1.
Engineering
–
The term Engineering is derived from the Latin ingenium, meaning cleverness and ingeniare, meaning to contrive, devise. Engineering has existed since ancient times as humans devised fundamental inventions such as the wedge, lever, wheel, each of these inventions is essentially consistent with the modern definition of engineering. The term engineering is derived from the engineer, which itself dates back to 1390 when an engineer originally referred to a constructor of military engines. In this context, now obsolete, a referred to a military machine. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, the word engine itself is of even older origin, ultimately deriving from the Latin ingenium, meaning innate quality, especially mental power, hence a clever invention. The earliest civil engineer known by name is Imhotep, as one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC. Ancient Greece developed machines in both civilian and military domains, the Antikythera mechanism, the first known mechanical computer, and the mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed, the first steam engine was built in 1698 by Thomas Savery. The development of this gave rise to the Industrial Revolution in the coming decades. With the rise of engineering as a profession in the 18th century, similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. The inventions of Thomas Newcomen and the Scottish engineer James Watt gave rise to mechanical engineering. The development of specialized machines and machine tools during the revolution led to the rapid growth of mechanical engineering both in its birthplace Britain and abroad. John Smeaton was the first self-proclaimed civil engineer and is regarded as the father of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbours and he was also a capable mechanical engineer and an eminent physicist. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of hydraulic lime and his lighthouse remained in use until 1877 and was dismantled and partially rebuilt at Plymouth Hoe where it is known as Smeatons Tower. The United States census of 1850 listed the occupation of engineer for the first time with a count of 2,000, there were fewer than 50 engineering graduates in the U. S. before 1865. In 1870 there were a dozen U. S. mechanical engineering graduates, in 1890 there were 6,000 engineers in civil, mining, mechanical and electrical. There was no chair of applied mechanism and applied mechanics established at Cambridge until 1875, the theoretical work of James Maxwell and Heinrich Hertz in the late 19th century gave rise to the field of electronics
2.
Force
–
In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
3.
Beam (structure)
–
A beam is a structural element that primarily resists loads applied laterally to the beams axis. Its mode of deflection is primarily by bending, the loads applied to the beam result in reaction forces at the beams support points. The total effect of all the acting on the beam is to produce shear forces and bending moments within the beam. Beams are characterized by their manner of support, profile, length, historically beams were squared timbers but are also metal, stone, or combinations of wood and metal such as a flitch beam. Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads, the loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members. In light frame construction joists may rest on beams, in carpentry a beam is called a plate as in a sill plate or wall plate, beam as in a summer beam or dragon beam. In engineering, beams are of types, Simply supported - a beam supported on the ends which are free to rotate and have no moment resistance. Fixed - a beam supported on both ends and restrained from rotation, over hanging - a simple beam extending beyond its support on one end. Double overhanging - a simple beam with both ends extending beyond its supports on both ends, continuous - a beam extending over more than two supports. Cantilever - a projecting beam fixed only at one end, trussed - a beam strengthened by adding a cable or rod to form a truss. In the beam equation I is used to represent the moment of area. It is commonly known as the moment of inertia, and is the sum, about the axis, of dA*r^2, where r is the distance from the neutral axis. Therefore, it not just how much area the beam section has overall. The greater I is, the stiffer the beam in bending, internally, beams experience compressive, tensile and shear stresses as a result of the loads applied to them. Above the supports, the beam is exposed to shear stress, there are some reinforced concrete beams in which the concrete is entirely in compression with tensile forces taken by steel tendons. These beams are known as prestressed concrete beams, and are fabricated to produce a more than the expected tension under loading conditions. High strength steel tendons are stretched while the beam is cast over them, then, when the concrete has cured, the tendons are slowly released and the beam is immediately under eccentric axial loads. This eccentric loading creates a moment, and, in turn
4.
Virtual work
–
Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements, among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the according to the principle of least action. The work of a force on a particle along a displacement is known as the virtual work. The principle of work had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, working with Leibnizian concepts, Johann Bernoulli systematized the virtual work principle and made explicit the concept of infinitesimal displacement. He was able to solve problems for both bodies as well as fluids. Bernoullis version of virtual work law appeared in his letter to Pierre Varignon in 1715 and this formulation of the principle is today known as the principle of virtual velocities and is commonly considered as the prototype of the contemporary virtual work principles. In 1743 DAlembert published his Traite de Dynamique where he applied the principle of work, based on the Bernoullis work. His idea was to convert a dynamical problem into static problem by introducing inertial force, consider a point particle that moves along a path which is described by a function r from point A, where r, to point B, where r. It is possible that the moves from A to B along a nearby path described by r + δr. The variation δr satisfies the requirement δr = δr =0, the components of the variation, δr1, δr2 and δr3, are called virtual displacements. This can be generalized to a mechanical system defined by the generalized coordinates qi. In which case, the variation of the qi is defined by the virtual displacements δqi. Virtual work is the work done by the applied forces. When considering forces applied to a body in equilibrium, the principle of least action requires the virtual work of these forces to be zero. Consider a particle P that moves from a point A to a point B along a trajectory r and it is important to notice that the value of the work W depends on the trajectory r. Suppose the force F is the same as F, the variation of the work δW associated with this nearby path, known as the virtual work, can be computed to be δ W = W ¯ − W = ∫ t 0 t 1 d t
5.
Direct integration of a beam
–
Direct integration is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam. These constants are determined by using either the forces at supports, for internal shear and moment, the constants can be found by analyzing the beams free body diagram. For rotation and displacement, the constants are found using conditions dependent on the type of supports, for a cantilever beam, the fixed support has zero rotation and zero displacement. For a beam supported by a pin and roller, both the supports have zero displacement, take the beam shown at right supported by a fixed pin at the left and a roller at the right. There are no applied moments, the weight is a constant 10 kN, taking x as the distance from the pin, w =10 Integrating, V = − ∫ w d x = −10 x + C1 where C1 represents the applied loads. For a more realistic situation, such as a load of 1 kN and an EI value of 5,000 kN·m². Note that for the rotation θ the units are divided by meters. This is because rotation is given as a slope, the displacement divided by the horizontal change. Mechanics Materials, sixth edition, Pearson Prentice Hall,2005, beam Deflection by Double Integration Method
6.
Macaulay's method
–
Macaulay’s method is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay’s technique is convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly distributed loads and uniformly varying loads over the span, the first English language description of the method was by Macaulay. The actual approach appears to have developed by Clebsch in 1862. This equation is simpler than the beam equation and can be integrated twice to find w if the value of M as a function of x is known. Using these integration rules makes the calculation of the deflection of Euler-Bernoulli beams simple in situations where there are multiple point loads, the Macaulay method predates more sophisticated concepts such as Dirac delta functions and step functions but achieves the same outcomes for beam problems. An illustration of the Macaulay method considers a simply supported beam with a single eccentric concentrated load as shown in the adjacent figure, the first step is to find M. e. The Macaulay brackets help as a reminder that the quantity on the right is zero when considering points with x < a, as w =0 at x =0, C2 =0. Assuming that this happens for x < a we have P b x 22 L − P b 6 L =0 or x = ±1 /23 Clearly x <0 cannot be a solution. Even when the load is as near as 0. 05L from the support, hence in most of the cases the estimation of maximum deflection may be made fairly accurately with reasonable margin of error by working out deflection at the centre
7.
Direct stiffness method
–
It is a matrix method that makes use of the members stiffness relations for computing member forces and displacements in structures. The direct stiffness method is the most common implementation of the finite element method, in applying the method, the system must be modeled as a set of simpler, idealized elements interconnected at the nodes. The material stiffness properties of elements are then, through matrix mathematics. The structure’s unknown displacements and forces can then be determined by solving this equation, the direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method originated in the field of aerospace, researchers looked at various approaches for analysis of complex airplane frames. These included elasticity theory, energy principles in structural mechanics, flexibility method and it was through analysis of these methods that the direct stiffness method emerged as an efficient method ideally suited for computer implementation. Between 1934 and 1938 A. R. Collar and W. J. Duncan published the first papers with the representation, aeroelastic research continued through World War II but publication restrictions from 1938 to 1947 make this work difficult to trace. Finally, on Nov.61959, M. J. Turner, head of Boeing’s Structural Dynamics Unit, a typical member stiffness relation has the following general form, Q m = k m q m + Q o m where m = member number m. Q m = vector of members characteristic forces, which are unknown internal forces, K m = member stiffness matrix which characterizes the members resistance against deformations. Q m = vector of members characteristic displacements or deformations, Q o m = vector of members characteristic forces caused by external effects applied to the member while q m =0. This implies that r will be the primary unknowns, the member forces Q m help to the keep the nodes in equilibrium under the nodal forces R. K = system stiffness matrix, which is established by assembling the members stiffness matrices k m. This vector is established by assembling the members Q o m, the system stiffness matrix K is square since the vectors R and r have the same size. In addition, it is symmetric because k m is symmetric, where q m can be found from r by compatibility consideration. It is common to have Eq. in a form where q m and Q o m are, respectively, in such case, K and R o can be obtained by direct summation of the members matrices k m and Q o m. The method is known as the direct stiffness method. The advantages and disadvantages of the stiffness method are compared and discussed in the flexibility method article. The first step using the direct stiffness method is to identify the individual elements which make up the structure. Once the elements are identified, the structure is disconnected at the nodes, each element is then analyzed individually to develop member stiffness equations
8.
Plate theory
–
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draws on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions, the typical thickness to width ratio of a plate structure is less than 0.1. A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two-dimensional problem, the aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads. Of the numerous theories that have been developed since the late 19th century. These are the Kirchhoff–Love theory of plates The Mindlin–Reissner theory of plates Note, the Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory was developed in 1888 by Love using assumptions proposed by Kirchhoff and it is assumed that a mid-surface plane can be used to represent the three-dimensional plate in two-dimensional form. If φ α are the angles of rotation of the normal to the mid-surface, If the rotations of the normals to the mid-surface are in the range of 10° to 15°, the strain-displacement relations can be approximated using the von Kármán strains. The equilibrium equations for the plate can be derived from the principle of virtual work, the quantities σ α β are the stresses. It is more convenient to work with the stress and moment results that enter the equilibrium equations and these are related to the displacements by = and = −. The moments corresponding to these stresses are = −2 h 3 E3 The displacements u 10 and u 20 are zero under pure bending conditions, in index notation, w,11110 +2 w,12120 + w,22220 =0. In index notation, w,11110 +2 w,12120 + w,22220 = − q D and in direct notation In cylindrical coordinates, for an orthotropic plate =11 − ν12 ν21. Therefore, =2 h 1 − ν12 ν21, the dynamic theory of plates determines the propagation of waves in the plates, and the study of standing waves and vibration modes. The governing equations simplify considerably for isotropic and homogeneous plates for which the in-plane deformations can be neglected and have the form D = − q −2 ρ h ∂2 w 0 ∂ t 2, where D is the bending stiffness of the plate. For a uniform plate of thickness 2 h, D, =2 h 3 E3, in direct notation Note, the Einstein summation convention of summing on repeated indices is used below. In the theory of plates, or theory of Raymond Mindlin and Eric Reissner. However, the strain is constant across the thickness of the plate. This cannot be accurate since the stress is known to be parabolic even for simple plate geometries. To account for the inaccuracy in the strain, a shear correction factor is applied so that the correct amount of internal energy is predicted by the theory
9.
Architect
–
An architect is someone who plans, designs, and reviews the construction of buildings. Etymologically, architect derives from the Latin architectus, which derives from the Greek, practical, technical, and academic requirements for becoming an architect vary by jurisdiction. The terms architect and architecture are used in the disciplines of landscape architecture, naval architecture. In most jurisdictions, the professional and commercial uses of the terms architect, throughout ancient and medieval history, most architectural design and construction was carried out by artisans—such as stone masons and carpenters, rising to the role of master builder. Until modern times, there was no distinction between architect and engineer. In Europe, the architect and engineer were primarily geographical variations that referred to the same person. It is suggested that various developments in technology and mathematics allowed the development of the gentleman architect. Paper was not used in Europe for drawing until the 15th century, pencils were used more often for drawing by 1600. The availability of both allowed pre-construction drawings to be made by professionals, until the 18th-century, buildings continued to be designed and set out by craftsmen with the exception of high-status projects. In most developed countries, only qualified people with appropriate license, certification, or registration with a relevant body, such licensure usually requires an accredited university degree, successful completion of exams, and a training period. To practice architecture implies the ability to independently of supervision. In many places, independent, non-licensed individuals may perform design services outside the professional restrictions, such design houses, in the architectural profession, technical and environmental knowledge, design and construction management, and an understanding of business are as important as design. However, design is the force throughout the project and beyond. An architect accepts a commission from a client, the commission might involve preparing feasibility reports, building audits, the design of a building or of several buildings, structures, and the spaces among them. The architect participates in developing the requirements the client wants in the building, throughout the project, the architect co-ordinates a design team. Structural, mechanical, and electrical engineers and other specialists, are hired by the client or the architect, the architect hired by a client is responsible for creating a design concept that meets the requirements of that client and provides a facility suitable to the required use. In that, the architect must meet with and question the client to ascertain all the requirements, often the full brief is not entirely clear at the beginning, entailing a degree of risk in the design undertaking. The architect may make proposals to the client which may rework the terms of the brief
10.
Engineer
–
Engineers design materials, structures, and systems while considering the limitations imposed by practicality, regulation, safety, and cost. The word engineer is derived from the Latin words ingeniare and ingenium, the work of engineers forms the link between scientific discoveries and their subsequent applications to human and business needs and quality of life. His/her work is predominantly intellectual and varied and not of a mental or physical character. It requires the exercise of original thought and judgement and the ability to supervise the technical, he/she is thus placed in a position to make contributions to the development of engineering science or its applications. In due time he/she will be able to give authoritative technical advice, much of an engineers time is spent on researching, locating, applying, and transferring information. Indeed, research suggests engineers spend 56% of their time engaged in various information behaviours, Engineers must weigh different design choices on their merits and choose the solution that best matches the requirements. Their crucial and unique task is to identify, understand, Engineers apply techniques of engineering analysis in testing, production, or maintenance. Analytical engineers may supervise production in factories and elsewhere, determine the causes of a process failure and they also estimate the time and cost required to complete projects. Supervisory engineers are responsible for major components or entire projects, Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of the system, device or mechanism under study. Most engineers specialize in one or more engineering disciplines, numerous specialties are recognized by professional societies, and each of the major branches of engineering has numerous subdivisions. Civil engineering, for example, includes structural and transportation engineering and materials engineering include ceramic, metallurgical, mechanical engineering cuts across just about every discipline since its core essence is applied physics. Engineers also may specialize in one industry, such as vehicles, or in one type of technology. Several recent studies have investigated how engineers spend their time, that is, research suggests that there are several key themes present in engineers’ work, technical work, social work, computer-based work, information behaviours. Amongst other more detailed findings, a recent work sampling study found that engineers spend 62. 92% of their time engaged in work,40. 37% in social work. The time engineers spend engaged in activities is also reflected in the competencies required in engineering roles. There are many branches of engineering, each of which specializes in specific technologies, typically engineers will have deep knowledge in one area and basic knowledge in related areas. When developing a product, engineers work in interdisciplinary teams. For example, when building robots an engineering team will typically have at least three types of engineers, a mechanical engineer would design the body and actuators
11.
Hooke's law
–
Hookes law is a principle of physics that states that the force needed to extend or compress a spring by some distance X is proportional to that distance. That is, F = kX, where k is a constant factor characteristic of the spring, its stiffness, the law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram and he published the solution of his anagram in 1678 as, ut tensio, sic vis. Hooke states in the 1678 work that he was aware of the law already in 1660, an elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean. Hookes law is only a linear approximation to the real response of springs. Many materials will deviate from Hookes law well before those elastic limits are reached. On the other hand, Hookes law is an approximation for most solid bodies, as long as the forces. For this reason, Hookes law is used in all branches of science and engineering. It is also the principle behind the spring scale, the manometer. The modern theory of elasticity generalizes Hookes law to say that the strain of an object or material is proportional to the stress applied to it. In this general form, Hookes law makes it possible to deduce the relation between strain and stress for complex objects in terms of properties of the materials it is made of. Consider a simple helical spring that has one end attached to some fixed object, suppose that the spring has reached a state of equilibrium, where its length is not changing anymore. Let X be the amount by which the end of the spring was displaced from its relaxed position. Hookes law states that F = k X or, equivalently, X = F k where k is a real number. Moreover, the formula holds when the spring is compressed. According to this formula, the graph of the applied force F as a function of the displacement X will be a line passing through the origin. Hookes law for a spring is often stated under the convention that F is the force exerted by the spring on whatever is pulling its free end. In that case, the equation becomes F = − k X since the direction of the force is opposite to that of the displacement
12.
Young's modulus
–
Youngs modulus, also known as the elastic modulus, is a measure of the stiffness of a solid material. It is a property of linear elastic solid materials. It defines the relationship between stress and strain in a material, Youngs modulus is named after the 19th-century British scientist Thomas Young. The term modulus is the diminutive of the Latin term modus which means measure, a solid material will deform when a load is applied to it. If it returns to its shape after the load is removed. In the range where the ratio between load and deformation remains constant, the curve is linear. Not many materials are linear and elastic beyond a small amount of deformation, although such a material cannot exist, a material with a very high Youngs modulus can be approximated as rigid. g. The technical definition is, the ratio of the stress along an axis to the strain along that axis in the range of stress in which Hookes law holds, Youngs modulus is the ratio of stress to strain, and so Youngs modulus has units of pressure. Its SI unit is therefore the pascal, the practical units used are megapascals or gigapascals. In United States customary units, it is expressed as pounds per square inch, the abbreviation ksi refers to kips per square inch. A kip is an Imperial unit of force and is equal to 1000 pounds-force, the Youngs modulus enables the calculation of the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression, the Youngs modulus directly applies to cases of uniaxial stress, that is tensile or compressive stress in one direction and no stress in the other directions. Youngs modulus is used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beams supports. Other elastic calculations usually require the use of one additional property, such as the shear modulus. Any two of these parameters are sufficient to fully describe elasticity in an isotropic material, Youngs modulus represents the factor of proportionality in Hookes law, which relates the stress and the strain. However, Hookes law is valid under the assumption of an elastic. If the range over which Hookes law is valid is large compared to the typical stress that one expects to apply to the material. Otherwise the material is said to be non-linear, steel, carbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear
13.
Area moment of inertia
–
The second moment of area is typically denoted with either an I for an axis that lies in the plane or with a J for an axis perpendicular to the plane. In both cases, it is calculated with an integral over the object in question. Its unit of dimension when working with the International System of Units is meters to the fourth power, in each case the integral is over all the infinitesimal elements of area, dA, in some two-dimensional cross-section. The MOI, in sense, is the analog of mass for rotational problems. In engineering, Moment of Inertia commonly refers to the moment of the area. The parallel axis theorem states I x ′ = I x + A d 2 where A is the area of the shape, a similar statement can be made about a y ′ axis and the parallel centroidal y axis. Or, in general, any centroidal B axis and a parallel B ′ axis, for the simplicity of calculation, it is often desired to define the polar moment of area in terms of two area moments of inertia. The simplest case relates J z to I x and I y, for more complex areas, it is often easier to divide the area into a series of simpler shapes. The second moment of area for the shape is the sum of the second moment of areas of all of its parts about a common axis. This can include shapes that are missing, in case the second moment of area of the missing areas are subtracted. In other words, the moment of area of missing parts are considered negative for the method of composite shapes. See list of moments of area for other shapes. Consider a rectangle with base b and height h whose centroid is located at the origin, because of the symmetry of the annulus, the centroid also lies at the origin. We can determine the moment of inertia, J z. This polar moment of inertia is equivalent to the moment of inertia of a circle with radius r 2 minus the polar moment of inertia of a circle with radius r 1. First, let us derive the polar moment of inertia of a circle with radius r with respect to the origin, in this case, it is easier to directly calculate J z as we already have r 2, which has both an x and y component. Instead of obtaining the second moment of area from Cartesian coordinates as done in the previous section and this would be done like this. A polygon is assumed to have n vertices, numbered in counter-clockwise fashion, if polygon vertices are numbered clockwise, returned values will be negative, but absolute values will be correct
14.
Bending
–
In applied mechanics, bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a fraction, typically 1/10 or less. When the length is longer than the width and the thickness. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any form where the length. A large diameter, but thin-walled, short tube supported at its ends, in the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the more precise, engineers refer to a specific object such as, the bending of rods, the bending of beams, the bending of plates. A beam deforms and stresses develop inside it when a load is applied on it. In the quasi-static case, the amount of bending deflection and the stresses that develop are assumed not to change over time. In a horizontal beam supported at the ends and loaded downwards in the middle and these last two forces form a couple or moment as they are equal in magnitude and opposite in direction. This bending moment resists the sagging deformation characteristic of a beam experiencing bending, the stress distribution in a beam can be predicted quite accurately when some simplifying assumptions are used. In the Euler–Bernoulli theory of beams, a major assumption is that plane sections remain plane. In other words, any deformation due to shear across the section is not accounted for, also, this linear distribution is only applicable if the maximum stress is less than the yield stress of the material. For stresses that exceed yield, refer to article plastic bending, at yield, the maximum stress experienced in the section is defined as the flexural strength. Simple beam bending is often analyzed with the Euler–Bernoulli beam equation, the conditions for using simple bending theory are, The beam is subject to pure bending. This means that the force is zero, and that no torsional or axial loads are present. The material is isotropic and homogeneous, the beam is initially straight with a cross section that is constant throughout the beam length. The beam has an axis of symmetry in the plane of bending, the proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling
15.
Homogeneity and heterogeneity
–
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity in a substance or organism. A material or image that is homogeneous is uniform in composition or character, the alternate spellings homogenous and heterogenous are commonly, but incorrectly, used. Heterogenous meanwhile is a term primarily confined to pathology which refers to the property of an object in the body having its origin outside the body, the concepts are the same to every level of complexity, from atoms to populations of animals or people, and galaxies. Hence, an element may be homogeneous on a larger scale and this is known as an effective medium approach, or effective medium approximations. Various disciplines understand heterogeneity, or being heterogeneous, in different ways, heterogeneous solids, liquids, and gases may be made homogeneous by melting, stirring, or by allowing time to pass for diffusion to distribute the molecules evenly. For example, adding dye to water will create a solution at first. Entropy allows for heterogeneous substances to become homogeneous over time, a heterogeneous mixture is a mixture of two or more compounds. Examples are, mixtures of sand and water or sand and iron filings, a rock, water and oil, a salad, trail mix. A mixture can be determined to be homogeneous when everything is settled and equal, various models have been proposed to model the concentrations in different phases. The phenomena to be considered are mass rates and reaction, homogeneous reactions are chemical reactions in which the reactants and products are in the same phase, while heterogeneous reactions have reactants in two or more phases. Reactions that take place on the surface of a catalyst of a different phase are also heterogeneous, a reaction between two gases or two miscible liquids is homogeneous. A reaction between a gas and a liquid, a gas and a solid or a liquid and a solid is heterogeneous, earth is a heterogeneous substance in many aspects. E. g. rocks are inherently heterogeneous, usually occurring at the micro-scale and mini-scale, in algebra, homogeneous polynomials have the same number of factors of a given kind. This can cause problems in attempts to summarize the meaning of the studies, in medicine and genetics, a genetic or allelic heterogeneous condition is one where the same disease or condition can be caused, or contributed to, by several factors. In the case of genetics, varying different genes or alleles, in cancer research, cancer cell heterogeneity is thought to be one of the underlying reasons that make treatment of cancer difficult. In physics, heterogeneous is understood to mean having physical properties that vary within the medium, in sociology, heterogeneous may refer to a society or group that includes individuals of differing ethnicities, cultural backgrounds, sexes, or ages. Academic Press Dictionary of Science and Technology
16.
Elasticity (physics)
–
In physics, elasticity is the ability of a body to resist a distorting influence or deforming force and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate forces are applied on them, if the material is elastic, the object will return to its initial shape and size when these forces are removed. The physical reasons for elastic behavior can be different for different materials. In metals, the atomic lattice changes size and shape when forces are applied, when forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied, perfect elasticity is an approximation of the real world. The most elastic body in modern science found is Quartz fibre which is not even a perfect elastic body, so perfect elastic body is an ideal concept only. Most materials which possess elasticity in practice remain purely elastic only up to very small deformations. In engineering, the amount of elasticity of a material is determined by two types of material parameter, the first type of material parameter is called a modulus, which measures the amount of force per unit area needed to achieve a given amount of deformation. The SI unit of modulus is the pascal, a higher modulus typically indicates that the material is harder to deform. The second type of measures the elastic limit, the maximum stress that can arise in a material before the onset of permanent deformation. Its SI unit is also pascal, when describing the relative elasticities of two materials, both the modulus and the elastic limit have to be considered. Rubbers typically have a low modulus and tend to stretch a lot, of two rubber materials with the same elastic limit, the one with a lower modulus will appear to be more elastic, which is however not correct. When an elastic material is deformed due to a force, it experiences internal resistance to the deformation. The various moduli apply to different kinds of deformation, for instance, Youngs modulus applies to extension/compression of a body, whereas the shear modulus applies to its shear. The elasticity of materials is described by a curve, which shows the relation between stress and strain. The curve is nonlinear, but it can be approximated as linear for sufficiently small deformations. For even higher stresses, materials exhibit behavior, that is, they deform irreversibly. Elasticity is not exhibited only by solids, non-Newtonian fluids, such as viscoelastic fluids, in response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, because the elasticity of a material is described in terms of a stress-strain relation, it is essential that the terms stress and strain be defined without ambiguity
17.
Angle
–
In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles
18.
Radian
–
The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
19.
Cantilever
–
A cantilever is a rigid structural element, such as a beam or a plate, anchored at only one end to a support from which it is protruding. Cantilevers can also be constructed with trusses or slabs, when subjected to a structural load, the cantilever carries the load to the support where it is forced against by a moment and shear stress. Cantilevers are widely found in construction, notably in cantilever bridges and balconies, in cantilever bridges the cantilevers are usually built as pairs, with each cantilever used to support one end of a central section. The Forth Bridge in Scotland is an example of a truss bridge. A cantilever in a timber framed building is called a jetty or forebay. In the southern United States a historic barn type is the barn of log construction. Temporary cantilevers are used in construction. The partially constructed structure creates a cantilever, but the structure does not act as a cantilever. This is very helpful when temporary supports, or falsework, cannot be used to support the structure while it is being built. So some truss arch bridges are built each side as cantilevers until the spans reach each other and are then jacked apart to stress them in compression before final joining. Nearly all cable-stayed bridges are built using cantilevers as this is one of their chief advantages, many box girder bridges are built segmentally, or in short pieces. This type of construction lends itself well to balanced cantilever construction where the bridge is built in both directions from a single support and these structures are highly based on torque and rotational equilibrium. In an architectural application, Frank Lloyd Wrights Fallingwater used cantilevers to project large balconies, the East Stand at Elland Road Stadium in Leeds was, when completed, the largest cantilever stand in the world holding 17,000 spectators. The roof built over the stands at Old Trafford Football Ground uses a cantilever so that no supports will block views of the field, the old, now demolished Miami Stadium had a similar roof over the spectator area. The largest cantilever in Europe is located at St James Park in Newcastle-Upon-Tyne, less obvious examples of cantilevers are free-standing radio towers without guy-wires, and chimneys, which resist being blown over by the wind through cantilever action at their base. Another use of the cantilever is in fixed-wing aircraft design, pioneered by Hugo Junkers in 1915, early aircraft wings typically bore their loads by using two wings in a biplane configuration braced with wires and struts. They were similar to bridges, having been developed by Octave Chanute. The wings were braced with crossed wires so they would stay parallel, the cables and struts generated considerable drag, and there was constant experimentation for ways to eliminate them
20.
Building code
–
A building code is a set of rules that specify the standards for constructed objects such as buildings and nonbuilding structures. Buildings must conform to the code to obtain planning permission, usually from a local council, the main purpose of building codes is to protect public health, safety and general welfare as they relate to the construction and occupancy of buildings and structures. The building code becomes law of a jurisdiction when formally enacted by the appropriate governmental or private authority. Codes regulating the design and construction of structures where adopted into law, examples of building codes began in ancient times. In the USA the main codes are the International Commercial or Residential Code, electrical codes and plumbing, fifty states and the District of Columbia have adopted the I-Codes at the state or jurisdictional level. In Canada, national model codes are published by the National Research Council of Canada, the practice of developing, approving, and enforcing building codes varies considerably among nations. In some countries building codes are developed by the government agencies or quasi-governmental standards organizations, such codes are known as the national building codes. In other countries, where the power of regulating construction and fire safety is vested in local authorities, model building codes have no legal status unless adopted or adapted by an authority having jurisdiction. The developers of model codes urge public authorities to reference model codes in their laws, ordinances, regulations, when referenced in any of these legal instruments, a particular model code becomes law. This practice is known as adoption by reference, there are instances when some local jurisdictions choose to develop their own building codes. At some point in all major cities in the United States had their own building codes. However, due to increasing complexity and cost of developing building regulations. For example, in 2008 New York City abandoned its proprietary 1968 New York City Building Code in favor of a version of the International Building Code. The City of Chicago remains the only municipality in America that continues to use a building code the city developed on its own as part of the Municipal Code of Chicago, in Europe, the Eurocode is a pan-European building code that has superseded the older national building codes. Each country now has National Annexes to localize the contents of the Eurocode, similarly, in India, each municipality and urban development authority has its own building code, which is mandatory for all construction within their jurisdiction. All these local building codes are variants of a National Building Code, Building codes have a long history. The earliest known written building code is included in the Code of Hammurabi, the book of Deuteronomy in the Hebrew Bible stipulated that parapets must be constructed on all houses to prevent people from falling off. The Laws of the Indies were passed in the 1680s by the Spanish Crown to regulate the urban planning for colonies throughout Spains worldwide imperial possessions, the first systematic national building standard was established with the London Building Act of 1844
21.
Fraction (mathematics)
–
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of an integer numerator displayed above a line, numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. The numerator represents a number of parts, and the denominator. For example, in the fraction 3/4, the numerator,3, tells us that the fraction represents 3 equal parts, the picture to the right illustrates 34 or ¾ of a cake. Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, an integer such as the number 7 can be thought of as having an implicit denominator of one,7 equals 7/1. Other uses for fractions are to represent ratios and to represent division, thus the fraction ¾ is also used to represent the ratio 3,4 and the division 3 ÷4. The test for a number being a number is that it can be written in that form. In a fraction, the number of parts being described is the numerator. Informally, they may be distinguished by placement alone but in formal contexts they are separated by a fraction bar. The fraction bar may be horizontal, oblique, or diagonal and these marks are respectively known as the horizontal bar, the slash or stroke, the division slash, and the fraction slash. In typography, horizontal fractions are known as en or nut fractions and diagonal fractions as em fractions. The denominators of English fractions are expressed as ordinal numbers. When the denominator is 1, it may be expressed in terms of wholes but is commonly ignored. When the numerator is one, it may be omitted, a fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. Fractions should always be hyphenated when used as adjectives, alternatively, a fraction may be described by reading it out as the numerator over the denominator, with the denominator expressed as a cardinal number. The term over is used even in the case of solidus fractions, Fractions with large denominators that are not powers of ten are often rendered in this fashion while those with denominators divisible by ten are typically read in the normal ordinal fashion. A simple fraction is a number written as a/b or a b
22.
Steel frame
–
The development of this technique made the construction of the skyscraper possible. The rolled steel profile or cross section of steel columns takes the shape of the letter I, the two wide flanges of a column are thicker and wider than the flanges on a beam, to better withstand compressive stress in the structure. Square and round tubular sections of steel can also be used, Steel beams are connected to the columns with bolts and threaded fasteners, and historically connected by rivets. The central web of the steel I-beams is often wider than a web to resist the higher bending moments that occur in beams. Wide sheets of steel deck can be used to cover the top of the frame as a form or corrugated mold, below a thick layer of concrete. Another popular alternative is a floor of precast concrete flooring units with some form of concrete topping, the frame needs to be protected from fire because steel softens at high temperature and this can cause the building to partially collapse. In the case of the columns this is usually done by encasing it in form of fire resistant structure such as masonry. The beams may be cased in concrete, plasterboard or sprayed with a coating to insulate it from the heat of the fire or it can be protected by a fire-resistant ceiling construction. Asbestos was a material for fireproofing steel structures up until the early 1970s. The exterior skin of the building is anchored to the using a variety of construction techniques. Bricks, stone, reinforced concrete, architectural glass, sheet metal, the dimension of the room is established with horizontal track that is anchored to the floor and ceiling to outline each room. The vertical studs are arranged in the tracks, usually spaced 16 apart, the typical profiles used in residential construction are the C-shape stud and the U-shaped track, and a variety of other profiles. Framing members are produced in a thickness of 12 to 25 gauge. The wall finish is anchored to the two sides of the stud, which varies from 1-1/4 to 3 thick, and the width of web ranges from 1-5/8 to 14. Rectangular sections are removed from the web to provide access for electrical wiring, Steel mills produce galvanized sheet steel, the base material for the manufacture of cold formed steel profiles. Sheet steel is then roll-formed into the final profiles used for framing, the sheets are zinc coated to prevent oxidation and corrosion. Steel framing provides excellent design flexibility due to the strength to weight ratio of steel, which allows it to span over a long distances. Thermal bridging can be protected against by installing a layer of externally fixed insulation along the steel framing - typically referred to as a thermal break, the spacing between studs is typically 16 inches on center for homes exterior and interior walls depending on designed loading requirements
23.
Fracture
–
A fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid, fracture strength or breaking strength is the stress when a specimen fails or fractures. The word fracture is often applied to bones of living creatures, or to crystalline materials, sometimes, individual crystals fracture without the structure actually separating into two or more pieces. Depending on the substance, a fracture reduces strength or inhibits transmission of waves, a detailed understanding of how fracture occurs in materials may be assisted by the study of fracture mechanics. Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture and this is usually determined for a given specimen by a tensile test, which charts the stress-strain curve. The final recorded point is the fracture strength, ductile materials have a fracture strength lower than the ultimate tensile strength, whereas in brittle materials the fracture strength is equivalent to the UTS. If a ductile material reaches its ultimate strength in a load-controlled situation, it will continue to deform, with no additional load application. However, if the loading is displacement-controlled, the deformation of the material may relieve the load, in brittle fracture, no apparent plastic deformation takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding. In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, the sinking of RMS Titanic in 1912 from an iceberg collision is widely reported to have been due to brittle fracture of the hulls steel plates. Putting these two together, we get σ f r a c t u r e = E γ ρ4 a r o. Looking closely, we can see that sharp cracks and large defects both lower the strength of the material. Recently, scientists have discovered supersonic fracture, the phenomenon of crack propagation faster than the speed of sound in a material and this phenomenon was recently also verified by experiment of fracture in rubber-like materials. Brittle fracture may be avoided by limiting pressure and temperature within limits, each system has a brittle fracture prevention limit curve defined by the weakest components at given temperatures and pressures allowing for the largest undetected preexisting flaw in each component. In ductile fracture, extensive plastic deformation takes place before fracture, the terms rupture or ductile rupture describe the ultimate failure of ductile materials loaded in tension. Rather than cracking, the material pulls apart, generally leaving a rough surface, in this case there is slow propagation and an absorption of a large amount energy before fracture. The ductility of a material is referred to as toughness. Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more strain before fracture under favorable loading condition, the strain at which the fracture happens is controlled by the purity of the materials
24.
Bending moment
–
A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam, the example shows a beam which is simply supported at both ends. Simply supported means that end of the beam can rotate. The ends can only react to the shear loads, other beams can have both ends fixed, therefore each end support has both bending moment and shear reaction loads. Beams can also have one end fixed and one end simply supported, the simplest type of beam is the cantilever, which is fixed at one end and is free at the other end. In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely, the internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple. For equilibrium, the moment created by external forces must be balanced by the couple induced by the internal loads, the resultant internal couple is called the bending moment while the resultant internal force is called the shear force or the normal force. The bending moment at a section through an element may be defined as the sum of the moments about that section of all external forces acting to one side of that section. If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause sagging, and a positive moment will cause hogging. It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is the point of transition from hogging to sagging or vice versa. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres, the concept of bending moment is very important in engineering and physics. Tensile and compressive stresses increase proportionally with bending moment, but are dependent on the second moment of area of the cross-section of a beam. Failure in bending will occur when the moment is sufficient to induce tensile stresses greater than the yield stress of the material throughout the entire cross-section. It is possible that failure of an element in shear may occur before failure in bending, however the mechanics of failure in shear. Moments are calculated by multiplying the external vector forces by the distance at which they are applied. Of course any pin-joints within a structure allow free rotation, and it is more common to use the convention that a clockwise bending moment to the left of the point under consideration is taken as positive. This then corresponds to the derivative of a function which. When defining moments and curvatures in this way calculus can be readily used to find slopes
25.
Slope deflection method
–
The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by George A. Maney. The slope deflection method was used for more than a decade until the moment distribution method was developed. By forming slope deflection equations and applying joint and shear equilibrium conditions, substituting them back into the slope deflection equations, member end moments are readily determined. Deformation of member is due to the bending moment and these rotation angles can be calculated using the unit dummy force into the cal method or Darcys Law. Joint equilibrium conditions imply that each joint with a degree of freedom should have no unbalanced moments i. e. be in equilibrium, when there are chord rotations in a frame, additional equilibrium conditions, namely the shear equilibrium conditions need to be taken into account. The statically indeterminate beam shown in the figure is to be analysed, members AB, BC, CD have the same length L =10 m. Flexural rigidities are EI, 2EI, EI respectively, concentrated load of magnitude P =10 k N acts at a distance a =3 m from the support A. Uniform load of intensity q =1 k N / m acts on BC, member CD is loaded at its midspan with a concentrated load of magnitude P =10 k N. In the following calculations, clockwise moments and rotations are positive, rotation angles θ A, θ B, θ C, of joints A, B, C, respectively are taken as the unknowns. There are no chord rotations due to causes including support settlement. Structural Analysis, A Classical and Matrix Approach
26.
International Standard Book Number
–
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker