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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] |
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] |
Bending Stiffness
The bending stiffness (K) is the resistance of a member against bending deformation. It is a function of the Young's modulus E, the second moment of area I of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force. :K = \frac where \mathrm is the applied force and \mathrm is the deflection. According to elementary beam theory, the relationship between the applied bending moment M and the resulting curvature \kappa of the beam is: :M = E I \kappa = E I \frac{\mathrm{d} x^2} where w is the deflection of the beam and x is the distance along the beam. Double integration of the above equation leads to computing the deflection of the beam, and in turn, the bending stiffness of the beam. Bending stiffness in beams is also known as Flexural rigidity. See also * Applied mechanics * Beam theory * Bending *Stiffness Stiffne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...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] |
Repeating Decimal
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is , whose decimal becomes periodic at the ''second'' digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals. The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Span (architecture)
Span is the distance between two intermediate supports for a structure, e.g. a beam (structure), beam or a bridge. A span can be closed by a solid beam or by a rope. The first kind is used for bridges, the second one for power lines, overhead telecommunication lines, some type of Antenna (radio), antennas or for aerial tramways. The span is a significant factor in finding the strength and size of a beam as it determines the maximum bending moment and Deflection (engineering), deflection. The maximum bending moment M_ and deflection \delta_in the pictured beam is found using: :M_ = \frac :\delta_ = \frac = \frac where :q = Uniformly distributed load :L = Length of the beam between two supports (span) :E = Modulus of elasticity :I = Area moment of inertia Note that the maximum bending moment and deflection occur midway between the two supports. From this it follows that if the span is doubled, the maximum moment (and with it the tensile stress, stress) will quadruple, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be Positive integer, positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. Consequently, a ratio may be considered as an ordered pair of numbers, a Fraction (mathematics), fraction with the first number in the numerator and the second in the denom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Moment Of Area
The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an I (for an axis that lies in the plane of the area) or with a J (for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension, when working with the International System of Units, is meters to the fourth power, m4, or inches to the fourth power, in4, when working in the Imperial System of Units. In structural engineering, the second moment of area of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam. In order to maximize the second moment of area, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulus Of Elasticity
An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form: :\delta \ \stackrel\ \frac where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of \delta will be the same as the units of stress. Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are: # ''Young's modulus'' (E) describes tensile and compressive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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