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Fixed End Moments
The fixed end moments are reaction moments developed in a beam member under certain load conditions with both ends fixed. A beam with both ends fixed is statically indeterminate to the 3rd degree, and any structural analysis method applicable on statically indeterminate beams can be used to calculate the fixed end moments. Examples In the following examples, clockwise moments are positive. The two cases with distributed loads can be derived from the case with concentrated load by integration. For example, when a uniformly distributed load of intensity q is acting on a beam, then an infinitely small part dx distance x apart from the left end of this beam can be seen as being under a concentrated load of magnitude qdx. Then, :M_^ = \int_^ \frac = \frac :M_^ = \int_^ \left \= - \frac Where the expressions within the integrals on the right hand sides are the fixed end moments caused by the concentrated load qdx. For the case with linearly distributed load of maximum intensity q_0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment (physics)
In physics, a moment is a mathematical expression involving the product of a distance and physical quantity. Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. In this way, the moment accounts for the quantity's location or arrangement. For example, the moment of force, often called torque, is the product of a force on an object and the distance from the reference point to the object. In principle, any physical quantity can be multiplied by a distance to produce a moment. Commonly used quantities include forces, masses, and electric charge distributions. Elaboration In its most basic form, a moment is the product of the distance to a point, raised to a power, and a physical quantity (such as force or electrical charge) at that point: : \mu_n = r^n\,Q, where Q is the physical quantity such as a force applied at a point, or a point charge, or a point mass, etc. If the quantity ... [...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] |
Statically Indeterminate
In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and reactions on that structure. Mathematics Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are: : \sum \mathbf F = 0 : the vectorial sum of the forces acting on the body equals zero. This translates to: :: \sum \mathbf H = 0 : the sum of the horizontal components of the forces equals zero; :: \sum \mathbf V = 0 : the sum of the vertical components of forces equals zero; : \sum \mathbf M = 0 : the sum of the moments (about an arbitrary point) of all forces equals zero. In the beam construction on the right, the four unknown reactions are , , , and . The equilibrium equations are: : \begin \sum \mathbf V = 0 \quad & \implies \quad \mathbf V_A - \mathbf F_v + \mathbf V_B + \mathbf V_C = 0 \\ \sum \mathbf H = 0 \quad & \im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clockwise
Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite sense of rotation or revolution is (in Commonwealth English) anticlockwise (ACW) or (in North American English) counterclockwise (CCW). Terminology Before clocks were commonplace, the terms " sunwise" and "deasil", "deiseil" and even "deocil" from the Scottish Gaelic language and from the same root as the Latin "dexter" ("right") were used for clockwise. "Widdershins" or "withershins" (from Middle Low German "weddersinnes", "opposite course") was used for counterclockwise. The terms clockwise and counterclockwise can only be applied to a rotational motion once a side of the rotational plane is specified, from which the rotation is observed. For example, the daily rotation of the Earth is clockwise when viewed from above the South Pole, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fem3
FEM3 is a television channel operated by the TV2 Group that broadcasts in Hungary. It is an entertainment channel, primarily dedicated to talk shows, reality series involving lifestyles, and family life. It was originally launched on New Year's Day 2010. On 5 September 2016 at 05:00 CET CET or cet may refer to: Places * Cet, Albania * Cet, standard astronomical abbreviation for the constellation Cetus * Colchester Town railway station (National Rail code CET), in Colchester, England Arts, entertainment, and media * Comcast En ..., the old FEM3 was replaced by PRIME, and a new FEM3 started its test broadcasts on a new frequency. Both channels officially launched at 21:00 CET. Prior to the launch, since 2008, the channel was planned with several names. First, they wanted to bring FEM to Hungary, the name then changed to TV3, as a reincarnation of an entertainment channel which closed down on 21 February 2000. The name was finalized in December 2009. Programming Talk Show ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Distribution Method
The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. The method only accounts for flexural effects and ignores axial and shear effects. From the 1930s until computers began to be widely used in the design and analysis of structures, the moment distribution method was the most widely practiced method. Introduction In the moment distribution method, every joint of the structure to be analysed is fixed so as to develop the ''fixed-end moments''. Then each fixed joint is sequentially released and the fixed-end moments (which by the time of release are not in equilibrium) are distributed to adjacent members until equilibrium is achieved. The moment distribution method in mathematical terms can be demonstrated as the process of solving a set of simultaneous equations by means of iteration. The moment distribution method falls into the category of displaceme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statically Indeterminate
In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and reactions on that structure. Mathematics Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are: : \sum \mathbf F = 0 : the vectorial sum of the forces acting on the body equals zero. This translates to: :: \sum \mathbf H = 0 : the sum of the horizontal components of the forces equals zero; :: \sum \mathbf V = 0 : the sum of the vertical components of forces equals zero; : \sum \mathbf M = 0 : the sum of the moments (about an arbitrary point) of all forces equals zero. In the beam construction on the right, the four unknown reactions are , , , and . The equilibrium equations are: : \begin \sum \mathbf V = 0 \quad & \implies \quad \mathbf V_A - \mathbf F_v + \mathbf V_B + \mathbf V_C = 0 \\ \sum \mathbf H = 0 \quad & \im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope Deflection Method
The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by George A. Maney. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. In the book, "The Theory and Practice of Modern Framed Structures", written by J.B Johnson, C.W. Bryan and F.E. Turneaure, it is stated that this method was first developed "by Professor Otto Mohr in Germany, and later developed independently by Professor G.A. Maney". According to this book, professor Otto Mohr introduced this method for the first time in his book, "Evaluation of Trusses with Rigid Node Connections" or "Die Berechnung der Fachwerke mit Starren Knotenverbindungen". Introduction By forming slope deflection equations and applying joint and shear equilibrium conditions, the rotation angles (or the slope angles) are calculated. Substituting them back into the slope deflection equations, member end moments are readily determined. Defo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Method
The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering. The method is carried out, using either a stiffness matrix or a flexibility matrix. See also * Direct stiffness method * Flexibility method In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the mem ... Structural analysis {{Civil-engineering-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
