Generalized Second Moment of Areas of Regular Polygons for Ludwick Type Material and its Application to Cantilever Column Buckling

2019 ◽  
Vol 19 (02) ◽  
pp. 1950010
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Cross Sections ◽  
Equilateral Triangle ◽  
Regular Polygon ◽  
Regular Hexagon ◽  
Type Material ◽  
Regular Polygons ◽  
Column Buckling ◽  
Second Moment ◽  
Regular Pentagon

This study deals with the generalized second moment of area (GSMA) of regular polygon cross-sections for the Ludwick type material and its application to cantilever column buckling. In the literature, the GSMA for the Ludwick type material has only been considered for rectangular, elliptical and superellipsoidal cross-sections. This study calculates the GSMAs of regular polygon cross-sections other than those mentioned above. The GSMAs calculated by varying the mechanical constant of the Ludwick type material for the equilateral triangle, square, regular pentagon, regular hexagon and circular cross-sections are reported in tables and figures. The GSMAs obtained from this study are applied to cantilever column buckling, with results shown in tables and figures.

scholarly journals The chord length distribution function for regular polygons

2009 ◽  
Vol 41 (2) ◽  
pp. 358-366 ◽  
Author(s):  
H. S. Harutyunyan ◽  
V. K. Ohanyan
Keyword(s):  
Distribution Function ◽  
Regular Polygon ◽  
Length Distribution ◽  
Chord Length ◽  
Regular Hexagon ◽  
Regular Polygons ◽  
Chord Length Distribution ◽  
Regular Pentagon ◽  
Regular Triangle ◽  
Elementary Expression

In this paper we obtain an elementary expression for the chord length distribution function of a regular polygon. The formula is derived using δ-formalism in Pleijel identity. In the particular cases of a regular triangle, a square, a regular pentagon, and a regular hexagon, our formula coincides with the results of Sulanke (1961), Gille (1988), Aharonyan and Ohanyan (2005), and Harutyunyan (2007), respectively.

scholarly journals The chord length distribution function for regular polygons

2009 ◽  
Vol 41 (02) ◽  
pp. 358-366
Author(s):  
H. S. Harutyunyan ◽  
V. K. Ohanyan
Keyword(s):  
Distribution Function ◽  
Regular Polygon ◽  
Length Distribution ◽  
Chord Length ◽  
Regular Hexagon ◽  
Regular Polygons ◽  
Chord Length Distribution ◽  
Regular Pentagon ◽  
Regular Triangle ◽  
Elementary Expression

In this paper we obtain an elementary expression for the chord length distribution function of a regular polygon. The formula is derived using δ-formalism in Pleijel identity. In the particular cases of a regular triangle, a square, a regular pentagon, and a regular hexagon, our formula coincides with the results of Sulanke (1961), Gille (1988), Aharonyan and Ohanyan (2005), and Harutyunyan (2007), respectively.

scholarly journals Spherical F-Tilings by Triangles and $r$-Sided Regular Polygons, $r \ge 5$

10.37236/746 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Catarina P. Avelino ◽  
Altino F. Santos
Keyword(s):  
Symmetry Group ◽  
Equilateral Triangle ◽  
Regular Polygon ◽  
Isosceles Triangle ◽  
Combinatorial Structure ◽  
Subsequent Paper ◽  
Regular Polygons ◽  
Spherical Triangles ◽  
Wide Family

The study of dihedral f-tilings of the sphere $S^2$ by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented by Breda and Santos [Beiträge zur Algebra und Geometrie, 45 (2004), 447–461]. Also, in a subsequent paper, the study of dihedral f-tilings of $S^2$ whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scalene triangles as the prototiles will lead to a wide family of f-tilings). In this paper we extend these results, presenting the study of dihedral f-tilings by spherical triangles and $r$-sided regular polygons, for any $r \ge 5$. The combinatorial structure, including the symmetry group of each tiling, is given.

New Theorems for Moments of Inertia

1993 ◽  
Vol 21 (4) ◽  
pp. 355-366 ◽  
Author(s):  
David L. Wallach
Keyword(s):  
Regular Polygon ◽  
Moment Of Inertia ◽  
Regular Polygons ◽  
Centre Of Mass ◽  
Moments Of Inertia ◽  
The Moment

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.

scholarly journals Investigations on Torsion of the Two-Chords Single Laced Members

2017 ◽  
Vol 25 (2) ◽  
pp. 147-160
Author(s):  
Paweł Lorkowski ◽  
Bronisław Gosowski
Keyword(s):  
Cross Sections ◽  
Experimental Studies ◽  
The Finite Element Method ◽  
Second Moment ◽  
Steel Columns ◽  
Numerical Studies ◽  
Traction Network ◽  
Railway Traction ◽  
Parametric Analyses ◽  
The Relationship

Abstract The paper presents experimental and numerical studies to determine the equivalent second moment of area of the uniform torsion of the two-chord steel single laced members. The members are used as poles of railway traction network gates, and steel columns of framed buildings as well. The stiffness of uniform torsion of this kind of columns allows to the determine the critical loads of the spatial stability. The experimental studies have been realized on a single - span members with rotation arrested at their ends, loaded by a torque applied at the mid-span. The relationship between angle of rotation of the considered cross-section and the torque has been determined. Appropriate numerical model was created in the ABAQUS program, based on the finite element method. A very good compatibility has been observed between experimental and numerical studies. The equivalent second moment of area of the uniform torsion for analysed members has been determined by comparing the experimental and analytical results to those obtained from differential equation of non-uniform torsion, based on Vlasov’s theory. Additionally, the parametric analyses of similar members subjected to the uniform torsion, for the richer range of cross-sections have been carried out by the means of SOFiSTiK program. The purpose of the latter was determining parametrical formulas for calculation of the second moment of area of uniform torsion.

scholarly journals Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II

10.37236/815 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
A. M. d'Azevedo Breda ◽  
Patrícia S. Ribeiro ◽  
Altino F. Santos
Keyword(s):  
Equilateral Triangle ◽  
Isosceles Triangle ◽  
Subsequent Paper ◽  
Euclidean Sphere ◽  
Regular Polygons ◽  
Combinatorial Description ◽  
Equilateral Triangles

The study of dihedral f-tilings of the Euclidean sphere $S^2$ by triangles and $r$-sided regular polygons was initiated in 2004 where the case $r=4$ was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and $r$-sided regular polygons, for any $r\ge 5$, was described. Later on, in [3], the classification of all f-tilings of $S^2$ whose prototiles are an equilateral triangle and an isosceles triangle is obtained. The algebraic and combinatorial description of spherical f-tilings by equilateral triangles and scalene triangles of angles $\beta$, $\gamma$ and $\delta$ $(\beta>\gamma>\delta)$ whose edge adjacency is performed by the side opposite to $\beta$ was done in [4]. In this paper we extend these results considering the edge adjacency performed by the side opposite to $\delta$.

The Torsionless Bending of a Hollow Beam by a Transverse Load

1937 ◽  
Vol 4 (1) ◽  
pp. A25-A30
Author(s):  
W. L. Schwalbe
Keyword(s):  
Cross Sections ◽  
Equilateral Triangle ◽  
Bending Moment ◽  
Longitudinal Section ◽  
Transverse Load ◽  
Shearing Stress ◽  
Numerical Work ◽  
Hollow Beam ◽  
Transverse Loads ◽  
Hollow Beams

Abstract The author discusses the bending of hollow beams when subjected to transverse loads, and points out that shearing stresses and strains in the cross sections are necessary, and a particular longitudinal section remains plane only if the resultant of the shearing stress, and hence the plane of the applied bending moment, possesses a particular location. The author determines the location of this resultant shearing stress by applying a method based on St. Venant’s theory. Applications of the method are made to two hollow sections. One of the sections is that of an equilateral triangle which serves as a measure of accuracy for the numerical work presented by the author, since the location of the resultant of the shearing stresses is known by symmetry.

KNOTTING OF REGULAR POLYGONS IN 3-SPACE

1994 ◽  
Vol 03 (03) ◽  
pp. 263-278 ◽  
Author(s):  
KENNETH C. MILLETT
Keyword(s):  
Regular Polygon ◽  
Regular Polygons ◽  
Homfly Polynomial ◽  
Linear Maps ◽  
Compact Variety ◽  
Linear Embedding

The probability that a linear embedding of a regular polygon in R3 is knotted should increase as a function of the number of sides. This assertion is investigated by means of an exploration of the compact variety of based oriented linear maps of regular polygons into R3. Asymptotically, an estimation of the probability of knotting is made by means of the HOMFLY polynomial.

Semiregular Tessellations with Pattern Blocks

2017 ◽  
Vol 111 (2) ◽  
pp. 90-94
Author(s):  
Debananda Chakraborty ◽  
Gunhan Caglayan
Keyword(s):  
New Jersey ◽  
Equilateral Triangle ◽  
Number Sense ◽  
Wall Painting ◽  
Regular Hexagon ◽  
Jersey City ◽  
Instructional Tools ◽  
Isosceles Trapezoid ◽  
Measurement Algebra ◽  
Geometry Measurement

Pattern blocks are multifunctional instructional tools with a variety of applications in various strands of mathematics (number sense, geometry, measurement, algebra, probability). The six pattern blocks are an equilateral triangle (green), a blue rhombus, an isosceles trapezoid (red), a regular hexagon (yellow), a square (orange), and a white rhombus. The sides of all pattern blocks are congruent, considered to be 1 unit in length for this article. Photograph 1 depicts a wall painting with squares and rhombuses found in Jersey City, New Jersey.

scholarly journals THE THE APPLICATION OF GENERIC GREEN SKILLS IN TESSELLATION OF REGULAR POLYGONS FOR ECONOMIC AND SOCIAL SUSTAINABILITY

2019 ◽  
Vol 4 (3) ◽  
pp. 121-124
Author(s):  
ABDULLAH Musa Cledumas ◽  
YUSRI BIN KAMIN ◽  
RABIU HARUNA ◽  
SHUAIBU HALIRU
Keyword(s):  
Regular Polygon ◽  
Social Sustainability ◽  
Regular Polygons ◽  
Environmentally Sustainable ◽  
Clothing Design ◽  
Proposed Model ◽  
The Right ◽  
Modelling Approach

Abstract This paper proposes an improved modelling approach for tessellating regular polygons in such a way that it is environmentally sustainable. In this paper, tessellation of polygons that have been innovated through the formed motifs, is an innovation from the traditional tessellations of objects and animals. The main contribution of this work is the simplification and innovating new patterns from the existing regular polygons, in which only three polygons (triangle, square and hexagon) that can free be tessellated are used, compared to using irregular polygons or other objects.  This is achieved by reducing the size of each polygon to smallest value and tessellating each of the reduced figure to the right or to left to obtain a two different designs of one unit called motif. These motifs are then combined together to form a pattern. In this innovation it is found that the proposed model is superior than tessellating ordinary regular polygon, because more designs are obtained, more colours may be obtained or introduced to give meaningful tiles or patterns. In particular Tessellations can be found in many areas of life. Art, architecture, hobbies, clothing design, including traditional wears and many other areas hold examples of tessellations found in our everyday surroundings.

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