Bob Morris presents a simplified model for understanding how wound rubber motors work. The model uses topological variables called twist and writhe to represent the rotations and crossings of a stretched rubber strand. It calculates the maximum number of turns a motor can achieve based on the motor dimensions and elastic properties of the rubber. The model predictions closely match experimental data and provide insight into optimizing motor winding sequences to maximize flights while minimizing strain on the rubber.
This document describes how to use Mohr's circle to analyze stresses in a stressed material. Mohr's circle provides a graphical representation of the relationships between normal and shear stresses on inclined planes. It can be used to calculate principal stresses, maximum shear stresses, and stresses on inclined planes. The document includes several numerical examples showing how to construct and use Mohr's circles to solve for these values given known stresses and orientations in a material.
This document discusses moment of inertia, which is a measure of an object's resistance to changes in rotation. It begins by defining moment of inertia as the second moment of force or mass of an object. It then provides formulas for calculating the moment of inertia of common shapes like rectangles, circles, and hollow sections. For rectangles, the moment of inertia depends on the cube of the distance of the axis from the object's sides. For circles, the moment of inertia is proportional to the diameter to the fourth power. The document also presents theorems for calculating moment of inertia about different axes, such as perpendicular axes and parallel axes. Sample problems are worked through to demonstrate calculating moment of inertia for rectangular and circular sections.
1. This document contains solutions to 6 physics problems. The first problem involves water flowing between two containers when one is heated. The second solves equations of motion for circular motion attached to a string. The third calculates the maximum distance a brick can travel when thrown at an angle. The fourth analyzes the motion of an expanding sheet on an inclined plane. The fifth derives forces and damping for a charged particle near a conducting plate. The sixth fully solves the motion of a ball attached to a string swinging from a pole.
This document discusses the concept of centroid and provides formulas to calculate the centroid of different geometric shapes. It defines centroid as the point within an object where the downward force of gravity appears to act. The centroid allows an object to remain balanced when placed on a pivot at the centroid point. Formulas are given for finding the centroid of triangles, rectangles, circles, semicircles, right circular cones, and composite figures. Real-life applications of centroid calculation in construction and engineering are also mentioned.
The first moment of area of a lamina is defined as the product of the lamina's area and the perpendicular distance of its center of gravity from a given axis. It is used to determine the center of gravity of an area. To calculate the first moment of area, the area is split into segments, and the area of each segment is multiplied by its distance from the axis and summed. This gives the first moment of area, which provides information about the distribution of the area.
1) The document discusses elastic instability in structures, using the example of buckling of bars and columns under compressive loading. Elastic instability occurs when a structure transitions from stable to unstable deformation modes with increasing load.
2) As an introductory example, the document analyzes a rigid bar with a torsional spring, subject to horizontal and vertical forces. It derives an expression for the critical vertical load that causes instability, equal to the torsional spring stiffness divided by the bar length.
3) Looking ahead, the document notes it will apply these concepts of instability and critical load to analyze the buckling of a compressed column, which has a continuous distribution of stiffness rather than
Leaf springs are made of beams with uniform strength and are commonly used in automobiles. They consist of multiple leafs stacked together to form a cantilever beam. This distributes the load from the road across the leaves. Stress and deflection analyses show that the stress in the master leaf is 50% higher than in the graduated leaves. However, giving the master leaf a curvature through residual stresses can equalize the stresses across leaves and increase the total load capacity. Equations are derived relating load shared, stresses developed, and maximum deflection to the number and dimensions of leaves.
This document contains solutions to problems from Chapter 16 related to sheet metal forming. Key points:
1) The values of L/L0 were calculated for brass and aluminum based on given strain equations and input values.
2) The contour of ε = 0.04 was plotted on a forming limit diagram for values of ε1 vs ε2 using von Mises and Tresca criteria.
3) It was explained that the dashed line in a figure showing the wrinkling limit would change for a material with an R-value of 2 compared to the original material.
This document describes how to use Mohr's circle to analyze stresses in a stressed material. Mohr's circle provides a graphical representation of the relationships between normal and shear stresses on inclined planes. It can be used to calculate principal stresses, maximum shear stresses, and stresses on inclined planes. The document includes several numerical examples showing how to construct and use Mohr's circles to solve for these values given known stresses and orientations in a material.
This document discusses moment of inertia, which is a measure of an object's resistance to changes in rotation. It begins by defining moment of inertia as the second moment of force or mass of an object. It then provides formulas for calculating the moment of inertia of common shapes like rectangles, circles, and hollow sections. For rectangles, the moment of inertia depends on the cube of the distance of the axis from the object's sides. For circles, the moment of inertia is proportional to the diameter to the fourth power. The document also presents theorems for calculating moment of inertia about different axes, such as perpendicular axes and parallel axes. Sample problems are worked through to demonstrate calculating moment of inertia for rectangular and circular sections.
1. This document contains solutions to 6 physics problems. The first problem involves water flowing between two containers when one is heated. The second solves equations of motion for circular motion attached to a string. The third calculates the maximum distance a brick can travel when thrown at an angle. The fourth analyzes the motion of an expanding sheet on an inclined plane. The fifth derives forces and damping for a charged particle near a conducting plate. The sixth fully solves the motion of a ball attached to a string swinging from a pole.
This document discusses the concept of centroid and provides formulas to calculate the centroid of different geometric shapes. It defines centroid as the point within an object where the downward force of gravity appears to act. The centroid allows an object to remain balanced when placed on a pivot at the centroid point. Formulas are given for finding the centroid of triangles, rectangles, circles, semicircles, right circular cones, and composite figures. Real-life applications of centroid calculation in construction and engineering are also mentioned.
The first moment of area of a lamina is defined as the product of the lamina's area and the perpendicular distance of its center of gravity from a given axis. It is used to determine the center of gravity of an area. To calculate the first moment of area, the area is split into segments, and the area of each segment is multiplied by its distance from the axis and summed. This gives the first moment of area, which provides information about the distribution of the area.
1) The document discusses elastic instability in structures, using the example of buckling of bars and columns under compressive loading. Elastic instability occurs when a structure transitions from stable to unstable deformation modes with increasing load.
2) As an introductory example, the document analyzes a rigid bar with a torsional spring, subject to horizontal and vertical forces. It derives an expression for the critical vertical load that causes instability, equal to the torsional spring stiffness divided by the bar length.
3) Looking ahead, the document notes it will apply these concepts of instability and critical load to analyze the buckling of a compressed column, which has a continuous distribution of stiffness rather than
Leaf springs are made of beams with uniform strength and are commonly used in automobiles. They consist of multiple leafs stacked together to form a cantilever beam. This distributes the load from the road across the leaves. Stress and deflection analyses show that the stress in the master leaf is 50% higher than in the graduated leaves. However, giving the master leaf a curvature through residual stresses can equalize the stresses across leaves and increase the total load capacity. Equations are derived relating load shared, stresses developed, and maximum deflection to the number and dimensions of leaves.
This document contains solutions to problems from Chapter 16 related to sheet metal forming. Key points:
1) The values of L/L0 were calculated for brass and aluminum based on given strain equations and input values.
2) The contour of ε = 0.04 was plotted on a forming limit diagram for values of ε1 vs ε2 using von Mises and Tresca criteria.
3) It was explained that the dashed line in a figure showing the wrinkling limit would change for a material with an R-value of 2 compared to the original material.
This presentation discusses transverse shear stress in beams. It begins with an introduction distinguishing bending stress from shear stress. The assumptions and derivation of the shear stress formula are then outlined. Analysis is shown for rectangular cross sections, where shear stress is highest at the neutral axis and zero at extreme fibers. Other cross section shapes are briefly discussed, including their maximum shear stress ratios. Key points are recapped about shear stress distribution across different cross section geometries. References are provided for further reading.
The document contains solutions to problems from Chapter 17-19 related to metal forming processes. It calculates pressures, strains, and radii required for tube expansion and hydroforming processes. It also analyzes stress states during hole expansion and describes the effect of aging times and temperatures on strain aging in low carbon steels.
Composites are made of two main components: fibers and a matrix. Fibers carry load and can be made of materials like glass, carbon, and Kevlar. Fibers come in various forms like strands, woven meshes, and chopped fibers. The matrix is a fluid that hardens and holds the fibers in place. It can be made of materials like plastic. Examples of composites include carbon fiber and plastic skis, Kevlar and fiberglass boats, and concrete reinforced with steel. The document then discusses stresses in beams including bending stresses, maximum bending stress, and shear stress.
Solution to first semester soil 2015 16chener Qadr
This document contains a soil mechanics exam with four questions. Question 1 involves determining properties like void ratio, dry density, and bulk density of a saturated soil sample. It also asks about changes if saturation is reduced and calculating soil requirements for an embankment. Question 2 asks to classify a soil sample using soil classification charts and determine its suitability as backfill. Question 3 involves calculating seepage flow from a canal into a ditch based on soil properties. Question 4, which is not fully summarized, involves analyzing seepage in an embankment dam.
The document discusses various types of combined stresses:
1) Biaxial bending stresses are the sum of stresses from bending in two perpendicular directions.
2) Combined bending and axial stresses add the axial stress to the bending stress.
3) Eccentrically loaded axial members have extra bending stress due to eccentricity.
4) Normal and shear stresses on a stress element are defined.
5) Principal stresses are the maximum normal stresses on perpendicular planes.
6) Maximum shear stress and its orientation are also defined.
7) Mohr's circle is introduced as a graphical method to represent the stresses on a plane.
Shear force and bending moment diagrams are constructed for a beam subjected to various loads. The shear force is maximum at supports and zero at points of inflection, while the bending moment is maximum at points of inflection and zero at supports. For the given beam under a uniform distributed load and two concentrated loads, the shear force and bending moment diagrams are drawn showing the variations along the length of the beam. Key points of zero shear force and maximum bending moment are identified.
The document presents a LuGre dynamic friction model for tire-road contact that describes friction forces and moments as a distributed system of partial differential equations across the contact patch. It uses the method of moments to derive an equivalent lumped model described by ordinary differential equations that captures the exact average dynamics of the distributed model. Three cases of normal load distribution across the contact patch are considered - uniform, trapezoidal, and quartic - and the lumped models for each case are compared through simulations.
This document provides information about centroids and moments of inertia. It defines key terms like centroid, center of mass, center of gravity, moment of area, mass moment of inertia, and radius of gyration. It then demonstrates how to calculate the centroid of common shapes like triangles, semicircles, and parabolic spandrels using integration. The document also discusses moment of inertia, polar moment of inertia, and the perpendicular and parallel axis theorems.
This document discusses shear force and bending moment diagrams (SFD & BMD) for beams under different loading conditions. It defines key terms like shear force, bending moment, sagging and hogging bending moments. It also describes the relationships between applied loads, shear forces and bending moments. Examples are provided to demonstrate how to draw SFDs and BMDs and calculate reactions, shear forces and bending moments at different sections of beams. Points of contraflexure, where the bending moment changes sign, are also identified.
Properties of surfaces-Centre of gravity and Moment of InertiaJISHNU V
The document discusses properties of surfaces, including centre of gravity and moment of inertia. It defines key terms like centre of gravity, centroid, area moment of inertia, radius of gyration, and mass moment of inertia. Methods for calculating these properties are presented for basic shapes like rectangles, triangles, circles, and composite shapes. Theorems like the perpendicular axis theorem and parallel axis theorem are also covered. Examples are provided for determining the moment of inertia of various plane figures and structures.
Solution to 2nd semeter eng. statistics 2015 2016chener Qadr
This document contains an exam for an engineering statistics class consisting of 5 problems:
1) Listing construction time combinations and finding number of engineer pair selections.
2) Calculating flood probability metrics over 31 years.
3) Determining town flooding probabilities from a dam considering earthquake damage.
4) Finding failure probabilities for a retaining wall considering sliding and overturning.
5) Defining performance metrics for a city's water delivery considering reservoir levels and tunnel outages.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Lecture slides on the calculation of the bending stress in case of unsymmetrical bending. The Mohr's circle is used to determine the principal second moments of area.
The document discusses the concepts of centroid and centre of gravity. It defines centroid as the point where the whole area of a plane figure can be assumed to be concentrated. The centre of gravity is the point where the entire weight of a body acts and can be balanced. The document then provides methods to determine the centroid of common geometric shapes such as rectangles, triangles, semicircles, and composite shapes using the principle of moments. It includes examples of calculating the x- and y-coordinates of the centroid for various geometric problems.
The document provides step-by-step instructions for drawing the shear force and bending moment diagrams of a cantilever beam subjected to various loads. It first finds the reactions at the support, then draws the shear force diagram showing the shear force values change from -45 kN to -75 kN over the length of the beam. It then draws the bending moment diagram, indicating the bending moment values change from -33.75 kN.m to -168.75 kN.m at the end of the beam due to the applied loads and moments. Key points on both diagrams are indicated.
This document defines key terms and concepts related to standard deviation and variance. It provides formulas for calculating range, deviation, variance, and standard deviation for both ungrouped and grouped data. Examples are given to demonstrate calculating these metrics from raw data sets and grouped data tables. Interpreting skewness is also discussed.
1) Poisson's ratio describes the strain in the perpendicular direction due to loading. Under uniaxial loads, the perpendicular strain is proportional to the parallel strain multiplied by Poisson's ratio. Under biaxial loads, the strains are calculated considering the effects of both loads.
2) Thermal expansion causes materials to expand or contract with changes in temperature. Temperature changes can also induce thermal stresses if expansion is constrained.
3) Composite members made of different materials experience stress based on their relative moduli of elasticity. The stress in each material is proportional to the other by their modular ratio.
This document discusses moments of inertia, which are a measure of an object's resistance to rotational acceleration about an axis. It defines the moment of inertia of an area and introduces key concepts like the parallel axis theorem, radius of gyration, and calculating moments of inertia through integration or for composite areas. Examples are provided to demonstrate calculating moments of inertia for various shapes, including rectangles, triangles, L-shapes, and composite profiles, about different axes. The document also covers determining moments of inertia at the centroidal axes versus other axes using the parallel axis theorem.
A empresa está enfrentando desafios financeiros devido à pandemia e precisa cortar custos. O diretor financeiro recomenda demitir funcionários para economizar em salários e reduzir outros gastos não essenciais para melhorar a situação financeira da empresa até o final do ano.
SlideShare es un sitio web donde los usuarios pueden subir presentaciones en formato PDF o diapositivas que pueden ser públicas o privadas, y que permiten ser vistas simultáneamente por múltiples personas; acepta la mayoría de programas para crear presentaciones pero limita los archivos a 30MB y reduce la resolución de fotografías, y para crear una cuenta se requiere llenar un formulario de registro e confirmar el correo electrónico.
This presentation discusses transverse shear stress in beams. It begins with an introduction distinguishing bending stress from shear stress. The assumptions and derivation of the shear stress formula are then outlined. Analysis is shown for rectangular cross sections, where shear stress is highest at the neutral axis and zero at extreme fibers. Other cross section shapes are briefly discussed, including their maximum shear stress ratios. Key points are recapped about shear stress distribution across different cross section geometries. References are provided for further reading.
The document contains solutions to problems from Chapter 17-19 related to metal forming processes. It calculates pressures, strains, and radii required for tube expansion and hydroforming processes. It also analyzes stress states during hole expansion and describes the effect of aging times and temperatures on strain aging in low carbon steels.
Composites are made of two main components: fibers and a matrix. Fibers carry load and can be made of materials like glass, carbon, and Kevlar. Fibers come in various forms like strands, woven meshes, and chopped fibers. The matrix is a fluid that hardens and holds the fibers in place. It can be made of materials like plastic. Examples of composites include carbon fiber and plastic skis, Kevlar and fiberglass boats, and concrete reinforced with steel. The document then discusses stresses in beams including bending stresses, maximum bending stress, and shear stress.
Solution to first semester soil 2015 16chener Qadr
This document contains a soil mechanics exam with four questions. Question 1 involves determining properties like void ratio, dry density, and bulk density of a saturated soil sample. It also asks about changes if saturation is reduced and calculating soil requirements for an embankment. Question 2 asks to classify a soil sample using soil classification charts and determine its suitability as backfill. Question 3 involves calculating seepage flow from a canal into a ditch based on soil properties. Question 4, which is not fully summarized, involves analyzing seepage in an embankment dam.
The document discusses various types of combined stresses:
1) Biaxial bending stresses are the sum of stresses from bending in two perpendicular directions.
2) Combined bending and axial stresses add the axial stress to the bending stress.
3) Eccentrically loaded axial members have extra bending stress due to eccentricity.
4) Normal and shear stresses on a stress element are defined.
5) Principal stresses are the maximum normal stresses on perpendicular planes.
6) Maximum shear stress and its orientation are also defined.
7) Mohr's circle is introduced as a graphical method to represent the stresses on a plane.
Shear force and bending moment diagrams are constructed for a beam subjected to various loads. The shear force is maximum at supports and zero at points of inflection, while the bending moment is maximum at points of inflection and zero at supports. For the given beam under a uniform distributed load and two concentrated loads, the shear force and bending moment diagrams are drawn showing the variations along the length of the beam. Key points of zero shear force and maximum bending moment are identified.
The document presents a LuGre dynamic friction model for tire-road contact that describes friction forces and moments as a distributed system of partial differential equations across the contact patch. It uses the method of moments to derive an equivalent lumped model described by ordinary differential equations that captures the exact average dynamics of the distributed model. Three cases of normal load distribution across the contact patch are considered - uniform, trapezoidal, and quartic - and the lumped models for each case are compared through simulations.
This document provides information about centroids and moments of inertia. It defines key terms like centroid, center of mass, center of gravity, moment of area, mass moment of inertia, and radius of gyration. It then demonstrates how to calculate the centroid of common shapes like triangles, semicircles, and parabolic spandrels using integration. The document also discusses moment of inertia, polar moment of inertia, and the perpendicular and parallel axis theorems.
This document discusses shear force and bending moment diagrams (SFD & BMD) for beams under different loading conditions. It defines key terms like shear force, bending moment, sagging and hogging bending moments. It also describes the relationships between applied loads, shear forces and bending moments. Examples are provided to demonstrate how to draw SFDs and BMDs and calculate reactions, shear forces and bending moments at different sections of beams. Points of contraflexure, where the bending moment changes sign, are also identified.
Properties of surfaces-Centre of gravity and Moment of InertiaJISHNU V
The document discusses properties of surfaces, including centre of gravity and moment of inertia. It defines key terms like centre of gravity, centroid, area moment of inertia, radius of gyration, and mass moment of inertia. Methods for calculating these properties are presented for basic shapes like rectangles, triangles, circles, and composite shapes. Theorems like the perpendicular axis theorem and parallel axis theorem are also covered. Examples are provided for determining the moment of inertia of various plane figures and structures.
Solution to 2nd semeter eng. statistics 2015 2016chener Qadr
This document contains an exam for an engineering statistics class consisting of 5 problems:
1) Listing construction time combinations and finding number of engineer pair selections.
2) Calculating flood probability metrics over 31 years.
3) Determining town flooding probabilities from a dam considering earthquake damage.
4) Finding failure probabilities for a retaining wall considering sliding and overturning.
5) Defining performance metrics for a city's water delivery considering reservoir levels and tunnel outages.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Lecture slides on the calculation of the bending stress in case of unsymmetrical bending. The Mohr's circle is used to determine the principal second moments of area.
The document discusses the concepts of centroid and centre of gravity. It defines centroid as the point where the whole area of a plane figure can be assumed to be concentrated. The centre of gravity is the point where the entire weight of a body acts and can be balanced. The document then provides methods to determine the centroid of common geometric shapes such as rectangles, triangles, semicircles, and composite shapes using the principle of moments. It includes examples of calculating the x- and y-coordinates of the centroid for various geometric problems.
The document provides step-by-step instructions for drawing the shear force and bending moment diagrams of a cantilever beam subjected to various loads. It first finds the reactions at the support, then draws the shear force diagram showing the shear force values change from -45 kN to -75 kN over the length of the beam. It then draws the bending moment diagram, indicating the bending moment values change from -33.75 kN.m to -168.75 kN.m at the end of the beam due to the applied loads and moments. Key points on both diagrams are indicated.
This document defines key terms and concepts related to standard deviation and variance. It provides formulas for calculating range, deviation, variance, and standard deviation for both ungrouped and grouped data. Examples are given to demonstrate calculating these metrics from raw data sets and grouped data tables. Interpreting skewness is also discussed.
1) Poisson's ratio describes the strain in the perpendicular direction due to loading. Under uniaxial loads, the perpendicular strain is proportional to the parallel strain multiplied by Poisson's ratio. Under biaxial loads, the strains are calculated considering the effects of both loads.
2) Thermal expansion causes materials to expand or contract with changes in temperature. Temperature changes can also induce thermal stresses if expansion is constrained.
3) Composite members made of different materials experience stress based on their relative moduli of elasticity. The stress in each material is proportional to the other by their modular ratio.
This document discusses moments of inertia, which are a measure of an object's resistance to rotational acceleration about an axis. It defines the moment of inertia of an area and introduces key concepts like the parallel axis theorem, radius of gyration, and calculating moments of inertia through integration or for composite areas. Examples are provided to demonstrate calculating moments of inertia for various shapes, including rectangles, triangles, L-shapes, and composite profiles, about different axes. The document also covers determining moments of inertia at the centroidal axes versus other axes using the parallel axis theorem.
A empresa está enfrentando desafios financeiros devido à pandemia e precisa cortar custos. O diretor financeiro recomenda demitir funcionários para economizar em salários e reduzir outros gastos não essenciais para melhorar a situação financeira da empresa até o final do ano.
SlideShare es un sitio web donde los usuarios pueden subir presentaciones en formato PDF o diapositivas que pueden ser públicas o privadas, y que permiten ser vistas simultáneamente por múltiples personas; acepta la mayoría de programas para crear presentaciones pero limita los archivos a 30MB y reduce la resolución de fotografías, y para crear una cuenta se requiere llenar un formulario de registro e confirmar el correo electrónico.
The document describes the Alegro project, which aims to provide musical education to underprivileged children in Curitiba, Brazil based on the El Sistema model. It provides details on Alegro's founder and leadership, educational programs and partnerships, operating structure and budgets. The project currently teaches 200 students across two locations but faces challenges due to Brazil's economic crisis and risks losing partnerships. It is seeking help to expand access to musical instruments for students.
Este documento presenta diferentes tipos de turismo como el ecoturismo, turismo metropolitano, agroturismo, etnoturismo, acuaturismo y turismo rural. El ecoturismo se desarrolla en áreas naturales y busca la recreación y conservación de la biodiversidad. El turismo metropolitano ofrece actividades culturales y lúdicas en grandes ciudades. El agroturismo involucra actividades agrícolas. El etnoturismo preserva culturas ancestrales. El acuaturismo se enfoca en actividades acu
Slideshare es un sitio web que permite a los usuarios subir presentaciones PowerPoint u Open Office en formato Flash para compartirlas públicamente. Los usuarios pueden ver las presentaciones en línea o compartirlas a través de correo electrónico. Flickr es un sitio para almacenar y compartir fotografías y videos personales. Ambos sitios requieren registro y conexión a Internet, y permiten a los usuarios crear y compartir contenido educativo como trabajos escolares, presentaciones y bibliotecas de imágenes.
Este documento apresenta um trecho da obra "Da Natureza" de Parmênides traduzida para o português. A introdução descreve brevemente a tradução e edição do texto original em grego. O trecho apresenta o diálogo entre a deusa e Parmênides, onde ela o convida a aprender sobre a verdadeira natureza do ser.
Flickr es un sitio web creado en 2004 para almacenar y compartir fotografías y videos. Los usuarios pueden clasificar y almacenar sus fotos de manera ilimitada en la versión gratuita, aunque la calidad y resolución se reducen. Flickr también funciona como una red social donde los usuarios comparten y enlazan fotos a otros sitios. Para crear una cuenta, solo se necesita una dirección de correo electrónico de Yahoo.
Memasukkan file dari SlideShare ke Blog dapat dilakukan dengan mengambil alamat embed dari SlideShare, menempelkannya ke dalam pos blog, dan memperbarui halaman blog.
The document is a 27-slide presentation created with Haiku Deck presentation software. Each slide contains an image taken by a different photographer. The presentation discusses how the past cannot be returned to and is titled "Aika entinen ei enää palaa" which means "the past time does not return" in Finnish.
El documento describe diferentes perspectivas del concepto de paisaje desde varios campos de estudio. Desde la geografía, el paisaje es el objeto de estudio principal y el documento básico para hacer geografía. Desde las artes, especialmente la pintura, el paisaje es la representación gráfica de un terreno extenso. En literatura, la descripción del paisaje es una forma literaria llamada topografía. Además, un paisaje cultural es aquel transformado por un grupo cultural a partir de uno natural.
Wall Street Derivative Risk Solutions Using Apache GeodeAndre Langevin
The document proposes a design for an event-based, cross-product risk management system using Apache Geode. Key elements include splitting data into regions for trades, markets, and results; placing regions to optimize performance of risk calculations; using PDX to bridge languages; integrating market and trade data streams; running a proprietary math library on a shared compute grid or inside Geode; and building real-time risk views. The system aims to provide a consolidated risk view across trading products and systems.
This document presents a computational analysis of the structural components and behavior of flexible aircraft. It describes a MATLAB code used to determine natural frequencies and loads of a cantilever wing with stores in different spanwise positions. The code calculates natural frequencies from mass and stiffness matrices. Basis functions are used to represent bending and torsional modes. Validation shows computed torsion frequencies match experimental data, while bending frequencies have some offset. Parameters like store mass and position are investigated and found to affect natural frequencies.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Gears are used to transmit mechanical power from one rotating shaft to another. There are several types of gears that are commonly used including spur gears, helical gears, bevel gears, and worm gears. Spur gears have straight teeth that allow for easy engagement and disengagement. This document discusses the design, specification, and selection of spur gears based on failure due to bending stress using the Lewis equation. It provides information on gear terminology, types of gear trains, tooth systems, force analysis, stresses, selection procedures, and wear failure. Examples are also included to demonstrate how to select suitable gears based on given design parameters and constraints.
This document discusses the effect of sweep angle on the rolling moment derivative of an oscillating supersonic or hypersonic delta wing. It presents analytical expressions derived using piston theory and similitude to model the pressure distribution on the wing. The results show that the rolling moment derivative decreases continuously with increasing sweep angle and Mach number. For lower sweep angles, the magnitude of decrease in the rolling moment derivative is much larger than for higher sweep angles. The rolling moment derivative also increases with angle of attack. Effects of wave reflection, leading edge bluntness and viscosity are not considered in the analysis. Results are obtained for a range of sweep angles, Mach numbers, planform areas and angles of attack.
The document summarizes a student design project to reduce stress and twist in a swept forward aircraft wing. The students analyzed straight and swept wing models to compare displacement and stress. They used MATLAB to calculate spar locations that increased torsional rigidity in a hollow wing. Models with two or three spars were then analyzed in ANSYS. A 27 Newton lifting force was applied based on lift coefficient calculations. Tables compare results of different spar arrangements and thicknesses, identifying a three-spar design with 0.025, 0.01, and 0.01 cm thicknesses as providing the least twist and stress. Increasing the front spar thickness further reduced twist but increased stress due to added weight and bending moment.
The researchers used strain gauges to experimentally determine the drag coefficient of a scale model Toyota car. Tests were conducted in a subsonic wind tunnel from 21.17 to 33 m/s. Drag coefficients were obtained ranging from 1.10 to 0.53, decreasing about 50% over the speed range tested. Flow visualization showed recirculating vortices at the rear that influence drag. Measurement errors for velocity, drag force, and drag coefficient decreased with increasing air speed.
This study investigates unsteady aerodynamic effects for a vertical axial wind turbine through computational fluid dynamics simulations. A two-dimensional model of the turbine was created using a NACA0015 airfoil for the blades. Simulations were run at different tip speed ratios to analyze blade forces, torque, and dynamic stall. Results showed that maximum average torque occurred at a tip speed ratio of 1.3. Blade forces were highest when the rotor was at 50 degrees. Dynamic stall phenomena, such as vortex shedding and detachment, were observed and affected turbine performance.
This document discusses torsion and torsion of circular shafts. It introduces torsion, defines the assumptions made in analyzing torsion of circular shafts, and derives the equations for shear strain, stress, angle of twist, and torque-twist relationship. It provides the torsion formulas for solid and hollow circular shafts. Sample problems are included to demonstrate calculating shear stress, torque, and angle of twist in statically indeterminate torsion problems.
Design of a vertical axis wind turbine how the aspect ratio affectsPhuong Dx
- The document analyzes how the aspect ratio of a vertical-axis wind turbine affects its performance.
- It finds that turbine performance is strongly influenced by the Reynolds number of the rotor blades, which is linked to the aspect ratio.
- A lower aspect ratio leads to a higher Reynolds number and improved turbine performance, as well as a lower rotational velocity.
Design of a vertical axis wind turbine- how the aspect ratio affectsPhuong Dx
- The document analyzes how the aspect ratio of a vertical-axis wind turbine affects its performance.
- It finds that turbine performance is strongly influenced by the Reynolds number of the rotor blades, which is linked to the aspect ratio.
- A lower aspect ratio leads to a higher Reynolds number and improved turbine performance, as well as a lower rotational velocity.
This document discusses various aspects of worm gears, including:
1. Key terms used such as lead, lead angle, pressure angle, and velocity ratio.
2. The three main types of worm gears: straight face, hobbed straight face, and concave face.
3. Formulas for determining efficiency, strength, wear load, and thermal rating of worm gears based on factors like lead angle, coefficient of friction, tooth geometry, and power transmitted.
This document discusses helical springs, leaf springs, and columns and struts. It provides details on:
1) Deflection calculations for helical springs under axial load and twisting moment using energy methods. Stress calculations for open and closed coil springs.
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And Examples
1. Bob Morris is a retired metallurgist/
materials scientist who has been dab-
bling in Free Flight modeling since
2005 with an interest in old timer,
Nostalgia and small gliders. He’s a
member of the Brooklyn Skyscrapers
and regular attendee at the Geneseo,
New York Great Grape Gathering.
A wound rubber motor is a complicat-
ed looking thing but I think I can offer
a relatively simple model that explains
a lot. This approach, previously pub-
lished in the April 2011 and July 2014
issues of Free Flight Quarterly (ref. 1),
uses the topological variables Twist
Tw and Writhe Wr, which apply to de-
formable ribbons like the short strip
of Tan Super Sport shown in the three
photos in Figure 1. Twist is the num-
ber of rotations about the long axis of
the strip and Writhe is the number of
times the axis appears to cross over
itself in an average side view. Tw and
Wr are related by a simple relationship
called the Calengareanu Invariant (ref.
2):
Tw + Wr = Linking Number eq.(1)
In a rubber motor, Linking Number
corresponds to the total number of
turns N; writhe turns Wr are the kinks
or knots. The Linking Number N in
the left photo is 0 and in the center
and right photos N = 1. Stretching a
wound motor will cause writhe turns
to transform to twist and visa-versa,
as illustrated in the center and right
photos. In general, an elastic strip will
tend to distribute applied turns be-
tween twist and writhe in a way that
minimizes total elastic energy (ref. 3).
However, in a wound rubber motor
this mechanical equilibration may be
impeded by friction.
The simplified geometrical model
of a rubber motor, shown in Figure 2,
is a single cylindrical strand. R and L
are the radius and length, respectively,
of the un-stretched motor. The maxi-
mum extension ratio is x so that the
length of the fully extended motor is
x L. The radius of the fully extended
motor is r. Assuming the rubber is
incompressible, the volume V is in-
dependent of stretching and twisting
etc.:
V=πR²L=πr²xL=πr²l=πr’²l’ eq.(2)
which can be rearranged to give:
r’ ² = R ² L / l’ eq. (3)
In the April 2011 FFQ article, max
turns Nmax was calculated by imagin-
ing that the fully stretched motor was
coiled around itself spool-wise so as
to fit in the original R by L cylinder,
as shown in the upper left corner of
Figure 2. Dividing the small stretched
cross-sectional area a into the rect-
angular area R L, or dividing the
stretched length x L by the average cir-
cumference of a coil π R both yield:
Nmax = x L / π R eq. (4)
Albert Einstein supposedly said “Make
everything as simple as possible but
not simpler.” This result for a pure
writhe motor is too simple. It gives the
correct dependence on motor cross-
section but underestimates breaking
26 Free Flight www.freeflight.org
SIMPLE THEORY OF A WOUND RUBBER MOTOR
PhotographY:CONTRIBUTED
2. turns by a factor of two or so.
To create a more realistic model
one needs to twist the fully-extended
motor prior to coiling, but twisting
at constant length would increase the
tension in the outer fibers. When the
stretched r-by-l cylinder is twisted
by nt turns, a straight line on the sur-
face of the motor becomes a helix, as
shown in Figure 2. To approximate
constant tension, the length of the
helical line is held constant at xL. As
twisting progresses, r increases to r’
while l shrinks to l’ to maintain con-
stant volume, which decreases the
number of writhe turns to:
nwr = R L / a’ = l’ / π R eq. (5)
Unwrapping the helix gives a triangle
with height 2 π r’ ntw
, base l’, and hy-
potenuse x L, so:
(ntw 2 π r’ ) ² + l’² = (x L) ² eq. (6)
ntw ² 4 π ² r’ ² + l’ ² = x ² L ²
substituting for r’ from equation (3):
ntw ² 4 π ² R ² L / l’ = x ² L ² - l’ ²
re-arranging and solving for ntw gives:
ntw =[(x²L²l’-l’³)/4π²R²L]1/2
eq. (7)
Ntotal = ntw + nwr = l’ / π R + [(x ² L ² l’
- l’ ³)/ 4 π ² R ² L ] 1/2
eq.(8)
COMPARISON WITH EXPERIMENT
Now we can plug some numbers
into a spreadsheet and see how this
works for a 12 inch long Coupe
motor made from 10 strands of 1/8"
wide, 0.043" thick rubber strip with
maximum extension ratio x = 10.5
(ref. 4). The volume of rubber is 0.645
cubic inches which implies a weight
of 9.83 grams (ref. 5). The motor is
initially stretched to 126 inches, 10.5
times the un-stretched length. With
no twist applied, the stretched cross-
section is 0.0048 square inches and
the calculated maximum number
of writhe turns, R L / a is 329.6.
The spreadsheet then decreases the
length in steps and calculates the
corresponding number of twist turns
using equation (7), and the new cross-
section. The number of writhe turns,
and total turns
Ntotal =ntw +nwr
follow from equation (5). The results
are shown as a graph in Figure 3.
Starting at the right side of
Figure 3, Ntotal initially increases
with increasing twist (decreasing
length), reaches a maximum at a
reduced length of about 96 inches,
then decreases with further twist.
The calculated Nmax of 532 turns,
comprises 281 twist turns and 251
writhe turns, or 1.12 twists per writhe,
not quite equal partitioning as had
been postulated in FFQ No. 39, but
not that far off. The Ntotal = nt + nw
maximum is very broad and a fourth
order polynomial gives a good fit to
the calculated Ntotal vs l’ curve.
Calculated max turns Nmax values
for a range of motor sizes are shown
in Figure 4 and all are a little below
experimental values. The curve fit to
the calculated values closely follows
the expected 1/√area dependence
on motor cross-section (number of
strands). The calculated twist-to-
writhe ratio at maximum turns ranges
between 1.12 and 1.25 with an average
of 1.19.
DISCUSSION
This model relies on several
simplifying assumptions, the most
important of which is that the stress
and strain are constant and directed
along the axis of the rubber strands.
Another key assumption is that the
volume is constant or, equivalently,
that Poisson’s ratio for the rubber
is exactly 0.5. This is an excellent
approximation for rubber up to strains
of 300% or so, but at higher extensions
Holt and McPherson (ref. 6) showed
that the volume decreases somewhat,
probably as a result of crystallization
of the rubber molecules. Extrapolating
Holt and McPherson’s results to an
extension ratio of 10 gives a volume
reduction of about 3% which would
translate to 3% smaller cross-sectional
area implying 3% more writhe turns.
An extension ratio x of 10.5 has been
assumed based on F1B/G flyer Tom
Vaccaro’s rubber tests. In a typical
test the rubber doesn’t quite break, so
the model predictions herein could be
interpreted as “almost breaking turns”
www.freeflight.org Free Flight 27
3. whereas the experimental values in
Figure 3 are actual breaking turns.
Agreement with these experiments
on Tan Super Sport is pretty good
given the simplicity of the model.
The remaining discrepancy might
be further reduced by using the
actual fracture strain value for x and
applying the Holt and McPherson
volume change correction. It appears
that this model predicts the twist-
to-writhe ratio that produces the
minimum strain value for a given
number of turns. To maximize motor
life it is important to minimize
exposure to high strain values. By
reducing the value of x, the model
could be used to devise a winding
sequence to maximize turns while not
exceeding say 80% of the breaking
strain. This might reliably provide five
or six runs on a given motor while
delivering respectable performance.
This model may help refine the rule-
of-thumb “stretch, wind half of the
expected number of turns then come
in gradually while continuing to
wind” by adding a little more twist
before coming in. This would probably
result in little if any altitude advantage
but standardizing the winding process
and twist-to-writhe ratio might reduce
the odds of motor breakage near max
turns.
An interesting feature of the twist-
plus-writhe model is the possibility
that the twist-to-writhe ratio may
vary along the length of a wound
motor depending on the stretching
and winding sequence and friction,
which could affect the final fore-and-
aft distribution of rubber weight for
motors longer than the hook-to-pin
distance, a problem discussed by Peter
Hall in (ref. 7).
Bob Morris, Flanders, N.J.
morrisresearch@gmail.com
REFERENCES
1) R. Morris, Twist and Writhe, Free
Flight Quarterly. No. 39, April 2011;
Twist and Writhe - Part 2, Free Flight
Quarterly No. 52, July 2014 (from
which the present article is adapted).
2) G. Calugareanu, Sur les
classes d’isotropie des noeuds
tridimensionnels et leurs invariants,
Czechoslovak Math. J., 11, 1961.
3) R. Ricca, The energy spectrum of
a twisted flexible string under elastic
relaxation, Journal of Physics A: Math.,
/Gen. 28, 1995.
4) Tom Vaccaro (private
communication) measured total
extension values for a box of 2012
Tan Super Sport ranging between 10.1
and 10.7. The test does not break the
samples.
5) Carrol Allen (private
communication) measured Tan Super
Sport specific gravity of 0.93 using
immersion in ethanol-water mixtures
which he probably then drank.
6) W. Holt and A.T. McPherson,
Change of volume of rubber on
stretching: effects of time, elongation
and temperature, Res. Paper RP936,/
Journal of Research of the National
Bureau of Standards/, 17, 1936.
7) P. Hall, A Knotty Problem, 2013
BMFA Free-Flight Forum.
28 Free Flight www.freeflight.org