Hinge Curvature Research Articles

Seismic Vulnerability Analysis of Double-column High-pier Rigid Frame Bridge with Tie-beams Subjected to Near-fault Earthquake Inputs

Due to short duration and high energy characteristics, near-fault earthquakes showed more destructive damage on bridges. For double-column hige-pier rigid frame bridges, tie-beams between double-columns play an important role in seismic resistance. Therefore, the influence of traditional reinforced concrete tie-beams and energy dissipation braces on the seismic performance of high-pier rigid frame bridges under near-fault earthquakes were analyzed base on the seismic vulnerability analysis. It was showed that as the number of tie beams increases, the plastic hinge curvature on the top and bottom of the pier gradually decreases, and the probability of exceeding each damage state also gradually decrease. Additionally the energy dissipation braces can greatly reduce the seismic response and the damage probability of the bridge structure.

Folding a ridge-spring

A ridge-spring is a thin-walled bent strip with flat side panels. It may be folded elastically along its length, to create a localised hinge region of mostly uniform cylindrical curvature and bending moment, which do not vary with the fold angle of hinge. A simple analysis shows a common grouping in closed-form expressions; α4/3 · (b/t)1/3, where α is the pitch angle of the ridge line, b is the strip width and t its thickness. More accurate calculations of the hinge curvature and moment confirm the robustness of simpler expressions, which are compared to data obtained from finite element simulations. It is shown that, for many initial geometries, theoretical predictions of curvature and moment are typically within 10% of the computational results—which project the same dimensional performance. We also compare a ridge-spring to a more familiar tape-spring of equal cross-sectional proportions. For moderate pitch angles and relatively small thicknesses, it is shown that a ridge-spring has a higher folded hinge curvature and bending moment, comparatively, which may prove attractive for certain applications.

STUDY ON THE SEISMIC VULNERABILITY OF A VIADUCT SUBJECTED TO NEAR-FAULT GROUND MOTIONS

Piers, abutments and bearings of viaducts may suffer severe damage during earthquakes, so it's not insufficient to evaluate the seismic vulnerability of a bridge system only by plastic hinge curvature, which is adopted in seismic design guidelines. In this paper, the seismic vulnerability evaluation of a viaduct is conducted by incremental dynamic analysis under 30 near-fault ground motions, which are selected from PEER database. Then several damage measures are recommended to make an overall estimation for the seismic vulnerability of the viaduct, including plastic hinge curvature, shear failure and sliding displacement failure of bearings and pounding force between abutments and the girder. The analysis results show that the transversal seismic excitations may lead to more severe damage than the longitudinal ground motions. No matter in which direction the ground motions are inputted, the bearings' seismic vulnerability resulted by shear force or sliding displacement is higher than the plastic hinge of piers, which indicates that the seismic vulnerability of the bridge system is determined by the bearings to an extent. As a result, bearings should be designed according to both static and seismic analyses to guarantee the safety during earthquakes.

Gradient of structural traits drives hygroscopic movements of scarious bracts surrounding Helichrysum bracteatum capitulum.

The capitulum of Helichrysum bracteatum is surrounded by scarious involucral bracts that perform hygroscopic movements leading to bract bending toward or away from the capitulum, depending on cell wall water status. The present investigation aimed at explaining the mechanism of these movements. Surface strain and bract shape changes accompanying the movements were quantified using the replica method. Dissection experiments were used to assess the contribution of different tissues in bract deformation. Cell wall structure and composition were examined with the aid of light and electron microscopy as well as confocal Raman spectroscopy. At the bract hinge (organ actuator) longitudinal strains at opposite surfaces differ profoundly. This results in changes of hinge curvature that drive passive displacement of distal bract portions. The distal portions in turn undergo nearly uniform strain on both surfaces and also minute shape changes. The hinge is built of sclerenchyma-like abaxial tissue, parenchyma and adaxial epidermis with thickened outer walls. Cell wall composition is rather uniform but tissue fraction occupied by cell walls, cell wall thickness, compactness and cellulose microfibril orientation change gradually from abaxial to adaxial hinge surface. Dissection experiments show that the presence of part of the hinge tissues is enough for movements. Differential strain at the hinge is due to adaxial-abaxial gradient in structural traits of hinge tissues and cell walls. Thus, the bract hinge of H. bracteatum is a structure comprising gradually changing tissues, from highly resisting to highly active, rather than a bi-layered structure with distinct active and resistance parts, often ascribed for hygroscopically moving organs.

Large sheath folds in the Briançonnais of the Ligurian Alps reconstructed by analysis of minor structures and stratigraphic mapping

This study presents a geometric and structural analysis of curvilinear sheath folds exposed in blueschist rocks of the Ligurian Alps. Field data are presented in a geological map of the structural synthesis with related geological sections (at the 1:10,000 scale) that illustrate the relationships and evolution of large-scale, sheath folds within metamorphic rocks. We based our analyses on the geometric parameters of more than 40 minor folds, as shape (hinge-Lm1 angle, main axial plane/S1 angle, interlimb angle and hinge curvature), asymmetry, fold hinge/stretching lineation obliquity and structural facing pattern. The summary of the whole data depicts a coherent 3D structure showing several orders of minor folds. Sense of asymmetry of minor folds and stratigraphic order has been used to reconstruct a reliable large-scale structure, and to define the sheath fold shape.

Numerical estimation of the initial hinge-line irregularity required for the development of sheath folds: A pure shear model

Non-cylindrical sheath folds often develop by the accentuation of inherent geometrical irregularities along the hinge line during progressive deformation. This paper presents an analysis of the growth of such non-cylindrical folds in pure shear as a function of a non-dimensional initial irregularity factor ζ o ( ζ o = −log 10 [ A o/ W o], where A o and W o are the amplitude and the wavelength of a sinuous hinge line, respectively). Curvature accentuation of the hinge line produces sheath-like non-cylindrical folds in passive layers only when ζ o ≤ 1. Folds with ζ o > 1 remain weakly or moderately non-cylindrical even after a large finite strain ( λ = 36). An increasing flattening strain (1 > k value > 0) component in the deformation reduces the degree of non-cylindricity. We extend the analysis into layered systems with viscosity contrasts (i.e. viscosity ratio, R), considering a strain-partitioning factor λ f (the strain ratio between the fold hinge and bulk medium). Using finite element methods, it is shown that λ f can be small even for low values of R (4–8). Consequently, strong non-cylindricity does not grow in higher-viscosity layers for ζ o = 1. We ran experiments using three-dimensional finite element models to investigate the additional effects of mechanical bending on curvature accentuation of the hinge line. These experiments also show little accentuation of hinge curvature irrespective of R, when ζ o > 1. However, for ζ o ≤ 1, hinge-line curvature accentuates moderately when R < 8. It follows from our analysis that strongly non-cylindrical folds cannot develop unless the magnitude of initial hinge-line irregularity is sufficiently large (i.e. ζ o ≪ 1). We also discuss the implications of the numerical results for pure shear models in the analysis of sheath folds in shear zones.

The structural evolution of sheath folds: A case study from Cap de Creus

It has long been recognised that within zones of intense non-coaxial deformation, fold hinges may rotate progressively towards the transport direction ultimately resulting in highly curvilinear sheath folds. However, there is a surprising lack of detailed and systematic field analysis of such “evolving” sheath folds. This case study therefore focuses on the sequential development of cm-scale curvilinear folds in the greenschist-facies El Llimac shear zone, Cap de Creus, Spain. This simple shear-dominated dextral shear zone displays superb three dimensional exposures of sheath folds defined by mylonitic quartz bands within phyllonite. Increasing amounts of fold hinge curvature ( δ) are marked by hinge segments rotating into sub-parallelism with the mineral lineation (Lm), whilst the acute angle between the axial-planar hinge girdle and foliation ( ω) also displays a sequential reduction. Although Lm bisects the noses of sheath folds, it is also clearly folded and wrapped-around the sheath hinges. Lm typically preserves a larger angle ( θ) with the fold hinge on the lower limb ( L) compared to the upper ( U) limb ( θL > θU), suggesting that Lm failed to achieve a steady orientation on the lower limb. Adjacent sheath fold hinges forming fold pairs may display the same sense of hinge arcing to define synthetic curvature, or alternatively opposing directions of antithetic curvature. Such patterns reflect original buckle fold geometries coupled with the direction of shearing. The ratio of long/short fold limbs decreases with increasing hinge curvilinearity, indicating sheath folds developed via stretching of the short limb, rather than migrating or rolling hinge models. This study unequivocally demonstrates that both hinges of fold pairs become curvilinear with sheaths closing in the transport direction recording greater hinge-line curvilinearity compared to adjacent return hinges. This may provide a useful guide to bulk shear sense.

Effect of material anisotropy on the self-positioning of nanostructures

An experimental and numerical investigation of the effect of material anisotropy on theself-positioning of epitaxial nanostructures has been performed. The self-positioningoccurs due to a lattice mismatch between two epitaxial material layers (GaAs andIn0.2Ga0.8As) of a hinge. Both materials have cubic crystal symmetry and possess anisotropicmechanical properties. The dependence of the hinge curvature radius on the materialorientation angle was obtained experimentally by creating self-positioning hinges withdifferent angles between the hinge axis and material crystallographic axes. The sameself-positioning structures were modelled by solving geometrically nonlinear problems withthe help of the finite element method. Experimental and numerical values of the hingecurvature radius are in qualitative agreement. It is found that material anisotropysignificantly affects the shape of self-positioning structures.

Conical folds produced by dome and basin fold interference and their application to determining strain: examples from North Canterbury, New Zealand

Conical folds associated with dome and basin interference are analysed using equal-area plots, which provide data on the geometry of the fold surface and estimates of the finite shortening. To describe individual folds, they are subdivided into subareas defining the domains of each interfering fold set. The resulting plots demonstrate that numerous partial cones of distinct geometry are required to adequately describe the folded surface. To help identify the presence and accurately determine the geometries of such folds, the expected variations in conical fold geometry for interfering folds with varying hinge curvature, tightness and limb dips are analysed and illustrated with examples from North Canterbury. The resulting cone geometries are complex and often difficult to detect, which may in part explain the apparent absence of conical folds in some areas of dome and basin interference. Where parallel folds interfere, the divergence of poles to the conical fold surface and cone apical angle provide estimates of the finite shortening associated with folding. These shortening estimates are consistently larger than those determined by constructing profiles parallel to shortening along the hinge line of the second fold set.

An alternative method for determining the behaviour of round stocky tubes subjected to an axial crush load

An approximate method for determining the range of load oscillations and load-deflection behaviour of axially crushed round stocky tubes which deform in an axisymmetric mode is developed. Theoretical estimates based on different kinematic models are compared with each other and with experimental observations. Results indicate that the effects of axial and hoop stresses, imperfection sensitivity, strain-hardening and hinge curvature, should be considered in the analysis if the tube's behaviour is to be predicted accurately.