Flexural Model Research Articles

A Quantitative Representation of Damage and Failure Response of Three-Dimensional Textile SiC/SiC Ceramics Matrix Composites Subjected to Flexural Loading

Abstract In the present work, the microstructure deformation and synergetic damage evolution of a three-dimensional textile SiC/SiC ceramic-matrix composite under flexural loading are investigated by in situ digital image correlation at ambient temperatures. The correlations between microstructure evolution and macro-mechanical degradation of 3D textile composites under flexural loading are established based on the experimental results. In addition, by establishing continuum damage mechanics and a thermodynamic framework with synergetic effects of microstructures, a flexural loading-induced damage evolution model is developed to reveal the relationship between the energy release rate and elastic modulus degradation. The proposed model can be used to predict the flexural stress–strain curves of 3D textile SiC/SiC composites to further improve the design and assessment of new textile architectures with specific mechanical properties.

Out-of-plane strengthening of URM walls using different fiber-reinforced materials

Fiber-reinforced polymers (FRPs), textile-reinforced mortars (TRMs), and engineered cementitious composites (ECCs) have been extensively employed to address the insufficient load-carrying capacity and low deformation capability of unreinforced masonry buildings. In this study, eight groups of unreinforced masonry walls were built to test the efficiencies of various reinforcing methods under out-of-plane four-point loading. A high-strength mortar reinforcement were employed as benchmarks. Four types of ECCs—low-cost, high-strength, lightweight insulation, and high-toughness ECCs—were compared with carbon FRP (CFRP) sheet and TRM systems. The failure modes, midspan load–displacement actions, energy absorption capabilities, initial bending stiffness values, and ductility of the different reinforcement systems were obtained and analyzed. The results revealed that the TRM-reinforced specimens experienced the maximum midspan deformation. The best ductility and maximum bearing capacity were obtained respectively after reinforcements with high-strength and high-toughness ECCs. However, the exploitation of the CFRP sheet was limited owing to excessive reinforcement. Finally, the moment capacity was evaluated using a flexural model. For the specimens that failed in the shear mode, a shear model based on the equilibrium condition was established to predict their load-carrying capacities.

Regional variations of Mercury's crustal density and porosity from MESSENGER gravity data

A new solution of Mercury's gravity field to degree and order 160, named HgM009, is retrieved through a reprocessing of MESSENGER radio science measurements. By combining our latest gravity field with topography data, localized spectral admittance analyses are carried out to investigate Mercury's crustal and lithospheric properties across the northern hemisphere. The measured spectra are compared with admittances predicted by lithospheric flexure models. The localized gravity/topography admittance analyses yield key information on the lateral variations of the bulk density of the upper crust. Elastic and crustal thicknesses are also adjusted in our study, but the local admittance spectra allow us to constrain these parameters only over a few regions. The average bulk density across the observed areas in the northern hemisphere is 2540 ±60 kg m−3. The crustal porosity is then constrained by using an estimate of the pore-free grain density of surface materials with our measured bulk density. Our estimate of the mean porosity is 14.7 ±1.6 %, which is comparable to, but slightly higher than, the average value measured on the Moon. Larger crustal porosities are observed over heavily cratered regions, suggesting that impact bombardment is the main cause of the crustal porosity.

Influence of strands corrosion on the flexural behavior of prestressed concrete beams

In this paper, the research goal was the determination of the flexural response of corroded pre-stressed reinforced concrete beams (PC). A simplified flexural model is bases on the calcualus of the moment and curvature/deflection curves for simply supported beam under uniformly distributed and concentrated loads. Primary research outcomes was the introduction in flexural model of the effects of pitting corrosion though the reduction of area, of the mechanical properties of steel strands and of the loss of bond of steel strands of precast pre-tensioned beams.A comparison with available experimental data of literature and with numerical simulation carried out with nonlinear finite element code (ABAQUS) was made. Results obtaiend showed that the corrosion of strands reduce the bearing capacity of the viaducts with prestressed beams especially and because of the reduction of strain capacity of steel strand, arises a risk of brittle collapse under service conditions due to the strand failure.

A flexural ductility model for UHPC beams reinforced with FRP bars

Ultra-high performance concrete (UHPC) beams reinforced with fiber-reinforced polymer (FRP) bars (FRP-UHPC beams) exhibit high flexural stiffness and small crack width at the serviceability limit state. However, a proper model considering FRP-UHPC beams’ mechanical characteristics is lacking to evaluate their flexural ductility. In this paper, based on a rigorous nonlinear cross-section analysis and the conjugate beam method, the applicability of existing ductility models of FRP bar-reinforced normal concrete beams (FRP-NC beams) to FRP-UHPC beams was discussed, and these ductility models were modified after investigating the FRP-UHPC beams’ strain limits in serviceability limit state. A new model by setting the FRP’s allowable strain in Newhook model as 3000με was finally adopted after considering that FRP-UHPC beams have smaller crack width. Calculation results by the modified Newhook model suggested that high reinforcement ratio in FRP-UHPC beams has unfavorable effect on the flexural ductility. Moreover, the influence of key material parameters, including the compressive strength of UHPC, peak compressive strain of UHPC, first cracking strength of UHPC and the type of FRP bars, on the flexural ductility was analyzed. Finally, a theoretical model for predicting overall factor-reinforcement ratio curve calculated by the modified Newhook model was proposed.

A Model of Plate Bending at the Transition Zone From Subduction to Collision in Northernmost Manila Trench

AbstractIt is not rare to observe subduction zones transferring into collision zones. However, it is poorly understood the lateral variation in flexural deformation. Constrained by newly published seismic reflection data, we investigate the mechanical behavior of lithosphere from oceanic subduction to collision at the northern Manila trench using the 3‐D flexural modeling. Results show that both plate rigidity and the loadings increase from the Manila subduction zone to the Taiwan orogenic belt. In order to fit all observations, an upward loading was required at the transition zone from subduction to collision, which may be related to the variation of buoyancy due to density contrast of plate from south to north. The resultant maximum bending stress is consistent with the concentrated seismic activity at the southwest of Taiwan, suggesting that huge loading from the orogeny and lateral density change of subducting plate play important roles in bending and seismicity.

Gravity‐Derived Antarctic Crustal Thickness Based on the Gauss‐FFT Method

AbstractThe information on crustal thickness in Antarctica can provide significant constraints on its crustal deformation and tectonic evolution. To generate reliable images of crustal features, we investigate the model of Moho depth and crustal thickness beneath Antarctica by applying the Bott‐Parker's formulas based on the Gauss‐fast Fourier transform method through a comprehensive analysis of gravity data, ice and sediment thicknesses and bedrock elevation, combined with seismic constraints. Tests with synthetic data indicate that the iterative inversion algorithm can yield a highly accurate Moho topography. Ultimately, inverted crustal thickness reveals a more detailed crustal image by clearly identifying more tectonic elements at different scales than previous results and correlates well with major tectonic provinces. Airy isostasy and flexural isostasy models are used to assess the crustal isostatic compensation. The distinctive negative isostatic anomalies are observed in the Transantarctic Mountains and the East Antarctic areas of the great escarpment in the Dronning Maud Land and Aurora and Wilkes Subglacial Basin, indicating that the low density of the uppermost mantle and lithospheric strength may play important roles in compensating for their elevations. Variations in crustal thickness in interior East Antarctica are analyzed; the thickened crust from Dronning Maud Land to the Gamburtsev Subglacial Mountains may be associated with the collision of continental blocks and is interpreted as the fossil sutures. We compare the relationship between the Moho and Curie interfaces and find that the uppermost mantle is magnetized in some areas of East Antarctica, which may indicate preserved Precambrian cratonic roots.

Flexural Strength Models for Normal Laterised and High Strength Laterised Concretes at Optimum Mix Proportions

This study develops mathematical models for obtaining optimum flexural strengths of normal laterised(NLC) and high strength laterised concretes (HSLC). The models can be expressly used to evaluate the indirect tensile strengths of both types of concretes without going through the traditional methods of mix design. Optimum mixing ratios and optimum flexural strengths predicted are also supplied by the models. The three point load method was adopted for testing for the flexural strengths. Laterite, has been widely used to partially or wholly replace sand in concrete with resultant low strengths. The production of HSLC using superplasticiser was achieved in this study. Scheffe’s simplex theory based on (5, 2) simplex lattice (for NLC) and (6, 2) simplex lattice (for HSLC) was used to optimize the mix proportions for the flexural strengths of each respective laterised concrete. Conplast SP 430 superplasticiser (a sulphonated naphthalene formaldehyde admixture) was used to obtain the high strength laterised concrete. Mathematical models were developed for the mix proportioning of the laterised concretes and all strengths predicted by the models agreed with their corresponding experimentally observed values. Using the model, the optimum flexural strength and the corresponding mix proportions for the targeted strength of laterised concrete could be easily evaluated with the help of the written Q-BASIC computer programme.

Flexural Strength Models for Normal Laterised and High Strength Laterised Concretes at Optimum Mix Proportions

Flexural Strength Models for Normal Laterised and High Strength Laterised Concretes at Optimum Mix Proportions

Total isostatic response to the complete unloading of the Greenland and Antarctic Ice Sheets

The land surface beneath the Greenland and Antarctic Ice Sheets is isostatically suppressed by the mass of the overlying ice. Accurate computation of the land elevation in the absence of ice is important when considering, for example, regional geodynamics, geomorphology, and ice sheet behaviour. Here, we use contemporary compilations of ice thickness and lithospheric effective elastic thickness to calculate the fully re-equilibrated isostatic response of the solid Earth to the complete removal of the Greenland and Antarctic Ice Sheets. We use an elastic plate flexure model to compute the isostatic response to the unloading of the modern ice sheet loads, and a self-gravitating viscoelastic Earth model to make an adjustment for the remaining isostatic disequilibrium driven by ice mass loss since the Last Glacial Maximum. Feedbacks arising from water loading in areas situated below sea level after ice sheet removal are also taken into account. In addition, we quantify the uncertainties in the total isostatic response associated with a range of elastic and viscoelastic Earth properties. We find that the maximum change in bed elevation following full re-equilibration occurs over the centre of the landmasses and is +783 m in Greenland and +936 m in Antarctica. By contrast, areas around the ice margins experience up to 123 m of lowering due to a combination of sea level rise, peripheral bulge collapse, and water loading. The computed isostatic response fields are openly accessible and have a number of applications for studying regional geodynamics, landscape evolution, cryosphere dynamics, and relative sea level change.

Study on Toughening and Temperature Sensitivity of Polyurethane Cement (PUC).

Polyurethane cement (PUC) is now commonly used in the reinforcement of old bridges, which exhibit various issues such as poor toughness, temperature-sensitive mechanical properties, and brittle failure. These problems can lead to the failure of the reinforcement effect of the PUC on old bridges in certain operating environments, leading to the collapse of such reinforced bridges. In order to alleviate these shortcomings, in this study, the toughness of PUC is improved by adding polyvinyl alcohol (PVA) fiber, carbon fiber, and steel fiber. In addition, we study the change law of the flexural strength of PUC between −40 °C and +40 °C. The control parameters evaluated are fiber type, fiber volume ratio, and temperature. A series of flexural tests and scanning electron microscope (SEM) test results show that the flexural strength first increases and then decreases with the increase in the volume-doping ratio of the three fibers. The optimum volume-mixing ratios of polyvinyl alcohol (PVA) fiber, carbon fiber, and steel fiber are 0.3%, 0.04% and 1%, respectively. Excessive addition of fiber will affect the operability and will adversely affect the mechanical properties. The flexural strength of both fiber-reinforced and control samples decreases with increasing temperature. Using the flexural test results, a two-factor (fiber content, temperature) BP neural network flexural strength prediction model is established. It is verified that the model is effective and accurate, and the experimental value and the predicted value are in good agreement.

Basement structure of the Appalachian Basin in Pennsylvania

Basement structure beneath the Pennsylvanian portion of the Appalachian basin, where some of the deepest basement in the basin is found, is investigated by constructing a map of the Precambrian unconformity using 3939 new point estimates of basement depth determined from seismic reflection profiles and P-wave receiver functions, combined with geophysical and well log data used in other published basement maps. The map shows a gradual and uniform deepening of the basement from depths of ~1500 m in the northwest to ~6000 m in the southeast, consistent with a foreland basin plate flexure model. However, basement depths in two regions, when compared to depths predicted by a plate flexure model, show basin over-deepening. One to two km of over-deepening coincides with the Neoproterozoic-early Paleozoic Rome Trough in southwestern Pennsylvania, and the Northumberland Deep Basement Zone (NDBZ) in east-central Pennsylvania shows two to two and a half km of over-deepening. Basin over-deepening in the Rome Trough does not extend into northern Pennsylvania, pointing to a termination of the trough within central Pennsylvania. The origin of basin over-deepening in the NDBZ is less certain but overlaps spatially with the southern portion of the Neoproterozoic Scranton Rift. The preservation of one or more failed Neoproterozoic-early Paleozoic rifts within the basement structure of the Appalachian Basin suggests crystalline basement was not significantly deformed by the Paleozoic orogenic events associated with basin formation. It also supports models placing the locus of Laurentian rifting from Rodinia well to the east of the Appalachian Basin.

Data-Driven Flexural Stiffness Model of FRP-Reinforced Concrete Slender Columns

Predicting the nominal axial capacity of slender fiber-reinforced polymer (FRP) reinforced concrete (RC) columns is dependent majorly on their flexural stiffness. However, the current design provisions do not incorporate design equations to estimate the flexural stiffness of slender FRP-RC columns yet due to the limited research work on this aspect. Although limited research studies proposed flexural stiffness models for slender FRP-RC columns, these models show inaccurate results with large discrepancies. This study, therefore, compiles and analyzes a surveyed database of 53 tested slender FRP-RC columns found in the literature to construct a simplified and accurate model to predict the flexural stiffness of the slender FRP-RC columns. In this approach, the experimental-based flexural stiffness values of the tested specimens were used to build a nonlinear regression flexural stiffness model and examine the influence of the critical design parameters affecting this value. As a result, the proposed model showed a strong agreement with the experimental flexural stiffness values evidenced by having the least root mean square error (RMSE) compared to the other proposed models in the literature. Moreover, the proposed model was theoretically evaluated accounting for the second-moment order effect by which a data set of 36,000 cases were generated and compared to the results of the proposed model to increase its creditability and repeatability. Moreover, a design example was presented to quantify the difference in predicting the flexural stiffness of the slender FRP-RC columns between the proposed and available models. Accordingly, the proposed model revealed better representation of the flexural stiffness with higher accuracy compared to the available models which will help the engineers to accurately design the FRP-RC columns.

A Seismic Tomography, Gravity, and Flexure Study of the Crust and Upper Mantle Structure of the Emperor Seamounts at Jimmu Guyot

AbstractThe intraplate Hawaiian‐Emperor Seamount Chain has long been considered a hotspot track generated by the motion of the Pacific plate over a deep mantle plume, and an ideal feature therefore for studies of volcanic structure, magma supply, plume‐crust interaction, flexural loading, and upper mantle rheology. Despite their importance as a major component of the chain, the Emperor Seamounts have been relatively little studied. In this paper, we present the results of an active‐source wide‐angle reflection and refraction experiment conducted along an ocean‐bottom‐seismograph (OBS) line oriented perpendicular to the seamount chain, crossing Jimmu guyot. The tomographic P wave velocity model, using ∼20,000 travel times from 26 OBSs, suggests that there is a high‐velocity (>6.0 km/s) intrusive core within the edifice, and the extrusive‐to‐intrusive ratio is estimated to be ∼2.5, indicating that Jimmu was built mainly by extrusive processes. The total volume for magmatic material above the top of the oceanic crust is ∼5.3 × 104 km3, and the related volume flux is ∼0.96 m3/s during the formation of Jimmu. Under volcanic loading, the ∼5.3‐km‐thick oceanic crust is depressed by ∼3.8 km over a broad region. Using the standard relationships between Vp and density, the velocity model is verified by gravity modeling, and plate flexure modeling indicates an effective elastic thickness (Te) of ∼14 km. Finally, we find no evidence for large‐scale magmatic underplating beneath the pre‐existing crust.

Durability Investigation on CFRP Strengthened Cementitious Materials in Cold Region.

Epoxy resin, CFRP (Carbon Fiber Reinforced Polymer) sheet, and concrete flexural specimens are selected to study the durability of carbon fiber strengthened cementitious materials in a cold region. Two exposure environments, chloride immersion and salt-freeze coupling, are set up, and the mechanical deterioration is discussed utilizing a microscopic observation mechanical test and finite element analysis. The damage to the epoxy resin, CFRP sheet, and concrete exerts a more severe performance degradation in the salt-freeze coupling environment when compared with the chlorine salt immersion environment. The freeze–thaw action destroys the bonding surface of CFRP and concrete based on the microscope observation. The flexural strength of the specimens strengthened with CFRP is 3.6 times higher than that of the specimens without CFRP, while the degradation rate is only 50%. These observations show that the strengthened CFRP effectively improves the cementitious material’s flexural performance in the cold region. The finite element model of epoxy and CFRP subjected to chloride immersion and salt-freeze coupling environment is established. The degradation formula of bond performance between CFRP and concrete is proposed. In addition, the flexural mechanical numerical model is established with and without CFRP strengthened concrete, respectively. Research results provide a technical reference for applying CFRP reinforced cementitious materials in a cold region.

Tracking the Cracking: A Holistic Analysis of Rapid Ice Shelf Fracture Using Seismology, Geodesy, and Satellite Imagery on the Pine Island Glacier Ice Shelf, West Antarctica.

Ice shelves regulate the stability of marine ice sheets. We track fractures on Pine Island Glacier, a quickly accelerating glacier in West Antarctica that contributes more to sea level rise than any other glacier. Using an on‐ice seismic network deployed from 2012 to 2014, we catalog icequakes that dominantly consist of flexural gravity waves. Icequakes occur near the rift tip and in two distinct areas of the shear margin, and TerraSAR‐X imagery shows significant fracture in each source region. Rift‐tip icequakes increase with ice speed, linking rift fracture to glaciological stresses and/or localized thinning. Using a simple flexural gravity wave model, we deconvolve wave propagation effects to estimate icequake source durations of 19.5–50.0 s and transient loads of 3.8–14.0 kPa corresponding to 4.3–15.9 m of crevasse growth per icequake. These long‐source durations suggest that water flow may limit the rate of crevasse opening.

Ground Surface Deformation in the Hanging Wall of the Jinshandian Underground Iron Mine in China

When sublevel caving is used in metal mines, the stress state in the rock mass that initially existed around the mined-out area will be destroyed. This will lead to the rock strata deforming and moving and also, potentially, to large-scale collapse and cracking of the ground surface. Such ground surface deformation can cause significant damage to buildings and other structures. Therefore, it is very important to study the mechanism responsible for this ground surface deformation so that methods can be devised to protect the mine’s production facilities as well as the property and safety of nearby residents. In this study, the mechanism responsible for the surface deformation of the hanging wall in the eastern part of the Jinshandian iron mine was investigated by analyzing monitoring data collected in situ on the surface (from 2008 to 2020) and other related information (occurrence of surface cracking and collapse and geological conditions). The results show that the ground surface deformation can be divided into four stages (initial, creep, slow, and accelerating deformation stages). A flexural toppling failure model is proposed to account for the surface deformation. The model suggests that large-scale deformation of the ground surface at the hanging wall occurs due to the combined effect of in situ ground stress, occurrence of steep dip discontinuities and faults, the dips and strikes of the two parallel orebodies, and underground mining activity. Furthermore, the surface deformation can be divided into six regions corresponding to caved, rapidly-accelerating deformation, slowly-accelerating deformation, acceptable deformation, slight deformation, and no deformation zones. In the rapidly-accelerating deformation zone, the ratio of the horizontal to vertical displacement is greater than 1 and some major cracks can be found. Large-scale cracks begin to form when the horizontal velocity of the ground surface is greater than 1 mm/day.

Flexural Analysis Model of Externally Prestressed Steel-Concrete Composite Beam with Nonlinear Interfacial Connection

Interfacial slip effects and the unbonded phenomenon of external tendons are the key mechanical features of the externally prestressed steel-concrete composite beams (EPCBs). In this paper, an 8-node fiber beam element is built for the nonlinear analysis of the composite beam with interfacial slip effects. A multi-node slipping cable element is proposed for the simulation of external tendons. The derived formulations are programmed in OpenSees as newly developed element classes to be conveniently used for the flexural analysis of EPCBs. The effectiveness of the proposed model is fully verified against the experimental tests of simply supported and continuous beams and then applied to the parametric study. The results show that the increasing deviator spacing will significantly decrease the tendon effective depth at ultimate states and further decrease the flexural capacity. The larger effective depth is beneficial to the tendon stress increments and further improves the flexural capacity. The enhancement of interfacial shear connection degree will increase the structural capacity but the effects on the tendon stress increments and second-order effects were not monotonic.

Seismic performance of semi-precast high-strength recycled concrete columns with ultra-high-strength steel bar

The purpose of this study is to promote the application of high-strength reinforcement and recycled aggregate concrete in post-earthquake repairable precast structures. Three large-scale recycled concrete columns with ultra-high-strength steel bar were designed and tested under quasi-static cyclic loads. The feasibility of semi-precast columns is verified, i.e., the concrete shell of the outer tube is precast first, and then the precast external shell is used as a formwork to cast concrete into the tube. The design parameters include axial load and the addition of steel fibers. The results indicate that all specimens exhibited a good deformation capacity with an ultimate drift ratio greater than 4%. Increasing axial load will increase the lateral load capacity of the specimen by 21%, while the deformability and repairability decrease. Adding steel fibers to the precast external shell can increase the lateral load capacity by 10%, as well as the deformability and repairability of the specimen. Due to the low bond strength of ultra-high-strength steel bar, it slips at the column footing in the tensile side. Eventually, the fiber-based model simplified flexural capacity calculation model considering the ultra-high-strength steel bar slippage in the tensile zone are established.

Flexural Models for Vacuum-Packed Particles as a Variable-Stiffness Mechanism in Smart Structures

Vacuum-packed particle (VPP) systems have been recently used in the development of smart structures due to their ability to actively change material stiffness through the mechanism of granular jamming. By altering the strength of the vacuum pressure applied to the particles, the material can be proportionally and reversibly transitioned from a liquidlike low-stiffness state to a stiff state. The ability to control material stiffness in this way opens up different possibilities for the design of morphing and smart structures by allowing them to soften during deformation to reduce actuation energy requirements and to then stiffen once the desired shape has been achieved to provide a zero-energy holding mechanism. The following research describes two useful models that predict the mechanical response of VPP beams under flexural loading. Firstly, four-point bending tests with digital image correlation strain mapping are performed in order to measure the axial and transverse strains in a bending beam made from vacuum-packed particles. The test results show a nonlinear mechanical response, including a change in beam thickness with deformation, that motivated an analytical model of the structure incorporating a nonlinear material stress model based on the Mohr-Coulomb failure envelope. In addition, finite-element simulations are implemented using a Johnson-Cook model extension to predict the response under loading of three-dimensional beam elements at different vacuum pressure levels. Lastly, the models are compared to the experimental results, indicating good agreement. Both methods are shown to be useful for predicting the variation of stiffness of vacuum-packed particle beams.