Information about Deflection
Deflection or deflexion is a term used in physics, automotive, engineering, and weapon applications to describe four separate phenomena.
In engineering mechanics, deflection is a term that is used to describe the degree to which a structural element is displaced under a load. The deflection of a member under a load is directly related to the slope of the deflected shape of the member under that load and can calculated by integrating the function that mathematically describes the slope of the member under that load. Deflection can be calculated by standard formulae (will only give the deflection of common beam configurations and load cases at discrete locations), or by methods such as "virtual work", "direct integration", "Castigliano's method", "Macaulay's method" or the "matrix stiffness method" amongst others. (See structural analysis textbooks for procedure.)
An example of the use of deflection in this context is in building construction. Architects and Engineers select materials for various applications. The beams used for frame work are selected on the basis of deflection, amongst other factors.
The elastic deflection f and angle of deflection φ (in radians) in the example image, a (weightless) cantilever beam, can be calculated (at the free end) using :
The deflection at any point along the span can be calculated using the above-mentioned methods.
From this formula it follows that the span L is the most determinating factor; if the span doubles, the deflection increases 2³ = 8 fold.
Building codes determine the maximum deflection, usually as a fraction of the span e.g. 1/400 or 1/600. Either the strength limit state (allowable stress) or the serviceability limit state (deflection considerations amongst others) may govern the minimum dimensions of the member required.
The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass.
The deflective shape of a beam can be represented by the moment diagram, integrated.
In physics deflection is the event where an object collides and bounces against a plane surface.
In such collisions involving a sphere and a plane, the collision angle formed with the surface normal (the incidental angle α) must equal the bounce angle (the accidental angle β),
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Structural engineering
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Deflection (f) in engineering
An example of the use of deflection in this context is in building construction. Architects and Engineers select materials for various applications. The beams used for frame work are selected on the basis of deflection, amongst other factors.
The elastic deflection f and angle of deflection φ (in radians) in the example image, a (weightless) cantilever beam, can be calculated (at the free end) using :
- fB = F·L3 / (3·E·I)
- φB = F·L2 / (2·E·I)
- F = force acting on the tip of the beam
- L = length of the beam (span)
The deflection at any point along the span can be calculated using the above-mentioned methods.
From this formula it follows that the span L is the most determinating factor; if the span doubles, the deflection increases 2³ = 8 fold.
Building codes determine the maximum deflection, usually as a fraction of the span e.g. 1/400 or 1/600. Either the strength limit state (allowable stress) or the serviceability limit state (deflection considerations amongst others) may govern the minimum dimensions of the member required.
The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass.
The deflective shape of a beam can be represented by the moment diagram, integrated.
Electronics
In electronic engineering, and more specifically cathode ray tube (CRT) technology, deflection refers to the use of electromagnetic or electrostatic fields to deflect an electron beam to provide a two-dimensional display on a screen formed by the flat face of the CRT.Automotive
Deflection as an automotive term is used as a measure of the tightness of car engine belts, which is measured using a belt gauge.Physics
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Deflection occurs when an object hits a plane surface
In such collisions involving a sphere and a plane, the collision angle formed with the surface normal (the incidental angle α) must equal the bounce angle (the accidental angle β),
See also
Weapons
Deflection is a tactic used in battle that describes "leading the target"; that is, shooting ahead of a moving target so that the target and projectile will collide. This tactic is only necessary when using slow projectiles, such as a crossbow bolt, or over long distances, such as in an aerial dogfight. During World War II, U.S. Navy pilots were taught explicitly on the concept in order to capitalize on the advantages of the Wildcat. Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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automobile (from Greek auto, self and Latin mobile moving, a vehicle that moves itself rather than being moved by another vehicle or animal) or motor car (usually shortened to just car) is a wheeled passenger vehicle that carries its own motor.
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Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
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weapon is a tool used to injure, incapacitate, or kill an adversary.[1][2] Weapons may be used to attack and defend, and consequently also to threaten or protect. Metaphorically, anything used to damage (even psychologically) can be referred to as a weapon.
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Applied mechanics is a branch of the physical sciences and the practical application of mechanics. Applied mechanics examines the response of bodies (solids and fluids) or systems of bodies to external forces.
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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Virtual work on a system is the work resulting from either virtual forces acting through a real displacement or real forces acting through a virtual displacement.
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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 , taking downward to be positive, the internal shear force is given by taking the negative integral of the
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For a beam with an applied weight , taking downward to be positive, the internal shear force is given by taking the negative integral of the
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Castigliano's method, named for Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the strain energy.
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Macaulay’s Method: The double integration method use of Macaulay’s technique is very convenient for cases of discontinuous and/or discrete loading. Typically partial u.d.l. and u.v.l.
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In structural engineering, the matrix stiffness method (or simply stiffness method, also known as Direct stiffness method) is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures.
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An architect is a person who is involved in the planning, designing and oversight of a building's construction. The word "architect" (Latin: architectus) derives from the Greek arkhitekton (arkhi (chief) + tekton (builder))")[1]
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engineer is someone who is trained or professionally engaged in a branch of engineering.[1] Engineers use technology, mathematics, and scientific knowledge to solve practical problems.
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beam is a structural element that carries load primarily in bending (flexure). Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e. loads due to an earthquake or wind).
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Elastic may refer to:
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- Elastic collision, a term describing collisions in which kinetic energy is conserved
- Elastic deformations, a term describing reversible deformations of materials
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angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept
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radian, in mathematics, is a unit of plane angle, equal to 180/π degrees, or about 57.2958 degrees. It is represented by the symbol "rad" or, more rarely, by the superscript c (for "circular measure"). For example, an angle of 1.2 radians would be written as "1.
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cantilever is a beam supported on only one end. The beam carries the load to the support where it is resisted by moment and shear stress. Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with trusses or slabs.
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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Span is a section between two intermediate supports, e.g. of a beam or a bridge. A span can be made of a solid beam or of a rope. The first kind of span is used for bridges, the second one used for power lines, overhead telecommunication lines, some type of antennas or for aerial
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An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e. non-permanently) when a force is applied to it.
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- This article is about the moment of inertia as related to the bending of a plane. For the moment of inertia dealing with rotation of an object, see Moment of inertia.
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A building code, or building control, is a set of rules that specify the minimum acceptable level of safety for constructed objects such as buildings and nonbuilding structures.
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fraction (from the Latin fractus, broken) is a concept of a proportional relation between an object part and the object whole. Each fraction consists of a denominator (bottom) and a numerator (top), representing (respectively) the number of equal parts that an object is
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Steel frame usually refers to a building technique with a "skeleton frame" of vertical steel columns and horizontal I-beams, constructed in a rectangular grid to support the floors, roof and walls of a building which are all attached to the frame.
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fracture is the (local) separation of a body into two, or more, pieces under the action of stress.
The word fracture is often applied to bones of living creatures, or to crystals or crystalline materials, such as gemstones or metal.
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The word fracture is often applied to bones of living creatures, or to crystals or crystalline materials, such as gemstones or metal.
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Moment may refer to:
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- Moment (time)
- Moment (physics)
- Moment (mathematics), used in probability theory and statistics
- Moment (magazine), an American Jewish publication
- Moment (album), an album by SPEED
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electrical and electronic engineering (many UK universities have departments of Electronic and Electrical Engineering). Both define a broad field that encompasses many subfields including those that deal with power, instrumentation engineering, telecommunications, and
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1. Electron guns 2. Electron beams 3. Focusing coils 4. Deflection coils 5. Anode connection 6. Mask for separating beams for red, green, and blue part of displayed image 7.
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Cathode rays are streams of electrons observed in vacuum tubes, i.e. evacuated glass tubes that are equipped with at least two electrodes, a cathode (negative electrode) and an anode (positive electrode) in a configuration known as a diode.
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