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Müller-Breslau's Principle
The Müller-Breslau principle is a method to determine influence lines. The principle states that the influence lines of an action (force or moment) assumes the scaled form of the deflection displacement. OR, This principle states that "ordinate of ILD for a reactive force is given by ordinate of elastic curve if a unit deflection is applied in the direction of reactive force." This method is named after the German engineer Heinrich Müller-Breslau and it is one of the easiest way to draw the influence lines. Example of using the Müller-Breslau principle to find qualitative influence lines Part (a) of the figure to the right shows a simply supported beam with a unit load traveling across it. The structure is statically determinate. Therefore, all influence lines will be straight lines. Parts (b) and (c) of the figure shows the influence lines for the reactions in the y-direction. Releasing the vertical reaction for A allows the beam to rotate to Δ. Likewise for part (c). Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Influence Lines
In engineering, an influence line graphs the variation of a function (such as the shear, moment etc. felt in a structural member) at a specific point on a beam or truss caused by a unit load placed at any point along the structure.Kharagpur"Structural Analysis.pdf, Version 2 CE IIT". 7 August 2008. Accessed on 26 November 2010.Dr. Fanous, Fouad 20 April 2000. Accessed on 26 November 2010."Influence Line Method of Analysis" The Constructor. 10 February 2010. Accessed on 26 November 2010. The Foundation Coalition. 2 December 2010. Accessed on 26 November 2010.Hibbel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newton (N). Force is represented by the symbol (formerly ). The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. Concepts related to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque, which produce ... [...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] |
Heinrich Müller-Breslau
Heinrich Franz Bernhard Müller (May 13, 1851 in Breslau – April 24, 1925 in Grunewald, Berlin, known as Müller-Breslau from around 1875 to distinguish him from other people with similar names) was a German civil engineer and high school teacher. He provided significant contributions to the theory of beams and frames in structural analysis. Müller-Breslau was both a practicing engineer and theoretical researcher during his lifetime. He brought the previously separate elements of classical structural analysis together in a unified theory of beams and frames. He systematized the computational methods, in particular the principle of virtual displacements, and applied the energy sets systematically. He also calculated structures of airships. After finishing school in 1869, he fought in the Franco-Prussian War, after which he began to study at the Berlin Trade Academy in 1871. He also attended lectures in mathematics taught by Elwin Bruno Christoffel and Karl Weierstrass at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statically Determinate
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 Reaction (physics), 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 moment (physics), moments (about an arbitrary point) of all forces equals zero. In the beam (structure), 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_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear And Moment Diagram
Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Another application of shear and moment diagrams is that the deflection of a beam can be easily determined using either the moment area method or the conjugate beam method. Convention Although these conventions are relative and any convention can be used if stated explicitly, practicing engineers have adopted a standard convention used in design practices. Normal convention The normal convention used in most engineering applications is to label a positive shear force - one that spins an element clockwise (up on the left, and down on the right). Likew ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bending Moment
In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple or fixed). In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely. The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Influence Line
In engineering, an influence line graphs the variation of a function (such as the shear, moment etc. felt in a structural member) at a specific point on a beam or truss caused by a unit load placed at any point along the structure.Kharagpur"Structural Analysis.pdf, Version 2 CE IIT". 7 August 2008. Accessed on 26 November 2010.Dr. Fanous, Fouad 20 April 2000. Accessed on 26 November 2010."Influence Line Method of Analysis" The Constructor. 10 February 2010. Accessed on 26 November 2010. The Foundation Coalition. 2 December 2010. Accessed on 26 November 2010.Hibbel ... [...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] |
Dead And Live Loads
A structural load or structural action is a force, deformation, or acceleration applied to structural elements. A load causes stress, deformation, and displacement in a structure. Structural analysis, a discipline in engineering, analyzes the effects of loads on structures and structural elements. Excess load may cause structural failure, so this should be considered and controlled during the design of a structure. Particular mechanical structures—such as aircraft, satellites, rockets, space stations, ships, and submarines—are subject to their own particular structural loads and actions. Engineers often evaluate structural loads based upon published regulations, contracts, or specifications. Accepted technical standards are used for acceptance testing and inspection. Types Dead loads are static forces that are relatively constant for an extended time. They can be in tension or compression. The term can refer to a laboratory test method or to the normal usage of a material or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
