Binishells are reinforced concrete thin-shell structures that are lifted and shaped by air pressure . The original technology was invented in the 1960s by Dante Bini , who built 1,600 of them in 23 countries.
105-415: The original Binishell method needs expensive and sophisticated equipment but it remains as one of the fastest and cost-effective ways to construct dome-shaped, monolithic, and reinforced shell structures. The original Binishells are circular in plan and are reinforced via a system of springs and rebars . They can often be constructed in less than one hour. The technology was derived from air structure, which
210-420: A flow of viscous liquid , the force F may not be perpendicular to S ; hence the stress across a surface must be regarded a vector quantity, not a scalar. Moreover, the direction and magnitude generally depend on the orientation of S . Thus the stress state of the material must be described by a tensor , called the (Cauchy) stress tensor ; which is a linear function that relates the normal vector n of
315-439: A "particle" as being an infinitesimal patch of the plate's surface, so that the boundary between adjacent particles becomes an infinitesimal line element; both are implicitly extended in the third dimension, normal to (straight through) the plate. "Stress" is then redefined as being a measure of the internal forces between two adjacent "particles" across their common line element, divided by the length of that line. Some components of
420-603: A Binishell was opened in 1978 as a sports hall for the Malvern Girls College. This Binishell had a size of 36 meters in diameter. Later, Bini designed a smaller version of the Binishell, known as a Minishell, as a low-cost, 8-meter by 8-meter shell structure. In 1971, several Binishells were constructed in Australia , for a governmental initiative that required rapid building system for multi-purpose centers. Bini also completed
525-485: A concrete structural member reinforced with steel will experience minimal differential stress as the temperature changes. Other readily available types of rebar are manufactured of stainless steel , and composite bars made of glass fiber , carbon fiber , or basalt fiber . The carbon steel reinforcing bars may also be coated in zinc or an epoxy resin designed to resist the effects of corrosion, especially when used in saltwater environments. Bamboo has been shown to be
630-392: A coordinate system with axes e 1 , e 2 , e 3 {\displaystyle e_{1},e_{2},e_{3}} , the stress tensor is a diagonal matrix, and has only the three normal components λ 1 , λ 2 , λ 3 {\displaystyle \lambda _{1},\lambda _{2},\lambda _{3}}
735-457: A cylindrical bar such as a shaft is subjected to opposite torques at its ends. In that case, the shear stress on each cross-section is parallel to the cross-section, but oriented tangentially relative to the axis, and increases with distance from the axis. Significant shear stress occurs in the middle plate (the "web") of I-beams under bending loads, due to the web constraining the end plates ("flanges"). Another simple type of stress occurs when
840-532: A device to reinforce arches, vaults , and cupolas . 2,500 meters of rebar was used in the 14th-century Château de Vincennes . During the 18th century, rebar was used to form the carcass of the Leaning Tower of Nevyansk in Russia, built on the orders of the industrialist Akinfiy Demidov . The cast iron used for the rebar was of high quality, and there is no corrosion on the bars to this day. The carcass of
945-454: A differential formula for friction forces (shear stress) in parallel laminar flow . Stress is defined as the force across a small boundary per unit area of that boundary, for all orientations of the boundary. Derived from a fundamental physical quantity (force) and a purely geometrical quantity (area), stress is also a fundamental quantity, like velocity, torque or energy , that can be quantified and analyzed without explicit consideration of
1050-499: A limited ability to carry tensile loads. When rebar is added they are known as "reinforced masonry". A similar approach (of embedding rebar vertically in designed voids in engineered blocks) is also used in dry-laid landscape walls, at least pinning the lowest course in place into the earth, also employed securing the lowest course and/or deadmen in walls made of engineered concrete or wooden landscape ties. In unusual cases, steel reinforcement may be embedded and partially exposed, as in
1155-466: A material may arise by various mechanisms, such as stress as applied by external forces to the bulk material (like gravity ) or to its surface (like contact forces , external pressure, or friction ). Any strain (deformation) of a solid material generates an internal elastic stress , analogous to the reaction force of a spring , that tends to restore the material to its original non-deformed state. In liquids and gases , only deformations that change
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#17330932848951260-463: A stretched elastic band, is subject to tensile stress and may undergo elongation . An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has dimension of force per area, with SI units of newtons per square meter (N/m ) or pascal (Pa). Stress expresses
1365-448: A surface S to the traction vector T across S . With respect to any chosen coordinate system , the Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers. Even within a homogeneous body, the stress tensor may vary from place to place, and may change over time; therefore, the stress within a material is, in general, a time-varying tensor field . In general,
1470-1007: A surface will always be a linear function of the surface's normal vector n {\displaystyle n} , the unit-length vector that is perpendicular to it. That is, T = σ ( n ) {\displaystyle T={\boldsymbol {\sigma }}(n)} , where the function σ {\displaystyle {\boldsymbol {\sigma }}} satisfies σ ( α u + β v ) = α σ ( u ) + β σ ( v ) {\displaystyle {\boldsymbol {\sigma }}(\alpha u+\beta v)=\alpha {\boldsymbol {\sigma }}(u)+\beta {\boldsymbol {\sigma }}(v)} for any vectors u , v {\displaystyle u,v} and any real numbers α , β {\displaystyle \alpha ,\beta } . The function σ {\displaystyle {\boldsymbol {\sigma }}} , now called
1575-434: A surface with normal vector n {\displaystyle n} (which is covariant - "row; horizontal" - vector) with coordinates n 1 , n 2 , n 3 {\displaystyle n_{1},n_{2},n_{3}} is then a matrix product T = n ⋅ σ {\displaystyle T=n\cdot {\boldsymbol {\sigma }}} (where T in upper index
1680-413: A system must be balanced by internal reaction forces, which are almost always surface contact forces between adjacent particles — that is, as stress. Since every particle needs to be in equilibrium, this reaction stress will generally propagate from particle to particle, creating a stress distribution throughout the body. The typical problem in stress analysis is to determine these internal stresses, given
1785-434: A system of partial differential equations involving the stress tensor field and the strain tensor field, as unknown functions to be determined. The external body forces appear as the independent ("right-hand side") term in the differential equations, while the concentrated forces appear as boundary conditions. The basic stress analysis problem is therefore a boundary-value problem . Stress analysis for elastic structures
1890-489: A two-dimensional one, and/or replace the general stress and strain tensors by simpler models like uniaxial tension/compression, simple shear, etc. Still, for two- or three-dimensional cases one must solve a partial differential equation problem. Analytical or closed-form solutions to the differential equations can be obtained when the geometry, constitutive relations, and boundary conditions are simple enough. Otherwise one must generally resort to numerical approximations such as
1995-553: A viable alternative to reinforcing steel in concrete construction. These alternative types tend to be more expensive or may have lesser mechanical properties and are thus more often used in specialty construction where their physical characteristics fulfill a specific performance requirement that carbon steel does not provide. Reinforcing bars in masonry construction have been used since antiquity , with Rome using iron or wooden rods in arch construction. Iron tie rods and anchor plates were later employed across Medieval Europe, as
2100-1092: Is transposition , and as a result we get covariant (row) vector) (look on Cauchy stress tensor ), that is [ T 1 T 2 T 3 ] = [ n 1 n 2 n 3 ] ⋅ [ σ 11 σ 21 σ 31 σ 12 σ 22 σ 32 σ 13 σ 23 σ 33 ] {\displaystyle {\begin{bmatrix}T_{1}&T_{2}&T_{3}\end{bmatrix}}={\begin{bmatrix}n_{1}&n_{2}&n_{3}\end{bmatrix}}\cdot {\begin{bmatrix}\sigma _{11}&\sigma _{21}&\sigma _{31}\\\sigma _{12}&\sigma _{22}&\sigma _{32}\\\sigma _{13}&\sigma _{23}&\sigma _{33}\end{bmatrix}}} The linear relation between T {\displaystyle T} and n {\displaystyle n} follows from
2205-412: Is a stub . You can help Misplaced Pages by expanding it . This article about a civil engineering topic is a stub . You can help Misplaced Pages by expanding it . Rebars Rebar (short for reinforcing bar ), known when massed as reinforcing steel or steel reinforcement , is a tension device added to concrete to form reinforced concrete and reinforced masonry structures to strengthen and aid
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#17330932848952310-410: Is actually the average of a very large number of atomic forces between their molecules; and physical quantities like mass, velocity, and forces that act through the bulk of three-dimensional bodies, like gravity, are assumed to be smoothly distributed over them. Depending on the context, one may also assume that the particles are large enough to allow the averaging out of other microscopic features, like
2415-424: Is also used in high-corrosion environments. It is available in many forms, such as spirals for reinforcing columns, common rods, and meshes. Most commercially available rebar is made from unidirectional fibers set in a thermoset polymer resin and is often referred to as FRP. Some special construction such as research and manufacturing facilities with very sensitive electronics may require the use of reinforcement that
2520-583: Is an essential tool in engineering for the study and design of structures such as tunnels, dams, mechanical parts, and structural frames, under prescribed or expected loads. It is also important in many other disciplines; for example, in geology, to study phenomena like plate tectonics , vulcanism and avalanches ; and in biology, to understand the anatomy of living beings. Stress analysis is generally concerned with objects and structures that can be assumed to be in macroscopic static equilibrium . By Newton's laws of motion , any external forces being applied to such
2625-424: Is approximated as (bar size/9)² square inches. For example, the area of #8 bar is (8/9)² = 0.79 square inches. Bar sizes larger than #8 follow the 1 ⁄ 8 -inch rule imperfectly and skip sizes #12–13, and #15–17 due to historical convention. In early concrete construction bars of one inch and larger were only available in square sections, and when large format deformed round bars became available around 1957,
2730-406: Is assumed fixed, the normal component can be expressed by a single number, the dot product T · n . This number will be positive if P is "pulling" on Q (tensile stress), and negative if P is "pushing" against Q (compressive stress). The shear component is then the vector T − ( T · n ) n . The dimension of stress is that of pressure , and therefore its coordinates are measured in
2835-478: Is based on the theory of elasticity and infinitesimal strain theory . When the applied loads cause permanent deformation, one must use more complicated constitutive equations, that can account for the physical processes involved ( plastic flow , fracture , phase change , etc.). Engineered structures are usually designed so the maximum expected stresses are well within the range of linear elasticity (the generalization of Hooke's law for continuous media); that is,
2940-525: Is cast into it to carry the tensile loads . Most steel reinforcement is divided into primary and secondary reinforcement: Secondary applications include rebar embedded in masonry walls, which includes both bars placed horizontally in a mortar joint (every fourth or fifth course of block) or vertically (in the horizontal voids of cement blocks and cored bricks, which is then fixed in place with grout . Masonry structures held together with grout have similar properties to concrete – high compressive resistance but
3045-456: Is erected just as a balloon is erected. Bini further drew insights from the pneumatic air-supported tennis dome. In 1965, the first Binishell was built. It had a 12-meter diameter, 6-meter height, and was lifted using Bini's patented pneumatic formwork. Uses for the Binishells range from schools , housing , tourist villages, sports arenas , storage, silos and discothèques . An example of
3150-637: Is given in the article on viscosity . The same for normal viscous stresses can be found in Sharma (2019). The relation between stress and its effects and causes, including deformation and rate of change of deformation, can be quite complicated (although a linear approximation may be adequate in practice if the quantities are small enough). Stress that exceeds certain strength limits of the material will result in permanent deformation (such as plastic flow , fracture , cavitation ) or even change its crystal structure and chemical composition . In some situations,
3255-522: Is non-conductive to electricity, and medical imaging equipment rooms may require non-magnetic properties to avoid interference. FRP rebar, notably glass fibre types have low electrical conductivity and are non-magnetic which is commonly used for such needs. Stainless steel rebar with low magnetic permeability is available and is sometimes used to avoid magnetic interference issues. Reinforcing steel can also be displaced by impacts such as earthquakes , resulting in structural failure. The prime example of this
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3360-507: Is often used for safety certification and monitoring. Most stress is analysed by mathematical methods, especially during design. The basic stress analysis problem can be formulated by Euler's equations of motion for continuous bodies (which are consequences of Newton's laws for conservation of linear momentum and angular momentum ) and the Euler-Cauchy stress principle , together with the appropriate constitutive equations. Thus one obtains
3465-408: Is perpendicular to the layer, the net internal force across S , and hence the stress, will be zero. As in the case of an axially loaded bar, in practice the shear stress may not be uniformly distributed over the layer; so, as before, the ratio F / A will only be an average ("nominal", "engineering") stress. That average is often sufficient for practical purposes. Shear stress is observed also when
3570-759: Is subject to the requirements of Australian Standards AS3600 (Concrete Structures) and AS/NZS4671 (Steel Reinforcing for Concrete). There are other standards that apply to testing, welding and galvanizing. The designation of reinforcement is defined in AS/NZS4671 using the following formats: Shape/ Section D- deformed ribbed bar, R- round / plain bar, I- deformed indented bar Ductility Class L- low ductility, N- normal ductility, E- seismic (Earthquake) ductility Standard grades (MPa) 250N, 300E, 500L, 500N, 500E Bars are typically abbreviated to simply 'N' (hot-rolled deformed bar), 'R' (hot-rolled round bar), 'RW' (cold-drawn ribbed wire) or 'W' (cold-drawn round wire), as
3675-412: Is subjected to tension by opposite forces of magnitude F {\displaystyle F} along its axis. If the system is in equilibrium and not changing with time, and the weight of the bar can be neglected, then through each transversal section of the bar the top part must pull on the bottom part with the same force, F with continuity through the full cross-sectional area , A . Therefore,
3780-703: Is the collapse of the Cypress Street Viaduct in Oakland, California as a result of the 1989 Loma Prieta earthquake , causing 42 fatalities. The shaking of the earthquake caused rebars to burst from the concrete and buckle . Updated building designs, including more circumferential rebar, can address this type of failure. US/Imperial bar sizes give the diameter in units of 1 ⁄ 8 inch (3.2 mm) for bar sizes #2 through #8, so that #8 = 8 ⁄ 8 inch = 1-inch (25 mm) diameter. There are no fractional bar sizes in this system. The "#" symbol indicates
3885-437: Is then reduced to a scalar (tension or compression of the bar), but one must take into account also a bending stress (that tries to change the bar's curvature, in some direction perpendicular to the axis) and a torsional stress (that tries to twist or un-twist it about its axis). Stress analysis is a branch of applied physics that covers the determination of the internal distribution of internal forces in solid objects. It
3990-576: Is too small to be detected. In a solid material, such strain will in turn generate an internal elastic stress, analogous to the reaction force of a stretched spring , tending to restore the material to its original undeformed state. Fluid materials (liquids, gases and plasmas ) by definition can only oppose deformations that would change their volume. If the deformation changes with time, even in fluids there will usually be some viscous stress, opposing that change. Such stresses can be either shear or normal in nature. Molecular origin of shear stresses in fluids
4095-476: Is touted as a sustainable building technology since it is said to have one-third the environmental impact over its lifespan. The prototype for this new technology, called System A was completed in Malibu for actor Robert Downey Jr. The latest Binishells technology no longer requires air pressure, but relies on tensile forces to give shape to a parabolic hyperboloid shaped building envelope. The resulting building has all
4200-505: The (Cauchy) stress tensor , completely describes the stress state of a uniformly stressed body. (Today, any linear connection between two physical vector quantities is called a tensor , reflecting Cauchy's original use to describe the "tensions" (stresses) in a material.) In tensor calculus , σ {\displaystyle {\boldsymbol {\sigma }}} is classified as a second-order tensor of type (0,2) or (1,1) depending on convention. Like any linear map between vectors,
4305-610: The capitals , arches , cupolas , trusses and the flying buttresses of Gothic cathedrals . Ancient and medieval architects did develop some geometrical methods and simple formulas to compute the proper sizes of pillars and beams, but the scientific understanding of stress became possible only after the necessary tools were invented in the 17th and 18th centuries: Galileo Galilei 's rigorous experimental method , René Descartes 's coordinates and analytic geometry , and Newton 's laws of motion and equilibrium and calculus of infinitesimals . With those tools, Augustin-Louis Cauchy
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4410-404: The number sign , and thus "#6" is read as "number six". The use of the "#" sign is customary for US sizes, but "No." is sometimes used instead. Within the trades rebar is known by a shorthand utilizing the bar diameter as descriptor, such as "four-bar" for bar that is four-eighths (or one-half) of an inch. The cross-sectional area of a bar, as given by πr ², works out to (bar size/9.027)², which
4515-989: The orthogonal shear stresses . The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates. A graphical representation of this transformation law is the Mohr's circle of stress distribution. As a symmetric 3×3 real matrix, the stress tensor σ {\displaystyle {\boldsymbol {\sigma }}} has three mutually orthogonal unit-length eigenvectors e 1 , e 2 , e 3 {\displaystyle e_{1},e_{2},e_{3}} and three real eigenvalues λ 1 , λ 2 , λ 3 {\displaystyle \lambda _{1},\lambda _{2},\lambda _{3}} , such that σ e i = λ i e i {\displaystyle {\boldsymbol {\sigma }}e_{i}=\lambda _{i}e_{i}} . Therefore, in
4620-457: The principal stresses . If the three eigenvalues are equal, the stress is an isotropic compression or tension, always perpendicular to any surface, there is no shear stress, and the tensor is a diagonal matrix in any coordinate frame. In general, stress is not uniformly distributed over a material body, and may vary with time. Therefore, the stress tensor must be defined for each point and each moment, by considering an infinitesimal particle of
4725-442: The strain rate can be quite complicated, although a linear approximation may be adequate in practice if the quantities are sufficiently small. Stress that exceeds certain strength limits of the material will result in permanent deformation (such as plastic flow , fracture , cavitation ) or even change its crystal structure and chemical composition . Humans have known about stress inside materials since ancient times. Until
4830-445: The 17th century, this understanding was largely intuitive and empirical, though this did not prevent the development of relatively advanced technologies like the composite bow and glass blowing . Over several millennia, architects and builders in particular, learned how to put together carefully shaped wood beams and stone blocks to withstand, transmit, and distribute stress in the most effective manner, with ingenious devices such as
4935-631: The United States, made a significant contribution to the development of reinforcing bars in concrete construction. He invented twisted iron rebar, which he initially thought of while designing self-supporting sidewalks for the Masonic Hall in Stockton, California. His twisted rebar was, however, not initially appreciated and even ridiculed at the Technical Society of California, where members stated that
5040-413: The United States, who produced and tested reinforced concrete beams. Joseph Monier of France is one of the most notable figures for the invention and popularization of reinforced concrete. As a French gardener, Monier patented reinforced concrete flowerpots in 1867, before proceeding to build reinforced concrete water tanks and bridges. Ernest L. Ransome , an English engineer and architect who worked in
5145-430: The absence of external forces; such built-in stress is important, for example, in prestressed concrete and tempered glass . Stress may also be imposed on a material without the application of net forces , for example by changes in temperature or chemical composition, or by external electromagnetic fields (as in piezoelectric and magnetostrictive materials). The relation between mechanical stress, strain, and
5250-486: The bar into place, while the second makes use of the high compressive strength of concrete. Common rebar is made of unfinished tempered steel, making it susceptible to rusting . Normally the concrete cover is able to provide a pH value higher than 12 avoiding the corrosion reaction. Too little concrete cover can compromise this guard through carbonation from the surface, and salt penetration . Too much concrete cover can cause bigger crack widths which also compromises
5355-574: The bars and corrosion under the epoxy film have been reported. These epoxy-coated bars are used in over 70,000 bridge decks in the US, but this technology was slowly being phased out in favor of stainless steel rebar as of 2005 because of its poor performance. Requirements for deformations are found in US-standard product specifications for steel bar reinforcing, such as ASTM A615 and ASTM A706, and dictate lug spacing and height. Fibre-reinforced plastic rebar
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#17330932848955460-673: The beams at the columns. This type of failure manifested in the partial collapse of the Bixby Hotel in Long Beach, California and total collapse of the Eastman Kodak Building in Rochester, New York, both during construction in 1906. It was, however, concluded that both failures were the consequences of poor-quality labor. With the increase in demand of construction standardization, innovative reinforcing systems such as Kahn's were pushed to
5565-449: The bulk of the material, varying continuously with position and time. Other agents (like external loads and friction, ambient pressure, and contact forces) may create stresses and forces that are concentrated on certain surfaces, lines or points; and possibly also on very short time intervals (as in the impulses due to collisions). In active matter , self-propulsion of microscopic particles generates macroscopic stress profiles. In general,
5670-578: The concrete under tension. Concrete is strong under compression , but has low tensile strength . Rebar usually consists of steel bars which significantly increase the tensile strength of the structure. Rebar surfaces feature a continuous series of ribs, lugs or indentations to promote a better bond with the concrete and reduce the risk of slippage. The most common type of rebar is carbon steel , typically consisting of hot-rolled round bars with deformation patterns embossed into its surface. Steel and concrete have similar coefficients of thermal expansion , so
5775-406: The concrete, it can still be pulled out of the concrete under high stresses, an occurrence that often accompanies a larger-scale collapse of the structure. To prevent such a failure, rebar is either deeply embedded into adjacent structural members (40–60 times the diameter), or bent and hooked at the ends to lock it around the concrete and other rebar. This first approach increases the friction locking
5880-475: The construction of a tourist village in Cairns , Australia, using Minishells in 1980. More recently the system is being re-launched by Dante Bini's son Nicoló Bini, AIA. Improvements to the original system include greater architectural flexibility, compliance to international building codes , simplification of the construction process and integration of latest material and passive heating / cooling technologies. It
5985-498: The cross-section), but will vary over the cross section: the outer part will be under tensile stress, while the inner part will be compressed. Another variant of normal stress is the hoop stress that occurs on the walls of a cylindrical pipe or vessel filled with pressurized fluid. Another simple type of stress occurs when a uniformly thick layer of elastic material like glue or rubber is firmly attached to two stiff bodies that are pulled in opposite directions by forces parallel to
6090-402: The deformations caused by internal stresses are linearly related to them. In this case the differential equations that define the stress tensor are linear, and the problem becomes much easier. For one thing, the stress at any point will be a linear function of the loads, too. For small enough stresses, even non-linear systems can usually be assumed to be linear. Stress analysis is simplified when
6195-709: The effect of gravity and other external forces can be neglected. In these situations, the stress across any imaginary internal surface turns out to be equal in magnitude and always directed perpendicularly to the surface independently of the surface's orientation. This type of stress may be called isotropic normal or just isotropic ; if it is compressive, it is called hydrostatic pressure or just pressure . Gases by definition cannot withstand tensile stresses, but some liquids may withstand very large amounts of isotropic tensile stress under some circumstances. see Z-tube . Parts with rotational symmetry , such as wheels, axles, pipes, and pillars, are very common in engineering. Often
6300-434: The elements σ x , σ y , σ z {\displaystyle \sigma _{x},\sigma _{y},\sigma _{z}} are called the orthogonal normal stresses (relative to the chosen coordinate system), and τ x y , τ x z , τ y z {\displaystyle \tau _{xy},\tau _{xz},\tau _{yz}}
6405-424: The external forces that are acting on the system. The latter may be body forces (such as gravity or magnetic attraction), that act throughout the volume of a material; or concentrated loads (such as friction between an axle and a bearing , or the weight of a train wheel on a rail), that are imagined to act over a two-dimensional area, or along a line, or at single point. In stress analysis one normally disregards
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#17330932848956510-412: The fundamental laws of conservation of linear momentum and static equilibrium of forces, and is therefore mathematically exact, for any material and any stress situation. The components of the Cauchy stress tensor at every point in a material satisfy the equilibrium equations ( Cauchy's equations of motion for zero acceleration). Moreover, the principle of conservation of angular momentum implies that
6615-457: The grains of a metal rod or the fibers of a piece of wood . Quantitatively, the stress is expressed by the Cauchy traction vector T defined as the traction force F between adjacent parts of the material across an imaginary separating surface S , divided by the area of S . In a fluid at rest the force is perpendicular to the surface, and is the familiar pressure . In a solid , or in
6720-405: The idea that Kahn's reinforcing system in concrete beams would act as a Warren truss and also noted that this system would not provide the adequate amount of shear stress reinforcement at the ends of the simply supported beams, the place where the shear stress is greatest. Furthermore, Turner warned that Kahn's system could result in a brittle failure as it did not have longitudinal reinforcement in
6825-929: The industry manufactured them to provide the cross-sectional area equivalent of standard square bar sizes that were formerly used. The diameter of the equivalent large format round shape is rounded to the nearest 1 ⁄ 8 inch to provide the bar size. For example, #9 bar has a cross section of 1.00 square inch (6.5 cm ), and therefore a diameter of 1.128 inches (28.7 mm). #10, #11, #14, and #18 sizes correspond to 1 1 ⁄ 8 inch, 1 1 ⁄ 4 , 1 1 ⁄ 2 , and 2-inch square bars, respectively. Sizes smaller than #3 are no longer recognized as standard sizes. These are most commonly manufactured as plain round undeformed rod steel but can be made with deformations. Sizes smaller than #3 are typically referred to as "wire" products and not "bar" and specified by either their nominal diameter or wire gage number. #2 bars are often informally called "pencil rod" as they are about
6930-423: The internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the relative deformation of the material. For example, when a solid vertical bar is supporting an overhead weight , each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure , each particle gets pushed against by all
7035-408: The layer; or a section of a soft metal bar that is being cut by the jaws of a scissors-like tool . Let F be the magnitude of those forces, and M be the midplane of that layer. Just as in the normal stress case, the part of the layer on one side of M must pull the other part with the same force F . Assuming that the direction of the forces is known, the stress across M can be expressed simply by
7140-682: The local guard. As rust takes up greater volume than the steel from which it was formed, it causes severe internal pressure on the surrounding concrete, leading to cracking, spalling , and, ultimately, structural failure . This phenomenon is known as oxide jacking . This is a particular problem where the concrete is exposed to salt water, as in bridges where salt is applied to roadways in winter, or in marine applications. Uncoated, corrosion-resistant low- carbon / chromium (microcomposite), silicon bronze , epoxy -coated, galvanized , or stainless steel rebars may be employed in these situations at greater initial expense, but significantly lower expense over
7245-429: The material body is under equal compression or tension in all directions. This is the case, for example, in a portion of liquid or gas at rest, whether enclosed in some container or as part of a larger mass of fluid; or inside a cube of elastic material that is being pressed or pulled on all six faces by equal perpendicular forces — provided, in both cases, that the material is homogeneous, without built-in stress, and that
7350-519: The medium surrounding that point, and taking the average stresses in that particle as being the stresses at the point. Human-made objects are often made from stock plates of various materials by operations that do not change their essentially two-dimensional character, like cutting, drilling, gentle bending and welding along the edges. The description of stress in such bodies can be simplified by modeling those parts as two-dimensional surfaces rather than three-dimensional bodies. In that view, one redefines
7455-448: The most general case, called triaxial stress , the stress is nonzero across every surface element. Combined stresses cannot be described by a single vector. Even if the material is stressed in the same way throughout the volume of the body, the stress across any imaginary surface will depend on the orientation of that surface, in a non-trivial way. Cauchy observed that the stress vector T {\displaystyle T} across
7560-420: The nature of the material or of its physical causes. Following the basic premises of continuum mechanics, stress is a macroscopic concept. Namely, the particles considered in its definition and analysis should be just small enough to be treated as homogeneous in composition and state, but still large enough to ignore quantum effects and the detailed motions of molecules. Thus, the force between two particles
7665-446: The nominal bar diameter in millimeters, as an "alternate size" specification. Substituting a true metric size for a US/Imperial size is called a hard conversion , and sometimes results in the use of a physically different sized bar. bar size size (soft) Metric bar designations represent the nominal bar diameter in millimeters, rounded to the nearest 5 mm. bar size (kg/m) (mm) Area (mm ) Metric bar designations represent
7770-508: The nominal bar diameter in millimetres. Preferred bar sizes in Europe are specified to comply with Table 6 of the standard EN 10080 , although various national standards still remain in force (e.g. BS 4449 in the United Kingdom). In Switzerland some sizes are different from European standard. bar size density (kg/m) diameter (mm) area (mm ) Reinforcement for use in concrete construction
7875-452: The physical causes of the forces or the precise nature of the materials. Instead, one assumes that the stresses are related to deformation (and, in non-static problems, to the rate of deformation) of the material by known constitutive equations . Stress analysis may be carried out experimentally, by applying loads to the actual artifact or to scale model, and measuring the resulting stresses, by any of several available methods. This approach
7980-424: The physical dimensions and the distribution of loads allow the structure to be treated as one- or two-dimensional. In the analysis of trusses, for example, the stress field may be assumed to be uniform and uniaxial over each member. Then the differential equations reduce to a finite set of equations (usually linear) with finitely many unknowns. In other contexts one may be able to reduce the three-dimensional problem to
8085-445: The plate). The analysis of stress can be considerably simplified also for thin bars, beams or wires of uniform (or smoothly varying) composition and cross-section that are subjected to moderate bending and twisting. For those bodies, one may consider only cross-sections that are perpendicular to the bar's axis, and redefine a "particle" as being a piece of wire with infinitesimal length between two such cross sections. The ordinary stress
8190-510: The qualification of “tentative” was removed when the updated standard ASTM A305-49 was issued in 1949. The requirements for deformations found in current specifications for steel bar reinforcing, such as ASTM A615 and ASTM A706, among others, are the same as those specified in ASTM A305-49. Concrete is a material that is very strong in compression , but relatively weak in tension . To compensate for this imbalance in concrete's behavior, rebar
8295-455: The safety and environmental benefits of the improved Binishells, but has added advantages. These additional advantages include a rectangular floor plan, multi-floor capabilities, built-in openings and natural venting. The two story prototype for this technology was built on Vancouver Island, BC Canada. This architecture -related article is a stub . You can help Misplaced Pages by expanding it . This article related to an architectural style
8400-491: The same size as a pencil. When US/Imperial sized rebar are used in projects with metric units, the equivalent metric size is typically specified as the nominal diameter rounded to the nearest millimeter. These are not considered standard metric sizes, and thus is often referred to as a soft conversion or the "soft metric" size. The US/Imperial bar size system recognizes the use of true metric bar sizes (No. 10, 12, 16, 20, 25, 28, 32, 36, 40, 50 and 60 specifically) which indicates
8505-657: The same units as pressure: namely, pascals (Pa, that is, newtons per square metre ) in the International System , or pounds per square inch (psi) in the Imperial system . Because mechanical stresses easily exceed a million Pascals, MPa, which stands for megapascal, is a common unit of stress. Stress in a material body may be due to multiple physical causes, including external influences and internal physical processes. Some of these agents (like gravity, changes in temperature and phase , and electromagnetic fields) act on
8610-413: The service life of the project. Extra care is taken during the transport, fabrication, handling, installation, and concrete placement process when working with epoxy-coated rebar, because damage will reduce the long-term corrosion resistance of these bars. Even damaged epoxy-coated bars have shown better performance than uncoated reinforcing bars, though issues from debonding of the epoxy coating from
8715-519: The side in favor of the concrete reinforcing systems seen today. Requirements for deformations on steel bar reinforcement were not standardized in US construction until about 1950. Modern requirements for deformations were established in "Tentative Specifications for the Deformations of Deformed Steel Bars for Concrete Reinforcement", ASTM A305-47T. Subsequently, changes were made that increased rib height and reduced rib spacing for certain bar sizes, and
8820-424: The single number τ {\displaystyle \tau } , calculated simply with the magnitude of those forces, F and the cross sectional area, A . τ = F A {\displaystyle \tau ={\frac {F}{A}}} Unlike normal stress, this simple shear stress is directed parallel to the cross-section considered, rather than perpendicular to it. For any plane S that
8925-533: The steel tie bars that constrain and reinforce the masonry of Nevyansk Tower or ancient structures in Rome and the Vatican. Steel has a thermal expansion coefficient nearly equal to that of modern concrete . If this were not so, it would cause problems through additional longitudinal and perpendicular stresses at temperatures different from the temperature of the setting. Although rebar has ribs that bind it mechanically to
9030-407: The stress T that a particle P applies on another particle Q across a surface S can have any direction relative to S . The vector T may be regarded as the sum of two components: the normal stress ( compression or tension ) perpendicular to the surface, and the shear stress that is parallel to the surface. If the normal unit vector n of the surface (pointing from Q towards P )
9135-501: The stress can be assumed to be uniformly distributed over any cross-section that is more than a few times D from both ends. (This observation is known as the Saint-Venant's principle ). Normal stress occurs in many other situations besides axial tension and compression. If an elastic bar with uniform and symmetric cross-section is bent in one of its planes of symmetry, the resulting bending stress will still be normal (perpendicular to
9240-411: The stress distribution in a body is expressed as a piecewise continuous function of space and time. Conversely, stress is usually correlated with various effects on the material, possibly including changes in physical properties like birefringence , polarization , and permeability . The imposition of stress by an external agent usually creates some strain (deformation) in the material, even if it
9345-475: The stress is evenly distributed over the entire cross-section. In practice, depending on how the bar is attached at the ends and how it was manufactured, this assumption may not be valid. In that case, the value σ {\displaystyle \sigma } = F / A will be only the average stress, called engineering stress or nominal stress . If the bar's length L is many times its diameter D , and it has no gross defects or built-in stress , then
9450-424: The stress is maximum for surfaces that are perpendicular to a certain direction d {\displaystyle d} , and zero across any surfaces that are parallel to d {\displaystyle d} . When the shear stress is zero only across surfaces that are perpendicular to one particular direction, the stress is called biaxial , and can be viewed as the sum of two normal or shear stresses. In
9555-399: The stress patterns that occur in such parts have rotational or even cylindrical symmetry . The analysis of such cylinder stresses can take advantage of the symmetry to reduce the dimension of the domain and/or of the stress tensor. Often, mechanical bodies experience more than one type of stress at the same time; this is called combined stress . In normal and shear stress, the magnitude of
9660-684: The stress state of the medium at any point and instant can be specified by only six independent parameters, rather than nine. These may be written [ σ x τ x y τ x z τ x y σ y τ y z τ x z τ y z σ z ] {\displaystyle {\begin{bmatrix}\sigma _{x}&\tau _{xy}&\tau _{xz}\\\tau _{xy}&\sigma _{y}&\tau _{yz}\\\tau _{xz}&\tau _{yz}&\sigma _{z}\end{bmatrix}}} where
9765-411: The stress tensor can be ignored, but since particles are not infinitesimal in the third dimension one can no longer ignore the torque that a particle applies on its neighbors. That torque is modeled as a bending stress that tends to change the curvature of the plate. These simplifications may not hold at welds, at sharp bends and creases (where the radius of curvature is comparable to the thickness of
9870-1620: The stress tensor can be represented in any chosen Cartesian coordinate system by a 3×3 matrix of real numbers. Depending on whether the coordinates are numbered x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} or named x , y , z {\displaystyle x,y,z} , the matrix may be written as [ σ 11 σ 12 σ 13 σ 21 σ 22 σ 23 σ 31 σ 32 σ 33 ] {\displaystyle {\begin{bmatrix}\sigma _{11}&\sigma _{12}&\sigma _{13}\\\sigma _{21}&\sigma _{22}&\sigma _{23}\\\sigma _{31}&\sigma _{32}&\sigma _{33}\end{bmatrix}}} or [ σ x x σ x y σ x z σ y x σ y y σ y z σ z x σ z y σ z z ] {\displaystyle {\begin{bmatrix}\sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{yx}&\sigma _{yy}&\sigma _{yz}\\\sigma _{zx}&\sigma _{zy}&\sigma _{zz}\\\end{bmatrix}}} The stress vector T = σ ( n ) {\displaystyle T={\boldsymbol {\sigma }}(n)} across
9975-431: The stress tensor is symmetric , that is σ 12 = σ 21 {\displaystyle \sigma _{12}=\sigma _{21}} , σ 13 = σ 31 {\displaystyle \sigma _{13}=\sigma _{31}} , and σ 23 = σ 32 {\displaystyle \sigma _{23}=\sigma _{32}} . Therefore,
10080-423: The stress within a body may adequately be described by a single number, or by a single vector (a number and a direction). Three such simple stress situations, that are often encountered in engineering design, are the uniaxial normal stress , the simple shear stress , and the isotropic normal stress . A common situation with a simple stress pattern is when a straight rod, with uniform material and cross section,
10185-440: The stress σ throughout the bar, across any horizontal surface, can be expressed simply by the single number σ, calculated simply with the magnitude of those forces, F , and cross sectional area, A . σ = F A {\displaystyle \sigma ={\frac {F}{A}}} On the other hand, if one imagines the bar being cut along its length, parallel to the axis, there will be no force (hence no stress) between
10290-402: The surrounding particles. The container walls and the pressure -inducing surface (such as a piston) push against them in (Newtonian) reaction . These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules . Stress is frequently represented by a lowercase Greek letter sigma ( σ ). Strain inside
10395-548: The tower was connected to its cast iron tented roof , crowned with one of the first known lightning rods . However, not until the mid-19th century, with the embedding of steel bars into concrete (thus producing modern reinforced concrete ), did rebar display its greatest strengths. Several people in Europe and North America developed reinforced concrete in the 1850s. These include Joseph-Louis Lambot of France, who built reinforced concrete boats in Paris (1854) and Thaddeus Hyatt of
10500-649: The twisting would weaken the iron. In 1889, Ransome worked on the West Coast mainly designing bridges. One of these, the Alvord Lake Bridge in San Francisco's Golden Gate Park, was the first reinforced concrete bridge built in the United States. He used twisted rebar in this structure. At the same time Ransome was inventing twisted steel rebar, C.A.P. Turner was designing his "mushroom system" of reinforced concrete floor slabs with smooth round rods and Julius Kahn
10605-440: The two halves across the cut. This type of stress may be called (simple) normal stress or uniaxial stress; specifically, (uniaxial, simple, etc.) tensile stress. If the load is compression on the bar, rather than stretching it, the analysis is the same except that the force F and the stress σ {\displaystyle \sigma } change sign, and the stress is called compressive stress. This analysis assumes
10710-421: The volume generate persistent elastic stress. If the deformation changes gradually with time, even in fluids there will usually be some viscous stress , opposing that change. Elastic and viscous stresses are usually combined under the name mechanical stress . Significant stress may exist even when deformation is negligible or non-existent (a common assumption when modeling the flow of water). Stress may exist in
10815-421: The yield strength and ductility class can be implied from the shape. For example, all commercially available wire has a yield strength of 500 MPa and low ductility, while round bars are 250 MPa and normal ductility. Stress (mechanics) In continuum mechanics , stress is a physical quantity that describes forces present during deformation . For example, an object being pulled apart, such as
10920-400: Was able to give the first rigorous and general mathematical model of a deformed elastic body by introducing the notions of stress and strain. Cauchy observed that the force across an imaginary surface was a linear function of its normal vector; and, moreover, that it must be a symmetric function (with zero total momentum). The understanding of stress in liquids started with Newton, who provided
11025-560: Was experimenting with an innovative rolled diamond-shaped rebar with flat-plate flanges angled upwards at 45° (patented in 1902). Kahn predicted concrete beams with this reinforcing system would bend like a Warren truss , and also thought of this rebar as shear reinforcement. Kahn's reinforcing system was built in concrete beams, joists, and columns. The system was both praised and criticized by Kahn's engineering contemporaries: Turner voiced strong objections to this system as it could cause catastrophic failure to concrete structures. He rejected
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