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Conjugate Beam Method
The conjugate-beam methods is an engineering method to derive the slope and displacement of a beam. A conjugate beam is defined as an imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by Flexural rigidity, EI. The conjugate-beam method was developed by Heinrich Müller-Breslau in 1865. Essentially, it requires the same amount of computation as the Moment-Area Theorem, moment-area theorems to determine a beam's slope or deflection; however, this method relies only on the principles of statics, so its application will be more familiar. The basis for the method comes from the similarity of Eq. 1 and Eq 2 to Eq 3 and Eq 4. To show this similarity, these equations are shown below. Integrated, the equations look like this. Here the shear stress, shear V compares with the slope θ, the moment of inertia, moment M compares with the Angular displacement, displac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elastic Load Method (full)
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Simple Beam
A beam is a structural element that primarily resists loads applied laterally across the beam's axis (an element designed to carry a load pushing parallel to its axis would be a strut or column). Its mode of deflection is primarily by bending, as loads produce reaction forces at the beam's support points and internal bending moments, shear, stresses, strains, and deflections. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and 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, such as automobile frames, aircraft components, machine frames, and other mechanical or structural systems. Any structural element, in any orientation, that primarily resists loads applied laterally across the element's axis is a beam. Overview Historically a beam is a squared timber ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cantilever Method
The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically include wind loads and earthquake loads, which must be taken into consideration while designing buildings. The assumptions used in this method are that the points of contraflexure (or points of inflection of the moment diagram) in both the vertical and horizontal members are located at the midpoint of the member, and that the direct stresses in the columns are proportional to their distances from the centroidal axis of the frame. The frame is analysed in step-wise (iterative) fashion, and the results can then be described by force diagrams drawn up at the end of the process. The method is quite versatile and can be used to analyse frames of any number of storeys or floors. The position of the centroidal axis (the center of gravity line for the frame) is determined by using the are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statics
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in mechanical equilibrium, equilibrium with its environment. If \textbf F is the total of the forces acting on the system, m is the mass of the system and \textbf a is the acceleration of the system, Newton's second law states that \textbf F = m \textbf a \, (the bold font indicates a Euclidean vector, vector quantity, i.e. one with both Magnitude (mathematics), magnitude and Direction (geometry), direction). If \textbf a =0, then \textbf F = 0. As for a system in static equilibrium, the acceleration equals zero, the system is either at rest, or its center of mass moves at constant velocity. The application of the assumption of zero acceleration to the summation of Moment (physics), moments acting on the system leads to \textbf M = I \alpha = 0, where \textbf M is the summation of all momen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deflection (engineering)
In structural engineering, deflection is the degree to which a part of a long structural element (such as Beam (structure), beam) is deformation (mechanics), deformed laterally (in the direction transverse to its longitudinal axis) under a Structural load, load. It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement (geometry), displacement). A longitudinal deformation (in the direction of the axis) is called ''elongation (mechanics), elongation''. The deflection distance of a member under a load can be calculated by Integral, integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common Beam (structure), beam configurations and load cases at discrete locations. Otherwise methods such as virtual work, Direct integration of a beam, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method are use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3 Spans Gerber's Beam (support-hinge-support)
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Both End Fixed And 2 Middle Hinged Beam
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