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Direct Integration Of A Beam
Direct integration is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam. For a beam with an applied weight w(x) , taking downward to be positive, the internal shear force is given by taking the negative integral of the weight: : V(x) = -\int w(x)\, dx The internal moment M(x) is the integral of the internal shear: : M(x) = \int V(x)\, dx = -\int \left int w(x)\, dx \rightdx The angle of rotation from the horizontal, \theta, is the integral of the internal moment divided by the product of the Young's modulus and the area moment of inertia: : \theta (x) = \frac \int M(x)\, dx Integrating the angle of rotation obtains the vertical displacement \nu : : \nu (x) = \int \theta (x)\, dx Integrating Each time an integration is carried out, a constant of integration needs to be obtained. These constants are determined by using either the forces at supports, or at free ends. : For internal shear and moment, the constants ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Analysis
Structural analysis is a branch of Solid Mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam (structure)
A beam is a structural element that primarily resists Structural load, loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of Deflection (engineering), deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beams, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and their material. Beams are traditionally descriptions of building or civil engineering structural elements, where the beams are horizontal and carry vertical loads. However, any structure may contain beams, for instance automobile frames, aircraft components, machine frames, and other mechanical or structural systems. In th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Mechanics
Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics such as materials science. It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. Solid mechanics is a vast subject because of the wide range of solid materials available, such as steel, wood, concrete, biological materials, textiles, geological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Bernoulli Beam Theory
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral loads only. By ignoring the effects of shear deformation and rotatory inertia, it is thus a special case of Timoshenko–Ehrenfest beam theory. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution. Additional mathematical models have been developed, such as plate theory, but the simplicity of beam theory makes it an important tool in the sciences, especially structural and mechanical engineering. Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Theory
Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized group of electrically charged particles ***Cathode ray, or electron beam or e-beam, streams of electrons observed in discharge tubes ***X-ray beam, a penetrating form of high-energy electromagnetic radiation ** Molecular beam, a beam of particles moving at approximately equal velocities Arts, entertainment and media * Beam (music), a connection line in musical notation * Beam, to transport matter using the Transporter in the ''Star Trek'' fictional universe * Beam (rapper), American hip hop artist * BEAM.TV, an online digital delivery and content management platform * BEAM Channel 31, a Philippines television network * Beam (website), later Mixer, a former video game live streaming platform * BeamNG.drive, an open-world vehicle simulation v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bending
In applied mechanics, bending (also known as flexure) 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 small fraction, typically 1/10 or less, of the other two.Boresi, A. P. and Schmidt, R. J. and Sidebottom, O. M., 1993, Advanced mechanics of materials, John Wiley and Sons, New York. When the length is considerably longer than the width and the thickness, the element is called a beam. 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 geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large diameter, but thin-walled, short tube supported at its ends and loa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as and it can also be found in Todhunter (1888) who wrote it as "''y'' = ''mx'' + ''c''". Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical – as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The ''steepness'', incline, or grade of a line is measured by the absolute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steel
Steel is an alloy made up of iron with added carbon to improve its strength and fracture resistance compared to other forms of iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistant typically need an additional 11% chromium. Because of its high tensile strength and low cost, steel is used in buildings, infrastructure, tools, ships, trains, cars, machines, electrical appliances, weapons, and rockets. Iron is the base metal of steel. Depending on the temperature, it can take two crystalline forms (allotropic forms): body-centred cubic and face-centred cubic. The interaction of the allotropes of iron with the alloying elements, primarily carbon, gives steel and cast iron their range of unique properties. In pure iron, the crystal structure has relatively little resistance to the iron atoms slipping past one another, and so pure iron is quite ductile, or soft and easily formed. In steel, small amounts of carbon, other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Member
Structural elements are used in structural analysis to split a complex structure into simple elements. Within a structure, an element cannot be broken down (decomposed) into parts of different kinds (e.g., beam or column). Structural elements can be lines, surfaces or volumes. Line elements: *Rod - axial loads *Beam - axial and bending loads *Pillar *Post (structural) *Struts or Compression members- compressive loads *Ties, Tie rods, eyebars, guy-wires, suspension cables, or wire ropes - tension loads Surface elements: *membrane - in-plane loads only *shell - in plane and bending moments **Concrete slab ** deck * shear panel - shear loads only Volumes: *Axial, shear and bending loads for all three dimensions See also * Load-bearing wall * Post and lintel * Stressed member engine A stressed member engine is a vehicle engine used as an active structural element of the chassis to transmit forces and torques, rather than being passively contained by the chassis with anti-vib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear And Moment
Shear may refer to: Textile production * Animal shearing, the collection of wool from various species ** Sheep shearing *The removal of nap during wool cloth production Science and technology Engineering * Shear strength (soil), the shear strength of soil under loading *Shear line (locksmithing), where the inner cylinder ends and the outer cylinder begins in a cylinder lock * Shearing (manufacturing), a metalworking process which cuts stock without the formation of chips or the use of burning or melting * Shear (sheet metal), various tools to shear sheet metal *Board shear, in bookbinding, a tool to cut board or paper * Shear pin, in machinery, such as a plough, designed to shear (break) when a certain force is exceeded, to protect other components of the machine. * Shearing interferometer, in optics, a simple and very common means to check the collimation of beams by observing interference *Shearing in computer graphics, more commonly called screen tearing *Shear wall, a wall co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Body Diagram
A free body diagram consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it. In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body may consist of multiple internal members (such as a truss), or be a compact body (such as a beam). A series of free bodies and other diagrams may be necessary to solve complex problems. Purpose Free body diagrams are used to visualize forces and moments applied to a body and to calculate reactions in mechanics problems. These diagrams are frequently used both to determine the loading of individual structural components and to calculate internal forces within a structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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