Cantilever Method
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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 ...
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Cantilever
A cantilever is a rigid structural element that extends horizontally and is unsupported at one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab. When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment. Cantilever construction allows overhanging structures without additional support. In bridges, towers, and buildings Cantilevers are widely found in construction, notably in cantilever bridges and balconies (see corbel). In cantilever bridges, the cantilevers are usually built as pairs, with each cantilever used to support one end of a central section. The Forth Bridge in Scotland is an example of a cantilever truss bridge. A cantilever in a traditionally timber framed building is called a jetty or forebay. In the sou ...
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Stress (mechanics)
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to ''tensile'' stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to ''compressive'' stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has dimension of force per area, with SI units of newtons per square meter (N/m2) or pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while ''strain'' is the measure of the relative deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each ...
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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 ...
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Portal Method
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Center Of Gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the c ...
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Storey
A storey (English in the Commonwealth of Nations, Commonwealth English) or story (American English), is any level part of a building with a floor that could be used by people (for living, work, storage, recreation, etc.). Plurals for the word are ''storeys'' (UK, CAN) and ''stories'' (US). The terms ''floor'', ''level'', or ''deck'' are used in similar ways as storey (e.g., "the 16th ''floor''"). However, when referring to an entire building, it is more usual to use storey or story (e.g., "a 16-''storey'' building"). The floor at ground or street level is called the ''ground floor'' (i.e. it needs no number); the floor below ground is called ''basement'', and the floor above ground is called "first" in many regions. However, in some regions, like the US, ''ground floor'' is synonymous with ''first floor'', leading to differing numberings of floors, depending on region – even between different national varieties of English. The words ''storey'' and ''floor'' normally exclud ...
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Diagram
A diagram is a symbolic Depiction, representation of information using Visualization (graphics), visualization techniques. Diagrams have been used since prehistoric times on Cave painting, walls of caves, but became more prevalent during the Age of Enlightenment, Enlightenment. Sometimes, the technique uses a Three-dimensional space, three-dimensional visualization which is then graphical projection, projected onto a two-dimensional surface. The word ''graphics, graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphics, graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In scie ...
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Cartesian Coordinate System
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative numbers, signed distances to the point from two fixed perpendicular oriented lines, called ''coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the ''Origin (mathematics), origin'' and has as coordinates. The axes direction (geometry), directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any di ...
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Contraflexure
In solid mechanics, a point along a beam under a lateral load is known as a point of contraflexure if the bending moment about the point equals zero. In a bending moment diagram, it is the point at which the bending moment curve intersects with the zero line (i.e. where the bending moment reverses direction along the beam). Knowing the place of the contraflexure is especially useful when designing reinforced concrete or structural steel beams and also for designing bridges. Flexural reinforcement may be reduced at this point. However, to omit reinforcement at the point of contraflexure entirely is inadvisable as the actual location is unlikely to realistically be defined with confidence. Additionally, an adequate quantity of reinforcement should extend beyond the point of contraflexure to develop bond strength and to facilitate shear force transfer. See also * Deformation * Engineering mechanics * Flexural rigidity * Flexural stress * Fluid mechanics * Inflection point * Str ...
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Shear Force
In solid mechanics, shearing forces are unaligned forces acting on one part of a Rigid body, body in a specific direction, and another part of the body in the opposite direction. When the forces are Collinearity, collinear (aligned with each other), they are called ''tension forces'' or ''compression forces''. Shear force can also be defined in terms of Plane (geometry), planes: "If a plane is passed through a body, a force acting along this plane is called a ''shear force'' or ''shearing force''." Force required to shear steel This section calculates the force required to cut a piece of material with a shearing action. The relevant information is the area of the material being sheared, i.e. the area across which the shearing action takes place, and the shear strength of the material. A round bar of steel is used as an example. The shear strength is calculated from the tensile strength using a factor which relates the two strengths. In this case 0.6 applies to the example steel, ...
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Wind
Wind is the natural movement of atmosphere of Earth, air or other gases relative to a planetary surface, planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hours, to global winds resulting from the difference in absorption (electromagnetic radiation), absorption of solar energy between the climate zones on Earth. The study of wind is called anemology. The two main causes of large-scale atmospheric circulation are the differential heating between the equator and the poles, and the rotation of the planet (Coriolis effect). Within the tropics and subtropics, thermal low circulations over terrain and high plateaus can drive monsoon circulations. In coastal areas the sea breeze/land breeze cycle can define local winds; in areas that have variable terrain, mountain and valley breezes can prevail. Winds are commonly classified by their scale (spatial), spatial ...
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Structure
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological organisms, minerals and chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space. Load-bearing Buildings, aircraft, skeletons, anthills, beaver dams, bridges and salt domes are all examples of load-bearing structures. The results of construction are divided into buildings and non-building structures, and make up the infrastructure of a human society. Built structures are broadly divided by their varying design approaches and standards, into categories including building struct ...
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