of reinforced concrete (RC) shear walls strength, ductility and effective stiffness of the elements must be taken into account and are important parameters in terms of structural safety. Accurate estimation of the ductility and effective stiffnesses of RC members has always been an attractive subject of study as it provides a reliable estimate of the capacity of buildings under seismic loads. In this study, RC shear wall models with different concrete strength, longitudinal and transverse reinforcement ratios were designed to investigate effective section stiffness and coefficients. The effective stiffness of the cracked section in the RC shear walls designed in different parameters were analytically obtained. Analytically investigated parameters were calculated from TBEC (2018), ACI318 (2014), ASCE/SEI41 (2017) and Eurocode8 (2004, 2005) regulations and nonlinear behaviors. The results obtained according to different design parameters were compared and examined. In the relations suggested for the effective section stiffness coefficient, the confining effect is not taken into account as in the regulations. Therefore, it means neglecting the effects of parameters such as concrete strength, confining effect and axial load levels acting on the section. This situation can lead to unrealistic results in the design and evaluation of RC elements. For this reason, determining the moment-curvature relationship in the design and evaluation of RC elements and obtaining effective section stiffness values are of great importance in order to obtain more realistic results.

Computer simulation of the effect of particle stiffness coefficient on the particle-fluid flows

The Computational fluid dynamics (CFD)–discrete element method (DEM) numerical simulation may be applied to predict the hydrodynamic behavior of dense particle–fluid flows. The main drawback of this simulation is the long computational time required owing to the large number of particles and the minute time-step required to maintain a stable solution. In this work, a new method to improve the efficiency and accuracy of CFD–DEM simulations is presented. The particle stiffness coefficient is used as a flexible parameter to improve the accuracy and efficiency of the model. The particle concentration distribution results are compared with experimental one’s to derive the optimum effective stiffness coefficient of particles for CFD-DEM simulations. The comparisons of the results indicate that although the application of stiffness coefficients with moderate values causes normal penetration depths of up to the particle radius, the simulations still show good results. The results also show that the stiffness coefficient and time step are strongly dependent of the fluid inlet velocities, particle diameters, particle inlet concentration and fluid type, and the simulation accuracy decreases greatly with increasing the time steps.

Determination of effective stiffness properties of multilayered composite beams

Starting from a Cosserat-type model for curved rods, we derive analytical expressions for the effective stiffness coefficients of multilayered composite beams with an arbitrary number of layers. For this purpose, we employ the comparison with analytical solutions of some bending, torsion, and extension problems for three-dimensional beams and rods. The layers of the composite beam consist of different orthotropic or isotropic non-homogeneous elastic materials. We apply the obtained general formulas to calculate exact analytical solutions of some beam problems and compare them with corresponding results of numerical simulations. The numerical study shows a wide range of validity and applicability of the obtained formulas.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle that leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuthally dependent, introduce a Gaussian function to describe the fractures’ azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over the azimuth. We investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the [Formula: see text] plane than in the [Formula: see text] plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can degenerate into the VFTI medium.

Usage of Coulomb friction acting on a wedge to attenuate vibration.

Considered herein is a small wedge-shaped block that contacts a rough surface on its angled face, with contact maintained by precompressed springs. The wedge is connected to a large mass that is subjected to a harmonic excitation. The development begins with a derivation of equations for the normal and friction forces, which are shown to depend on the displacement and acceleration of the wedge as well as the external force. Enforcing Coulomb's law for sliding leads to a differential equation of motion in which the effective inertia and stiffness coefficients switch values according to whether the wedge advances or retreats. Algebraic expressions for the displacement in either state are supplemented by an assessment of sticking based on Coulomb's static friction rule. The solutions for motion and the assessment of sticking are assembled in a simple, yet general, algorithm that only requires calculation of algebraic formulas. Transient waveforms of displacement, acceleration, and transmitted force are calculated for a harmonic excitation at the natural frequency of the frictionless system. It is found that very large viscous damping ratios would be required to obtain the same steady-state amplitude.

Seismic Performance of a New Type of Reinforced Concrete Energy Dissipation Structure

High-performance fiber-reinforced concrete (HPFRC) is an ideal energy dissipation material because of its high tensile ductility and multiple fine-crack development. An HPFRC energy dissipation wall was installed in a reinforced concrete (RC) frame to form a new RC frame-HPFRC energy dissipation wall aseismic structure. Two half-scale RC frame-HPFRC energy dissipation wall specimens were designed and constructed. Quasi-static tests were performed to study the failure mechanism, deformation performance, stiffness degradation, and energy dissipation performance. The effective stiffness of the RC frame-HPFRC energy dissipation wall at the peak load was analyzed. The test results indicate that RC frame-HPFRC energy dissipation wall structures can achieve the seismic fortification objective of being “repairable after major earthquake”. Compared with the RC frame with one energy dissipation wall, the lateral load capacity of the frame with two energy dissipation walls was improved by 38.3%, and the initial lateral stiffness increased by 1.78 times, while the post yield lateral stiffness increased by only 20% to 30%; the energy dissipation capacity at different damage states increased by 10% to 175%, while the lateral deformation capacity was basically the same. The energy dissipation mechanism of the RC frame-HPFRC energy dissipation wall structure includes the energy dissipation caused by the deformation of the wall, the slipping at the connections of the upper and lower ends of the wall with the frame beams, and the deformation of the RC frame. The effective stiffness coefficients of the RC frame and the HPFRC energy dissipation wall at the peak load are 0.11 and 0.13, respectively.

Numerical Modeling of Static and Rotordynamic Characteristics for Three Types of Helically Grooved Liquid Annular Seals

Abstract This paper deals with numerical predictions of the leakage flowrates, drag power, and rotordynamic force coefficients for three types of helically grooved liquid annular seals, which include a liquid annular seal with helically grooved stator (GS/SR seal), one with helically grooved rotor (SS/GR seal), and one with helical grooves on stator and rotor (GS/GR seal). A novel transient computational fluid dynamics (CFD)-based perturbation method was proposed for the predictions of the leakage flowrates, drag power, and rotordynamic force coefficients of helically grooved liquid annular seals. This method is based on the unsteady Reynolds-averaged Navier–Stokes (RANS) solution with the mesh-deformation technique and the multiple reference frame theory. The time-varying fluid-induced forces acting on the rotor/stator surface were obtained as a response to the time-dependent perturbation of the seal stator surface with the periodic motion, based on the multiple-frequency elliptical-orbit stator whirling model. The frequency-independent rotordynamic force coefficients were determined using curve fit and fast Fourier transform (FFT) in the frequency domain. The CFD-based method was adequately validated by comparisons with the published experiment data of leakage flowrates and fluid response forces for three types of helically grooved liquid annular seals. Based on the transient CFD-based perturbation method, numerical results of the leakage flowrates, drag powers, and rotordynamic force coefficients were presented and compared for three types of helically grooved liquid annular seals at five rotational speeds (n = 0.5 krpm, 1.0 krpm, 2.0 krpm, 3.0 krpm, and 4.0 krpm), paying special attention to the effective stiffness coefficient and effective damping coefficient.

Comparison of equivalent seismic load and response spectrum methods according to TSC 2018 and TSC 2007

In this study, two different analysis methods were compared; the first is a linear static analysis method and the second is a linear dynamic analysis method. First one is the Equivalent Seismic Load Method, which is a linear static method where seismic loads can be obtained by applying a simple calculation. The second method, the Response Spectrum method, is a linear dynamic analysis method which obtains the seismic loads using more complex statistical calculations. For this analysis study, 18 structural models with 3 different building heights were analyzed according to the conditions of Equivalent Seismic Load Method and Response Spectrum Method specified in both TSC 2007 and TSC 2018 and base shear forces obtained as a result of these analyzes were compared. As a result of analysis; compared to the results obtained from TSC 2007, due to the effective stiffness coefficients specified in TSC 2018, it was observed that the base shear forces obtained for both methods were lower and the modal period values were longer in the analyzes applied according to TSC 2018. This means that the structural systems created with the designs according to TSC 2018 are more ductile than the structural systems created with the designs made according to TSC 2007. Base shear forces obtained by 2 different analysis methods applied according to regulations stated in both TSC 2018 and TSC 2007; it was observed that the base shear forces obtained by the Equivalent Seismic Load Method were higher than the results of the Response Spectrum Method.

Doubly periodic array of coated cylindrical inclusions model and applications for nanocomposites

An analytical method is proposed to solve the problem of an infinite elastic matrix containing a doubly periodic array of coated cylindrical inclusions under antiplane shear. The elastic fields in the inclusions, the coatings/interphases and the matrix are derived, which are used to investigate the stresses and the effective stiffness coefficients of the nanofiber composites. Numerical examples demonstrate the size dependence of the stress and the effective stiffness coefficient, and the effects of the interphase thickness and stiffness and array configurations of the inclusions on the effective stiffness coefficient. A finite element analysis is used to benchmark the effective stiffness coefficient predicted by the proposed model, in which excellent agreement is observed. When letting the interphase be thin enough, the proposed coated inclusions model can be used to simulate the zero-thickness interface model, which is validated by the results comparisons of the two models. Instabilities of the stress fields are observed under certain conditions in simulating the zero-thickness interface model.

Failure tests and bearing performance of prototype segmental linings of shield tunnel under high water pressure

The occurrence and characteristics of structural failure under high water pressure and the evaluation of structural bearing capacity are of great significance in the rational design of shield tunnels. In this study, the failure process of two types of segmental lining structures used in the Shiziyang Tunnel in China, namely, the straight joint assembly structure (STRS) and staggered joint assembly structure (STGS), are investigated and summarized with prototype tests. The differences in the failure characteristics between the two types of lining structures are observed and analyzed, and two indexes are proposed to evaluate the damage status of the entire structure and local structure by analyzing and interpreting the failure phenomena during the tests. The results show that (1) The failure processes of both STRS and STGS under high water pressure perform as: the accumulation of previous occurred strength damage of segments ultimately leads to the displacement instability failure of structure. However, the difference is that besides the occurrence of large number longitudinal penetrating cracks at segments, there are local crushing and shear cracks occurred at the joints in STRS. (2) The failure processes of STRS and STGS under high water pressure can be divided into three stages: normal deformation stage, strength damage stage, and displacement instability stage. (3) With the proposed two indexes, the failure phenomena and structural bearing capacities at various stages of the failure process can be theoretically analyzed and quantitatively evaluated. The effective stiffness coefficient βe (specifically, βte for STRS and βce for STGS) is recommended to assess the structural bearing status, and the residual bearing capacity coefficient Rbc is suggested to evaluate the residual structural bearing capacity. (4) For STRS, when obvious cracks appear, βte is 0.83 and Rbc is 0.71; when significant deformation occurs, βte is 0.65 and Rbc is 0.52; and when the structure fails, βte is 0.4 and Rbc is 0.35. For STGS, when microcracks appear, βce is 0.67 and Rbc is 0.58; when the structure is significantly deformed, βce is 0.49 and Rbc is 0.43; and when the structure fails, βce is 0.18 and Rbc is 0.27. (5) In the loading process, βe and Rbc of STRS and STGS decrease constantly. For STRS, the two indexes rapidly decline after visible cracks appear, but for STGS, the decreasing amplitude is relatively small.