Twisting and Bending of Thin-Walled Prismatic Beams of Open Cross-Sectional Profile

1970 ◽  
Vol 12 (2) ◽  
pp. 130-134 ◽  
Author(s):  
T. Harrison
Keyword(s):  
Cross Sections ◽  
Virtual Work ◽  
Cross Sectional ◽  
Transverse Bending ◽  
Prismatic Beam ◽  
Loading System ◽  
Cross Sectional Profile ◽  
Thin Walled ◽  
Sectional Profile ◽  
Principle Of Virtual Displacements

Previous studies of the behaviour, in generalized co-ordinates, of thin-walled, prismatic beams of open cross-sectional profile have included, explicitly, only the effects of distributed transverse forces, q x and q y, distributed longitudinal forces, q z, and distributed torsional couples, m z. Using the principle of virtual displacements, the work of previous investigators is extended to include, quite generally, the effects of the hitherto neglected distributed couples, m x and m y. The derivation of the differential equation relating to the twisting of an open-section prismatic beam is presented fully whilst those relating to transverse and axial displacements of cross-sections are merely stated. The kinematic and static boundary conditions for a cantilever are also established from the virtual work equations. These show that the free-end shear boundary condition associated with transverse bending which is usually adopted in engineering calculations is inadequate for such a generalized loading system.

Torsional Stiffness of a Thin-Walled Beam Braced by Pinned or Rigidly Fixed Transverse Diaphragms

1973 ◽  
Vol 15 (5) ◽  
pp. 351-356
Author(s):  
T. Harrison ◽  
J. M. Siddall
Keyword(s):  
Experimental Evidence ◽  
Theoretical Work ◽  
Torsional Stiffness ◽  
Cross Sectional ◽  
Cross Sectional Profile ◽  
Thin Walled ◽  
Sectional Profile ◽  
Good Agreement

The torsional stiffness of a thin-walled beam of open cross-sectional profile braced by evenly spaced transverse diaphragms is studied. Diaphragms rigidly fixed or attached by frictionless pins are treated and it is seen that, in either case, the only effect is to modify the St Venant torsional constant for the thin-walled beam. The theoretical work is supported by experimental evidence from two braced perspex channels which simulate the two assumed methods of attaching the diaphragms. Good agreement is demonstrated.

scholarly journals Cutting the first ‘teeth’: a new approach to functional analysis of conodont elements

2013 ◽  
Vol 280 (1768) ◽  
pp. 20131524 ◽  
Author(s):  
Duncan J. E. Murdock ◽  
Ivan J. Sansom ◽  
Philip C. J. Donoghue
Keyword(s):  
Functional Analysis ◽  
Cross Sections ◽  
Functional Performance ◽  
Individual Element ◽  
Cross Sectional ◽  
New Approach ◽  
Functional Models ◽  
Cross Sectional Profile ◽  
Tomographic Data ◽  
Sectional Profile

The morphological disparity of conodont elements rivals the dentition of all other vertebrates, yet relatively little is known about their functional diversity. Nevertheless, conodonts are an invaluable resource for testing the generality of functional principles derived from vertebrate teeth, and for exploring convergence in a range of food-processing structures. In a few derived conodont taxa, occlusal patterns have been used to derive functional models. However, conodont elements commonly and primitively exhibit comparatively simple coniform morphologies, functional analysis of which has not progressed much beyond speculation based on analogy. We have generated high-resolution tomographic data for each morphotype of the coniform conodont Panderodus acostatus . Using virtual cross sections, it has been possible to characterize changes in physical properties associated with individual element morphology. Subtle changes in cross-sectional profile have profound implications for the functional performance of individual elements and the apparatus as a whole. This study has implications beyond the ecology of a single conodont taxon. It provides a basis for reinterpreting coniform conodont taxonomy (which is based heavily on cross-sectional profiles), in terms of functional performance and ecology, shedding new light on the conodont fossil record. This technique can also be applied to more derived conodont morphologies, as well as analogous dentitions in other vertebrates and invertebrates.

scholarly journals Effects of the Extrusion Process Parameter

2011 ◽  
Vol 8 (1) ◽  
pp. 65-74
Author(s):  
Prashant Baredar ◽  
Jitendra Kumar ◽  
Anil Kumar ◽  
Shankar Kumar
Keyword(s):  
Plastic Deformation ◽  
Cross Section ◽  
Cross Sections ◽  
Metal Forming ◽  
Extrusion Process ◽  
Cross Sectional ◽  
High Deformation ◽  
Tensile Forces ◽  
Cross Sectional Profile ◽  
Sectional Profile

Extrusion is an important Metal forming operation. It is a manufacturing process used to create long objects of a fixed cross sectional profile. The extrusion process is based on the plastic deformation of a material due to compressive and shears forces only. No tensile forces are applied to the extruded metal. The latter allows the material to withstand high deformation without tearing out the material. Basically, this procedure is based on the reducing and shaping the cross section of piece of metal squeezing the material through an orifice or a die. Typically the blocks of metal used for this procedure are long straight parts with circular cross sections.

X-Ray Replication of Submicrometer Linewidth Patterns

1977 ◽  
Vol 35 ◽  
pp. 136-137
Author(s):  
Henry I. Smith ◽  
D.C. Flanders
Keyword(s):  
Electron Beam Lithography ◽  
Cross Sectional ◽  
X Ray ◽  
Electron Backscattering ◽  
Spatial Frequencies ◽  
Cross Sectional Profile ◽  
Carbon Foils ◽  
Sectional Profile ◽  
And Control ◽  
Soft Radiation

Scanning electron beam lithography has been used for a number of years to write submicrometer linewidth patterns in radiation sensitive films (resist films) on substrates. On semi-infinite substrates, electron backscattering severely limits the exposure latitude and control of cross-sectional profile for patterns having fundamental spatial frequencies below about 4000 Å(l),Recently, STEM'S have been used to write patterns with linewidths below 100 Å. To avoid the detrimental effects of electron backscattering however, the substrates had to be carbon foils about 100 Å thick (2,3). X-ray lithography using the very soft radiation in the range 10 - 50 Å avoids the problem of backscattering and thus permits one to replicate on semi-infinite substrates patterns with linewidths of the order of 1000 Å and less, and in addition provides means for controlling cross-sectional profiles. X-radiation in the range 4-10 Å on the other hand is appropriate for replicating patterns in the linewidth range above about 3000 Å, and thus is most appropriate for microelectronic applications (4 - 6).

scholarly journals Bonding widths of Deposited Polymer Strands in Additive Manufacturing

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 871
Author(s):  
Cheng Luo ◽  
Manjarik Mrinal ◽  
Xiang Wang ◽  
Ye Hong
Keyword(s):  
Polymer Melt ◽  
Acrylonitrile Butadiene Styrene ◽  
High Viscosity ◽  
Numerical Results ◽  
Fused Filament Fabrication ◽  
Cross Sectional ◽  
Nozzle Height ◽  
Special Cases ◽  
Cross Sectional Profile ◽  
Sectional Profile

In this study, we explore the deformation of a polymer extrudate upon the deposition on a build platform, to determine the bonding widths between stacked strands in fused-filament fabrication. The considered polymer melt has an extremely high viscosity, which dominates in its deformation. Mainly considering the viscous effect, we derive analytical expressions of the flat width, compressed depth, bonding width and cross-sectional profile of the filament in four special cases, which have different combinations of extrusion speed, print speed and nozzle height. We further validate the derived relations, using our experimental results on acrylonitrile butadiene styrene (ABS), as well as existing experimental and numerical results on ABS and polylactic acid (PLA). Compared with existing theoretical and numerical results, our derived analytic relations are simple, which need less calculations. They can be used to quickly predict the geometries of the deposited strands, including the bonding widths.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Measurement of cross-sectional profile for sub-15nm hp LS patterns in nanoimprint templates using small-angle x-ray scattering

2020 ◽  
Author(s):  
Kazuki Hagihara ◽  
Eiji Yamanaka ◽  
Yoshiyasu Ito ◽  
Kiyoshi Ogata ◽  
Kazuhiko Omote ◽  
...  
Keyword(s):  
Small Angle ◽  
Cross Sectional ◽  
X Ray ◽  
X Ray Scattering ◽  
Cross Sectional Profile ◽  
Sectional Profile ◽  
Ray Scattering

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.

scholarly journals Simplified and Accurate Stiffness of a Prismatic Anisotropic Thin-Walled Box

2018 ◽  
Vol 12 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Giacomo Canale ◽  
Felice Rubino ◽  
Paul M. Weaver ◽  
Roberto Citarella ◽  
Angelo Maligno
Keyword(s):  
Cross Sections ◽  
Torsional Stiffness ◽  
Element Analysis ◽  
Cross Sectional ◽  
Analysis And Design ◽  
Proposed Model ◽  
Vertical Walls ◽  
Thin Walled ◽  
High Level ◽  
Realistic Geometries

Background:Beam models have been proven effective in the preliminary analysis and design of aerospace structures. Accurate cross sectional stiffness constants are however needed, especially when dealing with bending, torsion and bend-twist coupling deformations. Several models have been proposed in the literature, even recently, but a lack of precision may be found when dealing with a high level of anisotropy and different lay-ups.Objective:A simplified analytical model is proposed to evaluate bending and torsional stiffness of a prismatic, anisotropic, thin-walled box. The proposed model is an extension of the model proposed by Lemanski and Weaver for the evaluation of the bend-twist coupling constant.Methods:Bending and torsional stiffness are derived analytically by using physical reasoning and by applying bending and torsional stiffness mathematic definition. Unitary deformations have been applied when evaluation forces and moments arising on the cross section.Results:Good accuracy has been obtained for structures with different geometries and lay-ups. The model has been validated with respect to finite element analysis. Numerical results are commented upon and compared with other models presented in literature.Conclusion:For cross sections with a high level of anisotropy, the accuracy of the proposed formulation is within 2% for bending stiffness and 6% for torsional stiffness. The percentage of error is further reduced for more realistic geometries and lay-ups.The proposed formulation gives accurate results for different dimensions and length rations of horizontal and vertical walls.

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