Balanced cross sections

1969 ◽  
Vol 6 (4) ◽  
pp. 743-757 ◽  
Author(s):  
C. D. A. Dahlstrom
Keyword(s):  
Surface Area ◽  
Cross Section ◽  
Cross Sections ◽  
Geological Environment ◽  
Simple Test ◽  
Cross Sectional ◽  
Mountain Belt ◽  
Sectional Plane ◽  
Bed Thickness ◽  
Better Than

Post-depositional concentric deformation produces no significant change in rock volume. Since bed thickness remains constant in concentric deformation, the surface area of a bed and its length in a cross-sectional plane must also remain constant. Under these conditions, a simple test of the geometric validity of a cross section is to measure bed lengths at several horizons between reference lines located on the axial planes of major synclines or other areas of no interbed slip. These bed lengths must be consistent unless a discontinuity, like a décollement, intervenes. Consistency of bed length also requires consistency of shortening, whether by folding and (or) faulting, within one cross section and between adjacent cross sections.The number of possible cross-sectional explanations of a set of data is reduced by the fact that, in a specific geological environment, there is only a limited suite of structures which can exist. This imposes a set of local "ground rules" on interpretation. When these local restrictions are coupled with the geometric restrictions which follow from the law of conservation of volume, it is often possible to produce structural cross sections that have a better-than-normal chance of being right.The concept of consistency of shortening can be extrapolated to a mountain belt as a whole, thereby indicating the necessity for some kind of transfer mechanism wherein waning faults or folds are compensated by waxing en echelon features. These concepts are illustrated diagrammatically and by examples from the Alberta Foothills.

Automated 3D measurement of fiber cross section morphology in handsheets

2012 ◽  
Vol 27 (2) ◽  
pp. 264-269 ◽  
Author(s):  
Christian Lorbach ◽  
Ulrich Hirn ◽  
Johannes Kritzinger ◽  
Wolfgang Bauer
Keyword(s):  
Image Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Image Plane ◽  
3D Measurement ◽  
Cross Sectional ◽  
Fiber Cross Section ◽  
Fiber Wall ◽  
Sectional Shape ◽  
Cross Section Geometry

Abstract We present a method for 3D measurement of fiber cross sectional morphology from handsheets. An automated procedure is used to acquire 3D datasets of fiber cross sectional images using an automated microtome and light microscopy. The fiber cross section geometry is extracted using digital image analysis. Simple sample preparation and highly automated image acquisition and image analysis are providing an efficient tool to analyze large samples. It is demonstrated that if fibers are tilted towards the image plane the images of fiber cross sections are always larger than the true fiber cross section geometry. In our analysis the tilting angles of the fibers to the image plane are measured. The resulting fiber cross sectional images are distorted to compensate the error due to fiber tilt, restoring the true fiber cross sectional shape. We use an approximated correction, the paper provides error estimates of the approximation. Measurement results for fiber wall thickness, fiber coarseness and fiber collapse are presented for one hardwood and one softwood pulp.

scholarly journals Supplemental Material: Plate boundary trench retreat and dextral shear drive intracontinental fault-slip histories: Neogene dextral faulting across the Gabbs Valley and Gillis Ranges, Central Walker Lane, Nevada

2020 ◽  
Author(s):  
J. Lee ◽  
et al.
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Boundary ◽  
Fault Slip ◽  
Cross Sectional ◽  
Walker Lane ◽  
Dextral Shear ◽  
The Cross

<div>Figure 6. Interpretative cross sections illustrating the cross-sectional geometry of several paleovalleys. See Figure 3 for location of all cross sections and Figure 8 for location of cross section CCʹ. Cross sections AAʹ and BBʹ are plotted at the same scale, and cross section CCʹ is plotted at a smaller scale. Figure 6 is intended to be viewed at a width of 45.1 cm.</div>

scholarly journals Failure Analysis of Intersections of Large-Scale Variable Cross-Section Roadways in Deep Soft Rock and Study of Integrated Control Technology of Bolting and Grouting

2021 ◽  
Author(s):  
Shengrong Xie ◽  
Yiyi Wu ◽  
Dongdong Chen ◽  
Ruipeng Liu ◽  
Xintao Han ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Large Scale ◽  
Integrated Control ◽  
Soft Rock ◽  
Variable Cross Section ◽  
Surrounding Rock ◽  
Variable Cross ◽  
Geological Environment ◽  
Cable Bolt

Abstract In deep underground mining, achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge. Owing to the coupling action of multiple factors such as deep high stress, adjacent faults, cross-layer design, weak lithology, broken surrounding rock, variable cross-sections, wide sections up to 9.9 m, and clusters of nearby chambers, there was severe deformation and breakdown in the No. 10 intersection of the roadway of large-scale variable cross-section at the − 760 m level in the Nanfeng working area of the Wuyang Coal Mine. As there are insufficient examples in engineering methods pertaining to the geological environment described above, the numerical calculation model was oversimplified and support theory underdeveloped; therefore, it is imperative to develop an effective support system for the stability and sustenance of deep roadways. In this study, a quantitative analysis of the geological environment of the roadway through field observations, borehole peeking, and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model. This model is combined with the strain softening constitutive (surrounding rock) and Mohr-Coulomb constitutive (other deep rock formations) models to construct a compression arch mechanical model for deep soft rock, based on the quadratic parabolic Mohr criterion. An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modified cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting, based on the Heok-Brown criterion. As a result of on-site practice, the following conclusions are drawn: (1) The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment, the tectonic stress is nearly 30 MPa, and the surrounding rock is severely fractured. (2) The deformation of the roadway progressively increases from small to large cross-sections, almost doubling at the largest cross-section. The plastic zone is concentrated at the top plate and shoulder and decreases progressively from the two sides to the bottom corner. The range of stress concentration at the sides of the intersection roadway close to the passageway is wider and higher. (3) The 7 m-thick reinforced compression arch constructed under the strengthening support scheme has a bearing capacity enhanced by 1.8 to 2.3 times and increase in thickness of the bearing structure by 1.76 times as compared to the original scheme. (4) The increase in the mechanical parameters c and φ of the surrounding rock after anchoring causes a significant increase in σc and σt; the pulling force of the cable bolt beneath the new grouting material is more than twice that of ordinary cement grout, and according to the test, the supporting stress field shows that the 7.24 m surrounding rock is compacted and strengthened in addition to providing a strong foundation for the bolt (cable). On-site monitoring shows that the 60-day convergence is less than 30 mm, indicating that the stability control of the roadway is successful.

scholarly journals Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

2021 ◽  
Vol 15 (58) ◽  
pp. 77-85
Author(s):  
Amor Bouaricha ◽  
Naoual Handel ◽  
Aziza Boutouta ◽  
Sarah Djouimaa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Capacity ◽  
Cross Sectional ◽  
Short Columns ◽  
Cross Section Area ◽  
Section Area ◽  
Specimen Height ◽  
Steel Sections ◽  
Thin Walled

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results.

A shear center demonstration model using 3D-printing

2021 ◽  
pp. 030641902110574
Author(s):  
Lawrence N Virgin
Keyword(s):  
3D Printing ◽  
Cross Section ◽  
Cross Sections ◽  
Principal Axis ◽  
Practical Importance ◽  
Bending Moment ◽  
Shear Center ◽  
Cross Sectional ◽  
Thin Walls ◽  
Section Profile

Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment about a principal axis, results in uni-directional deflection, and no twisting. For example, in aerospace structures it is particularly important to assess the propensity of an airfoil section profile to resist bending and torsion under the action of aerodynamic forces. Cross-sections made of thin-walls, whether of open or closed form are of special practical importance and form the basis of the material in this paper. The advent of 3D-printing allows the development of tactile demonstration models based on non-trivial geometry and direct observation.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

scholarly journals Accuracy Verification of Magnetic Resonance Imaging (MRI) Technology for Lower-Limb Prosthetic Research: Utilising Animal Soft Tissue Specimen and Common Socket Casting Materials

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Reza Safari ◽  
Philip Rowe ◽  
Arjan Buis
Keyword(s):  
Surface Area ◽  
Cross Sections ◽  
Lower Limb ◽  
Residual Limb ◽  
Cross Sectional ◽  
Prosthetic Socket ◽  
Semiautomatic Segmentation ◽  
Segmented Images ◽  
Cad Cam ◽  
Volume Measurements

Lower limb prosthetic socket shape and volume consistency can be quantified using MRI technology. Additionally, MRI images of the residual limb could be used as an input data for CAD-CAM technology and finite element studies. However, the accuracy of MRI when socket casting materials are used has to be defined. A number of six, 46 mm thick, cross-sections of an animal leg were used. Three specimens were wrapped with Plaster of Paris (POP) and the other three with commercially available silicone interface liner. Data was obtained by utilising MRI technology and then the segmented images compared to corresponding calliper measurement, photographic imaging, and water suspension techniques. The MRI measurement results were strongly correlated with actual diameter, surface area, and volume measurements. The results show that the selected scanning parameters and the semiautomatic segmentation method are adequate enough, considering the limit of clinical meaningful shape and volume fluctuation, for residual limb volume and the cross-sectional surface area measurements.

scholarly journals Precise SEM Cross Section Polishing via Argon Beam Milling

2006 ◽  
Vol 14 (3) ◽  
pp. 22-25 ◽  
Author(s):  
N. Erdman ◽  
R. Campbell ◽  
S. Asahina
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Soft Materials ◽  
Mechanical Polishing ◽  
Water Soluble ◽  
Staining Procedure ◽  
Fibrous Materials ◽  
Cross Sectional ◽  
Hard Materials ◽  
Composite Samples

SEM observation of a specimen cross section can provide important information for research and development as well as failure analysis. In most cases, surface observation alone cannot provide information concerning the cross sectional structure of granular materials, layered materials, fibrous materials, and powders. Preparing highly-polished cross sections of these materials is both a science and an art.Typically, a cross section is prepared using mechanical means like conventional mechanical polishing methods or a microtome. The sample is first embedded in a holder or device, and then polished to achieve a flat cross section. In some cases, a staining procedure is used to highlight a specific component of the sample. Such methods can be lengthy procedures that require a great deal of skill, and can introduce artifacts into soft materials, deform the material around voids, or compress layers of soft and hard materials in composite samples. Mechanical polishing can miss fine details such as the presence of hairline cracks, and present a challenge to water-soluble phases.

scholarly journals Exact Longitudinal Vibration Characteristics of Rods with Variable Cross-Sections

2011 ◽  
Vol 18 (4) ◽  
pp. 555-562 ◽  
Author(s):  
Bulent Yardimoglu ◽  
Levent Aydin
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Cross Sections ◽  
Longitudinal Vibration ◽  
Transformation Method ◽  
Variable Cross ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Sinusoidal Functions

Longitudinal natural vibration frequencies of rods (or bars) with variable cross-sections are obtained from the exact solutions of differential equation of motion based on transformation method. For the rods having cross-section variations as power of the sinusoidal functions ofax+b, the differential equation is reduced to associated Legendre equation by using the appropriate transformations. Frequency equations of rods with certain cross-section area variations are found from the general solution of this equation for different boundary conditions. The present solutions are benchmarked by the solutions available in the literature for the special case of present cross-sectional variations. Moreover, the effects of cross-sectional area variations of rods on natural characteristics are studied with numerical examples.

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