Rigidity Ratio Research Articles

Bayesian Inference and Condition Assessment Based on the Deflection of Aging Reinforced Concrete Hollow Slab Bridges

This paper presents a Bayesian inference framework for updating the structural rigidity ratio of aging hollow slab RC bridges using deflection measurements. The framework models the structural rigidity ratio as a stochastic field along the hollow RC slabs, using the Karhunen–Loeve (KL) transform to capture spatial correlation and variation. Bayesian inference is then applied using deflection data from static loading tests, supported by a finite element model (FEM) and a Kriging surrogate model to enhance computational efficiency. The posterior distribution of the structural rigidity ratio is derived using a Markov chain Monte Carlo (MCMC) sampler. The proposed method was tested on an RC bridge with hollow slabs, using deflection measurements taken before and after reinforcement. The Bayesian updates indicated increased structural rigidity ratios after reinforcement, validating the effectiveness of the reinforcement. The deflection predictions from the updated models closely matched the measurements, with the 95% confidence bounds encompassing most of the data. This demonstrates the method’s validity and robustness in capturing the structural improvements post-reinforcement.

Static deformation of a two-phase medium consisting of a rigid boundary elastic layer and an isotropic elastic half-space induced by a very long tensile fault

An analytical model is proposed to determine the static response of a multi-layered medium comprising of an underlying isotropic (ISO) elastic half-space that is in welded contact with an isotropic (ISO) elastic layer of uniform thickness H with a rigid boundary, induced by a tensile dislocation embedded in the layer. The integral expressions for stress fields are obtained by using the airy stress function. These integrals are calculated approximately, using Sneddon’s approach, by substituting the terms under the integral sign with a finite sum of exponential expressions. It is studied numerically and graphically how stresses vary with the change in the epicentral distance for different source locations embedded in the layer. The effect of the rigidity ratio is also analysed on the stress field. To examine the impact of the internal boundary, the stress fields in the layered and uniform half-spaces are compared graphically.

Patterning of multicomponent elastic shells by gaussian curvature.

Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.

Evaluation of Hysteretic Performance of Horizontally Placed Corrugated Steel Plate Shear Walls with Vertical Stiffeners

Corrugated steel plate shear walls (CSPSWs) have been widely utilized as lateral-resistant and energy-dissipating components in multistory and high-rise buildings. To improve their buckling stability, shear resistance, and energy-dissipating capacity, stiffeners were added to the CSPSW, forming stiffened CSPSWs (SCSPSWs). Evaluating the hysteretic performances of SCSPSWs is crucial for guiding seismic design in engineering practice. In this paper, the dissipated energy values of the SCSPSWs with different parameters were calculated. Based on the obtained dissipated energy values, the elastoplastic design theory of stiffeners was established, and the evaluation of the hysteretic performance of the SCSPSWs was provided. Firstly, a finite element (FE) model for analyzing the hysteretic performance of the SCSPSWs was developed and validated against hysteretic tests of the CSPSW conducted by the authors previously. Subsequently, using the validated FE model, approximately 81 examples of SCSPSWs subjected to cyclic loads were analyzed. Hysteretic curves, skeleton curves, secant stiffness, stress distribution, and out-of-plane displacement were obtained and examined. Results indicate that increasing the bending rigidity of the vertical stiffeners and the thickness of the corrugated steel plates, as well as reducing the aspect ratio of the corrugated steel plates, is beneficial for enhancing the load-carrying capacity, stiffness, and energy dissipation capacity of the SCSPSWs. Finally, the transition rigidity ratio μ0,h was proposed to describe the hysteretic performances. When the rigidity ratio is μ = 50, dissipated energy values of the SCSPSW could achieve 95% of the corresponding maximum dissipated energy. In engineering practice, hence, it is recommended to use stiffeners with a rigidity ratio of μ ≥ μ0,h = 50 to ensure desirable energy-dissipating capacity in the SCSPSW.

Hydrodynamic interactions and membrane damage for a pair of microcapsules in shear flow: Effect of membrane mechanical properties

We model the hydrodynamic interaction of two equal size capsules in simple shear flow. The capsules may have different mechanical membrane properties. The results are analyzed in terms of a macro scale model of capsule membrane damage. We show how the interaction between two capsules with a membrane rigidity mismatch may lead to damage of the more deformable capsule even when the base flow strength is below the damage threshold of both capsules. We provide charts of the peak deformation energy density in the two membranes as a function of the flow strength and the ratio of the elastic rigidity of the two capsules. Given a damage criterion, those charts can be used to determine when flow-induced damage will occur in a suspension of capsules with a distribution of mechanical properties.

Method of matched sections as a beam-like approach for plate analysis

A new numerical method in application to the plate problem is suggested. It starts from consideration of the rectangular elements, each operating by 6 beam-like parameters: four bending parameters (displacement, angle of rotation, bending moment, transverse force) and two rotation parameters (angle of rotation and twisting moment). So, contrary to the classical FEM approach, the conjugation between the adjacent elements occurs between the adjacent sections rather than in polygon vertexes (nodes), and this gives the name to the method – method of matched sections, MMS. Technically, 6 left-side and 6 lower-side parameters are 12 inlet parameters, while 6 upper-side and right-side parameters are 12 outlet parameters; each element is defined by 24 parameters. Outlet parameters are related to inlet ones by 12 matrix relations, which are derived from the approximate solution of each differential equation (equilibrium, physical, and geometrical equations) of the plate theory. The matrix relation between inlet and outlet parameters is written in a form suitable for applying the transfer matrix method. The numerical examples for the thin and Mindlin plates show the high efficiency and accuracy of the method. In particular, the results for the Mindlin plate for minimal thickness give the same results as the thin plate (no shear locking); the method is insensitive to cases when, for adjacent elements, the ratio of dimensions or ratio of rigidities (elastic constants) differ by several orders of magnitude. The application of the method for the thermal as well as for the vibration problem is considered. The possible extension of the method to any curved geometry is discussed, too.

DETERMINATION OF THE IMPACT ZONE OF ENABLING WORKS OF A NEW CONSTRUCTION ON THE SURROUNDING BUILDINGS

For modern urban construction in the compacted conditions of new sites, the question of the stability of soil massifs under existing buildings is relevant. The intensity of development of possible deformations largely depends on the mutual location of the base of the previously erected foundation and the pit for the new building. The article provides a methodology for determining the area of influence of the pit on the soil foundations of adjacent buildings, depending on the type of enclosing structures and the depth of the pit used. The impact zone was calculated for the pit using protective structures in the form of Larsen sheet piles, bored piles and a diaphragm wall. Corresponding zones of influence of a pit excavated to different depths using different types of pit construction are graphically determined. The scientific result can be explained by the fact that the idealized model of the influence zone takes into account the conditions under which the boundary of the influence zone of a new building can be limited to a distance at which the calculated value of additional subsidence of the soil massif or the base of the existing structure of the surrounding building does not exceed 1 mm. The dimensions of the influence zones are determined at different pit depths, which roughly correspond to the location of the one-, two-, and three-level underground structures of the building. Increasing the depth of the pit to two underground floors increases the zone of influence by 24-31% for the considered types of pit enclosure, and up to three floors - by 14-17%. It was established that the nature of the change in the zone of influence is similar for different types of enclosure structures, and the transition from rigid to flexible functioning of the pit enclosure depends on the ratio of the enclosure's rigidity and the excavation depth. As a practical result of the research, it can be used when choosing the type of construction of the pit to prevent the negative impact of the construction works of the new construction on the surrounding buildings. Keywords: underground construction, pit, concrete, piles, impact, modeling, optimization, parameters

A novel beam element with nine DOFs per node for resolving the warping-distortion compatibility in analysis of frames and curved beams made of I-sections

Warping-distortion coupling is common in frames and curved beams made of I-sections, which tends to decrease significantly the lateral and torsional resistance of structures. Traditionally, it has been difficult to consider such effects in structural analysis, because the warping and distortional degrees of freedom (DOFs) of two connected elements at a common joint cannot be easily transformed to a common coordinate system for global stiffness assembly. The purpose of this paper is to conquer such a problem. By introducing the symmetric and anti-symmetric distortion modes, in addition to the warping and conventional six DOFs, this paper develops a new theory that consists of nine DOFs per node for the two-node I-beam element. The three deformational DOFs of the cross-section, i.e., the symmetric distortion, anti-symmetric distortion and warping, can be regarded as three mechanical couples relating to the twisting, shearing and bending, respectively, of the two flanges in the opposite sense. This allows all the DOFs of the connected elements at a common joint to be easily transformed to the global coordinates for stiffness assembly. As a result, the warping-distortion compatibility problem that occurs in frames and curved beams is resolved. In the exemplar studies, the present beam element has been demonstrated to be capable of producing results that are in excellent agreement with those of the shell element for the lateral deformation of angled frames with unstiffened and stiffened joints and of curved beams with various boundary conditions. It is also observed that the cross-sectional distortion effect becomes more manifest in curved I-beams of high curvature or of high flange-to-web rigidity ratio.

Cyclic tests and shear resistance design of stiffened corrugated steel plate shear walls

Corrugated steel plate shear walls (CSPSWs) are commonly employed as lateral-load-resisting components in regions with high seismic activity. In order to enhance their shear resistance, stiffeners can be affixed to CSPSWs, forming stiffened CSPSWs (S-CSPSWs). This paper presents experimental and numerical investigations into S-CSPSWs. Firstly, two specimens were tested under cyclic shear loads, one of which was an unstiffened CSPSW specimen, while the other was an S-CSPSW specimen. The typical failure modes observed from the test were global buckling and fracture of the corrugated steel plate (CSP). Both specimens exhibited stable hysteretic loops and excellent energy dissipation. It was observed that the stiffeners could constrain the out-of-plane deformation of the CSP, thus increasing its energy dissipation capacity. However, the fracture during the initial stage reduced the shear-carrying capacity and energy dissipation capacity. Subsequently, a finite element (FE) model is developed to simulate the test results. Additionally, the elastic buckling loads of S-CSPSWs are investigated by employing the validated FE model. The shear buckling coefficient is estimated by introducing a rigidity ratio between the stiffeners and the CSP. Finally, the shear resistance design method is established and is helpful in promoting the application of S-CSPSWs. The design formulas proposed in this paper agree well with the FE analysis results and can be effectively implemented in practice.

An experimental and numerical study of ultra-high strength concrete filled circular tube column post-fire

Extensive experimental research was conducted on 10 ultra-high strength concrete filled tubular (UCFCT) columns to investigate their performance after exposure to the ISO-834 standard fire and external load. Two different diameters of steel tubes (219.1 mm and 273 mm) with concrete strength ranging from 161 MPa to 181 MPa were included in the study. The primary parameter examined was temperature, ranging from 94 °C to 618 °C. The study obtained data on the residual capacity, working mechanism, and ductility of the columns under compressive load after the fire. The compression experiments revealed that the load capacity of the UCFCT columns remained high. As the columns deformed beyond the inflection point, the load capacity increased gradually without decline. This indicates that the UCFCT columns exhibited notable ductility even after the fire and cooling process. The residual capacity of the columns was influenced by the highest temperature experienced during the experiment. The study also observed the splitting of the ultra-high strength concrete (UHSC) inside the specimens and described the failure mode. Local wall buckling did not occur prior to yielding, and the specimens demonstrated strain-hardening after reaching the plastic point. The mechanical properties of the steel and UHSC were investigated and incorporated into a numerical model that satisfactorily described the post-fire behavior of the composite columns compared to the test data. Based on this theoretical model, the influence of changing material strength (steel and concrete), fire duration time, specimen diameter, and steel ratio on the residual capacity ratio and residual rigidity ratio was discussed. It was generally observed that sectional dimensions and fire duration time had a significant impact on the residual capacity ratio. Finally, formulas suitable for calculating the residual strength of ultra-high strength concrete-filled circular tube columns after exposure to the ISO-834 standard fire were developed based on the results of the parametric analysis.

Snap-through dynamics of a buckled flexible filament with different edge conditions

The flow-induced snap-through dynamics of a buckled flexible filament under different edge conditions were explored using the penalty immersed boundary method. Three filament edge conditions were simulated: a simply supported leading edge and a clamped trailing edge (SC), a clamped leading edge and a simply supported trailing edge, and both edges clamped. The effects of the bending rigidity and density ratio on the energy harvesting performance were systematically examined. Two different modes were observed: an equilibrium mode and a snap-through oscillation mode. The parameter range under which the modes were observed changed depending on the edge conditions. Mode transitions, induced by an increase in transverse fluid force, occurred when the bending rigidity was low. A clamped leading edge enhanced filament stability, whereas a simply supported leading edge reduced stability. Among the three configurations, the SC case showed the highest critical bending rigidity and oscillation frequency, resulting in superior energy harvesting performance. The greater energy harvesting ability of the SC case derives from the larger deflection and the higher strain energy in this system. The strain energy in the filament with SC edges tended to concentrate in two regions of the filament: the rear part and the section near the clamped end. The SC case, coupled with low density and high rigidity, offers favorable conditions for energy harvesting purposes.

3D printed wood-fiber reinforced architected cellular composite beams with engineered flexural properties

This study explores the integration of cellulose-based compounds into a biobased polymer to create high-performance sustainable materials with improved properties. The elastic flexural characteristics of 3D printed composites, comprised of polylactic-acid (PLA) biopolymer reinforced by a variety of waste wood fiber weight percentage (2.5%−15%), are investigated. Initial steps involve producing wood-fiber reinforced PLA (WF-PLA) filaments and the 3D printing of test specimens. Experimental outcomes reveal enhanced flexural modulus (60% increase), rigidity (72% increase), strength (39% increase), and failure strain (21% increase) alongside reduced composite coupon density (5.2% decrease), attributed to wood fiber incorporation. To achieve lightweight and sustainable structural components with tunable attributes, architected composite cellular beams are introduced. These beams comprised of wood-fiber reinforced composites feature cross-sectional unit cells with one or two reflection symmetries, showcasing the synergy between architecture and material composition in enhancing quasi-isotropic flexural rigidity. Investigation on the flexural rigidity ratio ([EI]yy/[EI]xx) involves theoretical modeling, computational analysis, and experimental validation using 3D printed samples. WF-PLA filaments enable the 3D printing of engineered quasi-isotropic cellular beams, termed “Isoflex”, that demonstrate up to 130% enhanced specific flexural rigidity (bending rigidity-to-mass ratio) and up to 70% improvement in flexural rigidity ratio to have isotropic flexural properties, compared to pure PLA beams. This study introduces WF-PLA engineered cellular composites as a sustainable avenue for tuning structural properties, contributing to the realm of additive manufacturing.

Dynamic response of a shallow lined circular tunnel by incident P1 and SV waves in an unsaturated half-plane

The dynamic response of a shallow lined circular tunnel in the unsaturated half-plane during earthquakes is investigated in this paper using the complex function method. The wave fields of the unsaturated medium with unknown coefficients are solved by Fredlund’s theory and Helmholtz’s decomposition based on the momentum and mass balance equations. General expressions for the displacements and total stresses of the solid skeleton, pore pressures, and seepage are derived using the complex function method and conformal mapping technique. The half-plane surface and the tunnel in the physical domain are mapped onto two bonded ring regions in the image plane using two conformal mapping functions. The boundary value problem yields a series of algebraic equations by the boundary conditions and the continuity conditions along the liner-medium interface. The unknown coefficients in the infinite series of algebraic equations can be solved numerically by truncating the series number. A parametric study is performed to investigate the dynamic responses of the medium and the liner by the incident P1 waves. Numerical results reveal that the embedded depth of the tunnel, the saturation degree of the medium, the liner-medium rigidity ratio, the frequency and angle of the incident P1 waves significantly affect the dynamic responses of the medium and the liner. The shielding effect on the tunnel to the incident P1 waves is obvious. The response of the liner-medium system to the incident waves is independent of the saturation degree of the unsaturated medium when its value is high. The effect of the liner-medium rigidity ratio is great on the dynamic stress concentrations of the liner-medium system and weak on the displacements along the half surface. The frequency of the incident excitation has a great influence on the displacements of the half surface.

Mechanical design of a convex-deformable polymer plate

The authors’ previous study introduced a convex-deformable sandwich plate consisting of a pyramid truss core and two face sheets that exhibit a two-dimensional auxetic pattern. Owing to its unique micro-architecture, the sandwich plate successfully underwent adequate convex deformation under bending, even when many chips were embedded in its core. However, the plate was fabricated by adhesively bonding stainless-steel face sheets to a polymer truss core, and this fabrication process was complex and expensive. Moreover, the detailed dimensions of this plate were determined iteratively through trial-and-error. In this study, we develop a fresh approach to monolithically fabricate the entire body of the auxetic plate from a polymer by using three-dimensional printing. First, three mechanical constraints, which are needed for designing the face sheets and the core to realize compliant and convex deformation, unlike that of an ordinary sandwich plate, are defined. A precise mechanical design procedure is applied for dimensional optimization of the plate, and the mechanical behaviors of the fabricated specimen are observed by subjecting it to tensile and bending loads. The optimally designed polymer specimen exhibited a high level of convex deformation, as indicated by its adequate flexural rigidity (D = 0.0565 Nm2) and curvature ratio (0.625) when bent to the minimum curvature radius of ρ = 150 mm.

The influence of claw morphology on gripping efficiency.

This paper considers the effects of claw morphology on the gripping efficiency of arboreal (Varanus varius) and burrowing (Varanus gouldii and Varanus panoptes) lizards. To ensure a purely morphological comparison between the lizards, we circumvent the material effects of claws from different species, by modelling and testing claw replicates of the same material properties. We correlate climbing efficiency to critical morphological features including; claw height (hc), width (wc), length (lc), curvature () and tip angle (γ), which are expressed as ratios to normalise mechanically beneficial claw structures. We find that there is strong correlation between the static grip force Fsg and the claw aspect and the cross-sectional rigidity ratio , and milder correlation (i.e. higher scatter) with the profile rigidity ratio . These correlations are also true for the interlocking grip force Fint over different shaped and sized protuberances, though we note that certain protuberance size-shape couplings are of detriment to the repeatability of Fint. Of the three lizard species, the claws of the arboreal (V. varius) are found to be superior to those of the burrower lizards (V. gouldii and V. panoptes) as a result of the V. varius claws having a smaller aspect, a higher cross-sectional rigidity ratio and a small profile rigidity ratio, which are deemed noteworthy morphological parameters that influence a claw's ability to grip effectively.

Performance of vertically-placed stiffened corrugated panels in steel plate shear walls: Shear elastic buckling analysis

Adding horizontal stiffeners to vertically-placed corrugated panels is an effective way to improve their shear buckling strength. Since the shear elastic buckling loads (Ncr) of vertically-placed stiffened corrugated steel walls (VSCSWs) are related to their practical design, this study investigates the VSCSWs' shear elastic buckling behaviors and aims to determine the formulas for predicting the Ncr of VSCSWs. Firstly, the number of horizontal stiffeners required by VSCSWs is discussed utilizing the calculation model of VSCSWs’ shear elastic buckling load established based on the minimum potential energy and the Ritz method. Then, the shear elastic buckling behaviors of VSCSWs with one pair and two pairs of horizontal stiffeners are analyzed, and formulas for predicting their shear elastic buckling coefficients are proposed. Lastly, finite element shear elastic buckling analyses are conducted to verify the accuracy of the proposed formulas. It is found that the shear elastic buckling coefficient of VSCSWs first grows and then almost remains unchanged with the increased rigidity ratio of the stiffening system. It has been observed that the equations proposed are in good agreement with the numerical results and can be applied to the design of the VSCSWs.

Correlation study some dynamic properties with density, point load Index and Uniaxial compressive strength of some units of Mukdadya (lowerBakhtiari) Formation

Geotechnical study conducted upon 10 rock samples have been taken from outcroup of Mukdadiya Formation (Lower Bakhtiari) which are located in Kirkuk anticline. Seismic wave velocities (shear and compressional), the dynamic modulus of rigidity, young, bulk and poisson's ratio, density, point load index test and uniaxial compressive strength test were measured of the rock samples in the laboratory. The dynamic properties values were correlated with geotechnical properties inculding uniaxial compressive strength, point load index and dry density. The rock samples have low to medium seismic velocites and very weak to weak mechanical strength. The mathematical relations showed a good correlation coefficient between the dynamic and geotechnical properties of the rock samples, that confident relations could use to estimate the geotechnical properies in the field by measuring sciesmic wave velocities in any future engineering projects.

Rapid prototyping for high-pressure microfluidics

Soft lithography has permitted rapid prototyping of precise microfluidic features by patterning a deformable elastomer such as polydimethylsiloxane (PDMS) with a photolithographically patterned mold. In microfluidics applications where the flexibility of PDMS is a drawback, a variety of more rigid materials have been proposed. Compared to alternatives, devices fabricated from epoxy and glass have superior mechanical performance, feature resolution, and solvent compatibility. Here we provide a detailed step-by-step method for fabricating rigid microfluidic devices from soft lithography patterned epoxy and glass. The bonding protocol was optimized yielding devices that withstand pressures exceeding 500 psi. Using this method, we demonstrate the use of rigid high aspect ratio spiral microchannels for high throughput cell focusing.

Numerical Analysis of Reinforcing Effect for Scissors-Type Bridge with Strut Members

Recently, a scissor mechanism was efficiently applied in the safety engineering field as an emergency structure owing to the advantages of mobility, transformability, and re-usability. This paper focuses on the advantages of this mechanism and puts forward a deployable emergency bridge called Mobile Bridge as a smart bridge. To deploy this bridge in an emergency situation, the structural safety, such as strength and stiffness, must be ensured through proper reinforcing methods. Several research studies concerning the reinforcing effect to scissors structures have been conducted using a cable and/or strut. However, the reinforcing situation was limited, and it is not clear where and how much reinforcement should be introduced. In this paper, we discuss the reinforcing effect of simple struts through a theoretical and numerical approach. Then, we evaluate their applicability to the Mobile Bridge based on numerical simulation. The advantage of the proposed reinforcing method is evaluated, focusing on the reduction of the bending moment which is the dominant sectional force in the scissor structure. We found the reinforcing effect has a nonlinear relationship between the stress and ratio of extension rigidity. The most effective reinforcing configuration was a double warren truss with the vertical element in a two-unit scissors-type bridge and a double warren truss without the vertical element in a three-unit scissors-type bridge. The necessary sectional area of the strut elements was more than 0.2 times that of the scissors member. These results imply that the smart bridge can enhance its performance by using proper reinforcement of the struts.

Numerical Optimization of the Dendritic Arm of a Radial Gate Based on Stability and Light Weight

A new dendritic arm structure was proposed to achieve the stability and lightness of a large-scale radial gate arm. The arm structure was arranged in accordance with the current gate design specifications for steel. The optimization aims were to achieve the highest possible overall structural stability and the lowest possible weight. As the failure criterion for the entire structure, the simultaneous instability of the trunks and branches of the dendritic arm was considered. The constraints of strength, stiffness, and stability were identified, and an optimization model of a dendritic arm with two branches was established. A geometric and material nonlinear buckling analysis and optimization solution was implemented for the dendritic arm with a different radius, type, and unit rigidity ratios. Compared to a conventional radial gate structure with two arms, the Y-type dendritic arm structure was lighter and more stable. The optimal dendritic arm had the following parameter settings: the angle ratio between two branches and two arms was [1.92, 2.04], the unit rigidity ratio between the trunk and branch was [5.33, 6.02], the length ratio between the branch and trunk was [0.96, 1.09], the height ratio of the trunk and branch was 1.805, and the flange thickness ratio of the trunk and branch was 1.405. In this case, the overall buckling load ratio between the dendritic arm and two arms was [2.50, 4.34], and the material saving rate was [37, 53] (%). Within the aforementioned parameters, the Y-type dendritic arm performed better overall. Moreover, the radius of the radial gate had minimal influence on the shape and mechanical properties of the Y-type dendritic arm structure. This paper proposes a dendritic arm that can be utilized in most radial gate projects.