Geometry is a branch of mathematics concerned with questions of shape, relative position of figures, the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience.
While geometry has evolved throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, planes, surfaces and curves, as well as the more advanced notions of manifolds and topology or metric. Geometry has applications to many fields, including art, physics, as well as to other branches of mathematics. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense; the mandatory educational curriculum of the majority of nations includes the study of points, planes, triangles, similarity, solid figures and analytic geometry. Euclidean geometry has applications in computer science and various branches of modern mathematics. Differential geometry uses techniques of linear algebra to study problems in geometry, it has applications in physics, including in general relativity. Topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this means dealing with large-scale properties of spaces, such as connectedness and compactness.
Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues using techniques of real analysis. It has close connections to convex analysis and functional analysis and important applications in number theory. Algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques, it has applications including cryptography and string theory. Discrete geometry is concerned with questions of relative position of simple geometric objects, such as points and circles, it shares many principles with combinatorics. Computational geometry deals with algorithms and their implementations for manipulating geometrical objects. Although being a young area of geometry, it has many applications in computer vision, image processing, computer-aided design, medical imaging, etc; the earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles and volumes, which were developed to meet some practical need in surveying, construction and various crafts.
The earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum. Clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space; these geometric procedures anticipated the Oxford Calculators, including the mean speed theorem, by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history.
Eudoxus developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures, as well as a theory of ratios that avoided the problem of incommensurable magnitudes, which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose Elements considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom and proof. Although most of the contents of the Elements were known, Euclid arranged them into a single, coherent logical framework; the Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, gave remarkably accurate approximations of Pi.
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American Institute of Steel Construction
The American Institute of Steel Construction is a not-for-profit technical institute and trade association for the use of structural steel in the construction industry of the United States. AISC publishes the AISC 360 Specification for Structural Steel Buildings, an authoritative reference in the USA for steel building structure design and, referenced in all U. S. building codes
3D computer graphics
3D computer graphics or three-dimensional computer graphics, are graphics that use a three-dimensional representation of geometric data, stored in the computer for the purposes of performing calculations and rendering 2D images. Such images may be stored for viewing or displayed in real-time. 3D computer graphics rely on many of the same algorithms as 2D computer vector graphics in the wire-frame model and 2D computer raster graphics in the final rendered display. In computer graphics software, 2D applications may use 3D techniques to achieve effects such as lighting, 3D may use 2D rendering techniques. 3D computer graphics are referred to as 3D models. Apart from the rendered graphic, the model is contained within the graphical data file. However, there are differences: a 3D model is the mathematical representation of any three-dimensional object. A model is not technically a graphic. A model can be displayed visually as a two-dimensional image through a process called 3D rendering or used in non-graphical computer simulations and calculations.
With 3D printing, 3D models are rendered into a 3D physical representation of the model, with limitations to how accurate the rendering can match the virtual model. William Fetter was credited with coining the term computer graphics in 1961 to describe his work at Boeing. One of the first displays of computer animation was Futureworld, which included an animation of a human face and a hand that had appeared in the 1972 experimental short A Computer Animated Hand, created by University of Utah students Edwin Catmull and Fred Parke.3D computer graphic s software began appearing for home computers in the late 1970s. The earliest known example is 3D Art Graphics, a set of 3D computer graphics effects, written by Kazumasa Mitazawa and released in June 1978 for the Apple II. 3D computer graphics creation falls into three basic phases: 3D modeling – the process of forming a computer model of an object's shape Layout and animation – the placement and movement of objects within a scene 3D rendering – the computer calculations that, based on light placement, surface types, other qualities, generate the image The model describes the process of forming the shape of an object.
The two most common sources of 3D models are those that an artist or engineer originates on the computer with some kind of 3D modeling tool, models scanned into a computer from real-world objects. Models can be produced procedurally or via physical simulation. A 3D model is formed from points called vertices that define the shape and form polygons. A polygon is an area formed from at least three vertexes. A polygon of n points is an n-gon; the overall integrity of the model and its suitability to use in animation depend on the structure of the polygons. Materials and textures are properties that the render engine uses to render the model, in an unbiased render engine like blender cycles, one can give the model materials to tell the engine how to treat light when it hits the surface. Textures are used to give the material color using a color or albedo map, or give the surface features using a bump or normal map, it can be used to deform the model itself using a displacement map. Before rendering into an image, objects must be laid out in a scene.
This defines spatial relationships including location and size. Animation refers to the temporal description of an object; these techniques are used in combination. As with animation, physical simulation specifies motion. Rendering converts a model into an image either by simulating light transport to get photo-realistic images, or by applying an art style as in non-photorealistic rendering; the two basic operations in realistic rendering are scattering. This step is performed using 3D computer graphics software or a 3D graphics API. Altering the scene into a suitable form for rendering involves 3D projection, which displays a three-dimensional image in two dimensions. Although 3D modeling and CAD software may perform 3D rendering as well, exclusive 3D rendering software exists. 3D computer graphics software produces computer-generated imagery through 3D modeling and 3D rendering or produces 3D models for analytic and industrial purposes. 3D modeling software is a class of 3D computer graphics. Individual programs of this class are called modeling modelers.
3D modelers allow users to alter models via their 3D mesh. Users can add, subtract and otherwise change the mesh to their desire. Models can be viewed from a variety of angles simultaneously. Models can be rotated and the view can be zoomed in and out. 3D modelers can export their models to files, which can be imported into other applications as long as the metadata are compatible. Many modelers allow importers and exporters to be plugged-in, so they can read and write data in the native formats of other applications. Most 3D modelers contain a number of related features, such as ray tracers and other rendering alternatives and texture mapping facilities; some contain features that support or allow animation of models. Some may be able to generate full-motion video of a series of rendered scenes. Computer aided design software may employ the same fundamental 3D modeling techniques that 3D modeling software use but their goal differs, they are used in computer-aided engineering, computer-aided man
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 from a local council; the main purpose of building codes is to protect public health and general welfare as they relate to the construction and occupancy of buildings and structures. The building code becomes law of a particular jurisdiction when formally enacted by the appropriate governmental or private authority. Building codes are intended to be applied by architects, interior designers and regulators but are used for various purposes by safety inspectors, environmental scientists, real estate developers, manufacturers of building products and materials, insurance companies, facility managers and others. Codes regulate the 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, mechanical codes.
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 and enforcing building codes varies among nations. In some countries building codes are developed by the government agencies or quasi-governmental standards organizations and enforced across the country by the central government; 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, a system of model building codes is used. 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 and administrative orders. When referenced in any of these legal instruments, a particular model code becomes law; this practice is known as adoption by reference.
When an adopting authority decides to delete, add, or revise any portions of the model code adopted, it is required by the model code developer to follow a formal adoption procedure in which those modifications can be documented for legal purposes. There are instances. At some point in time all major cities in the United States had their own building codes. However, due to increasing complexity and cost of developing building regulations all municipalities in the country have chosen to adopt model codes instead. For example, in 2008 New York City abandoned its proprietary 1968 New York City Building Code in favor of a customized 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.
In India, each municipality and urban development authority has its own building code, mandatory for all construction within their jurisdiction. All these local building codes are variants of a National Building Code, which serves as model code proving guidelines for regulating building construction activity. Building codes have a long history; the earliest known written building code is included in the Code of Hammurabi, which dates from circa 1772 BC. The book of Deuteronomy in the Hebrew Bible stipulated that parapets must be constructed on all houses to prevent people from falling off. After the Great Fire of London in 1666, able to spread so through the densely built timber housing of the city, the Rebuilding of London Act was passed in the same year as the first significant building regulation. Drawn up by Sir Matthew Hale, the Act regulated the rebuilding of the city, required housing to have some fire resistance capacity and authorised the City of London Corporation to reopen and widen roads.
The Laws of the Indies were passed in the 1680s by the Spanish Crown to regulate the urban planning for colonies throughout Spain's worldwide imperial possessions. The first systematic national building standard was established with the London Building Act of 1844. Among the provisions, builders were required to give the district surveyor two days' notice before building, regulations regarding the thickness of walls, height of rooms, the materials used in repairs, the dividing of existing buildings and the placing and design of chimneys and drains were to be enforced and streets had to be built to minimum requirements; the Metropolitan Buildings Office was formed to regulate the construction and use of buildings throughout London. Surveyors were empowered to enforce building regulations, which sought to improve the standard of houses and business premises, to regulate activities that might threaten public health. In 1855 the assets and responsibilities of the office passed to the Metropolitan Board of Works.
The City of Baltimore passed its first building code in 1859. The Great Baltimore Fire occurred in February, 1904. Subsequent changes were made that matched other cities. In 1904, a Handbook of the Baltimore City Building Laws was published, it served as the building code for four years. Soon, a formal building code was drafted and adopted in 1908. In Paris, under the reconstruction o
Anchor bolts are used to connect structural and non-structural elements to the concrete. The connection is made by an assembling of different components such as: anchor bolts, steel plates, stiffeners. Anchor bolts transfer different types of load: shear forces. A connection between structural elements can be represented by steel column attached to reinforced concrete foundation. Whereas, a common case of non-structural element attached to a structural one is represented by the connection between a facade system and a reinforced concrete wall; the simplest – and strongest – form of anchor bolt is cast-in-place, with its embedded end consisting of a standard hexagonal head bolt and washer, 90-bend, or some sort of forged or welded flange. The last are used in concrete-steel composite structures as shear connectors. Other uses include anchoring machines to poured concrete floors and buildings to their concrete foundations. Various disposable aids of plastic, are produced to secure and align cast-in-place anchors prior to concrete placement.
Moreover their position must be coordinated with the reinforcement layout. Different types of cast-in-place anchors might be distinguished: Lifting inserts: used for lifting operations of plain or prestressed RC beams; the insert can be a threaded rod. See Bolt. Anchor channels: used in precast concrete connections; the channel can be a hot-rolled or a cold-formed steel shape in which a T-shape screw is placed in order to transfer the load to the base material. Headed Stud: consist of a steel plate with headed studs welded on. Threaded sleeves: consist of a tube with an internal thread, anchored back into the concrete. For all the type of the cast-in-place anchors, the load-transfer mechanisms is the mechanical interlock, i.e. the embedded part of the anchors in concrete transfers an the applied load via bearing pressure at the contact zone. At failure conditions, the level of bearing pressure can be higher than 10 times the concrete compressive strength, if a pure tension force is transferred.
Cast-in-place type anchors are utilized in masonry applications, placed in wet mortar joints during the laying of brick and cast blocks. Post-installed anchors can be installed in any position of hardened concrete after a drilling operation. A distinction is made according to their principle of operation; the force-transfer mechanism is based on friction mechanical interlock guaranteed by expansion forces. They can be furtherly divided into two categories: torque controlled: the anchor is inserted into the hole and secured by applying a specified torque to the bolt head or nut with a torque wrench. A particular sub-category of this anchor is called wedge type; as shown in the figure, tightening the bolt results in a wedge being driven up against a sleeve, which expands it and causes it to compress against the material it is being fastened to.displacement controlled: consist of an expansion sleeve and a conical expansion plug, whereby the sleeve is internally threaded to accept a threaded element.
The force-transfer mechanism is based on mechanical interlock. A special drilling operation allows to create a contact surface between the anchor head and the hole's wall where bearing stresses are exchanged; the force-transfer mechanism is based on bond stresses provided by binding organic materials. Both Ribbed bars and threaded rods can be used and a change of the local bond mechanism can be appreciated experimentally. In ribbed bars the resistance is prevalently due to shear behavior of concrete between the ribs whereas for threaded rods friction prevails.. Bonded anchors are referred as adhesive anchors; the anchoring material is an adhesive consisting of epoxy, polyester, or vinylester resins. The performance of this anchor's types in terms of'load-bearing capacity' under tension loads, is related to the cleaning condition of the hole. Experimental results showed that the reduction of the capacity is up to 60%; the same applies for moisture condition of concrete, for wet concrete the reduction is of 20% using polyester resin.
Other issues are represented by high temperature creep response. The force-transfer mechanism of the screw anchor is based on concentrated pressure exchange between the screw and concrete through the pitches. Tapcon screws are a popular anchor. Larger diameter screws are referred to as LDT's; this type of fastener requires a pre-drilled hole—using a Tapcon drillbit—and are screwed into the hole using a standard hex or phillips bit. These screws are blue, white, or stainless, they are available in versions for marine or high stress applications. Their force-transfer mechanism is similar to mechanical expansion anchors. A torque moment is applied to a screw, inserted in a plastic sleeve; as the torque is applied the plastic expands the sleeve against the sides of the hole acting as expansion force. They act transferring the forces via mechanical interlock; this fastening technology is used in steel-to-steel connection, for instance to connect cold-formed profiles. A screw is inserted into the base material via a gas actuated gas gun.
The driving energy is provided by firing a combustible propellant in powder form. The fastener's insertion provokes the plastic deformation of the base material which accommodates the fastener's head where the force transfer takes place. Anchors can fail in different way when loaded in tension: Steel failure: the weak part of the connection is represented by the rod; the failure corresponds to the tensile break-out of steel as in
A building, or edifice, is a structure with a roof and walls standing more or less permanently in one place, such as a house or factory. Buildings come in a variety of sizes and functions, have been adapted throughout history for a wide number of factors, from building materials available, to weather conditions, land prices, ground conditions, specific uses, aesthetic reasons. To better understand the term building compare the list of nonbuilding structures. Buildings serve several societal needs – as shelter from weather, living space, privacy, to store belongings, to comfortably live and work. A building as a shelter represents a physical division of the outside. Since the first cave paintings, buildings have become objects or canvasses of much artistic expression. In recent years, interest in sustainable planning and building practices has become an intentional part of the design process of many new buildings; the word building is the act of making it. As a noun, a building is'a structure that has a roof and walls and stands more or less permanently in one place'.
In the broadest interpretation a fence or wall is a building. However, the word structure is used more broadly than building including natural and man-made formations and does not have walls. Structure is more to be used for a fence. Sturgis' Dictionary included that " differs from architecture in excluding all idea of artistic treatment; as a verb, building is the act of construction. Structural height in technical usage is the height to the highest architectural detail on building from street-level. Depending on how they are classified and masts may or may not be included in this height. Spires and masts used as antennas are not included; the definition of a low-rise vs. a high-rise building is a matter of debate, but three storeys or less is considered low-rise. A report by Shinichi Fujimura of a shelter built 500 000 years ago is doubtful since Fujimura was found to have faked many of his findings. Supposed remains of huts found at the Terra Amata site in Nice purportedly dating from 200 000 to 400 000 years ago have been called into question.
There is clear evidence of homebuilding from around 18 000 BC. Buildings became common during the Neolithic. Single-family residential buildings are most called houses or homes. Multi-family residential buildings containing more than one dwelling unit are called a duplex or an apartment building. A condominium is an apartment rather than rents. Houses may be built in pairs, in terraces where all but two of the houses have others either side. Houses which were built as a single dwelling may be divided into apartments or bedsitters. Building types may range from huts to multimillion-dollar high-rise apartment blocks able to house thousands of people. Increasing settlement density in buildings is a response to high ground prices resulting from many people wanting to live close to work or similar attractors. Other common building materials are concrete or combinations of either of these with stone. Residential buildings have different names for their use depending if they are seasonal include holiday cottage or timeshare.
If the residents are in need of special care such as a nursing home, orphanage or prison. Many people lived in communal buildings called longhouses, smaller dwellings called pit-houses and houses combined with barns sometimes called housebarns. Buildings are defined to be substantial, permanent structures so other dwelling forms such as houseboats and motorhomes are dwellings but not buildings. Sometimes a group of inter-related builds are referred to as a complex – for example a housing complex, educational complex, hospital complex, etc; the practice of designing and operating buildings is most a collective effort of different groups of professionals and trades. Depending on the size and purpose of a particular building project, the project team may include: A real estate developer who secures funding for the project. Other possible design Engineer specialists may be involved such as Fire, facade engineers, building physics, Telecomms, AV (Audio V
Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed. Technical drawing is essential for communicating ideas in engineering. To make the drawings easier to understand, people use familiar symbols, units of measurement, notation systems, visual styles, page layout. Together, such conventions constitute a visual language and help to ensure that the drawing is unambiguous and easy to understand. Many of the symbols and principles of technical drawing are codified in an international standard called ISO 128; the need for precise communication in the preparation of a functional document distinguishes technical drawing from the expressive drawing of the visual arts. Artistic drawings are subjectively interpreted. Technical drawings are understood to have one intended meaning. A drafter, draftsperson, or draughtsman is a person. A professional drafter who makes technical drawings is sometimes called a drafting technician.
A sketch is a executed, freehand drawing, not intended as a finished work. In general, sketching is a quick way to record an idea for use. Architect's sketches serve as a way to try out different ideas and establish a composition before a more finished work when the finished work is expensive and time-consuming. Architectural sketches, for example, are a kind of diagrams; these sketches, like metaphors, are used by architects as a means of communication in aiding design collaboration. This tool helps architects to abstract attributes of hypothetical provisional design solutions and summarize their complex patterns, hereby enhancing the design process. Italic text The basic drafting procedure is to place a piece of paper on a smooth surface with right-angle corners and straight sides—typically a drawing board. A sliding straightedge known as a T-square is placed on one of the sides, allowing it to be slid across the side of the table, over the surface of the paper. "Parallel lines" can be drawn by moving the T-square and running a pencil or technical pen along the T-square's edge.
The T-square is used to hold other devices such as set triangles. In this case, the drafter places one or more triangles of known angles on the T-square—which is itself at right angles to the edge of the table—and can draw lines at any chosen angle to others on the page. Modern drafting tables come equipped with a drafting machine, supported on both sides of the table to slide over a large piece of paper; because it is secured on both sides, lines drawn along the edge are guaranteed to be parallel. In addition, the drafter uses several technical drawing tools to draw circles. Primary among these are the compasses, used for drawing simple arcs and circles, the French curve, for drawing curves. A spline is a rubber coated articulated metal. Drafting templates assist the drafter with creating recurring objects in a drawing without having to reproduce the object from scratch every time; this is useful when using common symbols. Templates are sold commercially by a number of vendors customized to a specific task, but it is not uncommon for a drafter to create his own templates.
This basic drafting system requires an accurate table and constant attention to the positioning of the tools. A common error is to allow the triangles to push the top of the T-square down thereby throwing off all angles. Tasks as simple as drawing two angled lines meeting at a point require a number of moves of the T-square and triangles, in general, drafting can be a time-consuming process. A solution to these problems was the introduction of the mechanical "drafting machine", an application of the pantograph which allowed the drafter to have an accurate right angle at any point on the page quite quickly; these machines included the ability to change the angle, thereby removing the need for the triangles as well. In addition to the mastery of the mechanics of drawing lines and circles onto a piece of paper—with respect to the detailing of physical objects—the drafting effort requires a thorough understanding of geometry and spatial comprehension, in all cases demands precision and accuracy, attention to detail of high order.
Although drafting is sometimes accomplished by a project engineer, architect, or shop personnel, skilled drafters accomplish the task, are always in demand to some degree. Today, the mechanics of the drafting task have been automated and accelerated through the use of computer-aided design systems. There are two types of computer-aided design systems used for the production of technical drawings" two dimensions and three dimensions. 2D CAD systems such as AutoCAD or MicroStation replace the paper drawing discipline. The lines, circles and curves are created within the software, it is down to the technical drawing skill of the user to produce the drawing. There is still much scope for error in the drawing when producing first and third angle orthographic projections, auxiliary projections and cross sections. A 2D CAD system is an electronic drawing board, its greatest strength over direct to paper technical drawing is in the making of revisions. Whereas in a conventional hand dr