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| {{Two other uses|structural studies in engineering|social-science usage|structuralism|other uses|structure (disambiguation)}}
| | This Halloween, make a new tradition. Instead of it being a day, or days, of indulging inside a favorite sugary treats, create it a day for creating healthy resolutions.<br><br>There are very a few sites which make it truly simple to obtain out how many calories you require for weight repair and weight reduction. Just type [http://safedietplans.com/bmr-calculator bmr calculator] into a look engine plus follow the procedures they provide we. BMR stands for basal metabolic rate, plus acquiring this number usually enable provide we an idea of how various calories you need to consume for your specific goals. You'll be asked to answer several issues about a activity level and possibly even the degree of weight reduction you wish to achieve. Some BMR calculators might go thus far as to supply you with the amounts of proteins, carbohydrates and fats you need to consume also. They're a very useful tool!<br><br>Do you know a basal metabolic rate or BMR? BMR is the resting metabolic rate. This is the total number of calories needed to maintain your current fat in the event you are completely sedentary. There are several kinds of online calculators that could give we this rate and the calculators could fluctuate as it is very based on several factors including weight, age, and gender. Different calculators employ different methods to determine the rate. BMR refuses to consider the calories expended through exercise and other daily activities. As an example, if your BMR is 2100 kcals plus the exercise for the day burns 500 kcals, you'd end the day with 1600 kcals.<br><br>A low calorie diet may do we more damage than wise. If you are wanting more calories, this usually in turn affect a metabolism. Where might the body receive the stamina it demands? It could really get power from the muscle mass, because there are no food reserves available. When this occurs, it may be highly detrimental to a wellness, because the proper method to lose fat is to gain muscle mass, not take it away.<br><br>Another advantage of gaining lean muscle mass is that metabolically this kind of tissue needs more energy so a bmr actually increases because a outcome of having greater lean muscle. Burning more calories whilst at rest does not sound too bad, does it?<br><br>To calculate a activity level, see this free online calculator: http://exercise.about.com/cs/fitnesstools/l/blcalorieburn.htm which usually use your weight, the kind of exercise, and the amount of time you are able to afford to spend doing that exercise to tell you how numerous calories you're going to burn. Take note of the results - when you utilize this calculator realistically, you are able to plug it right into the BMR results.<br><br>Add it up. Take the BMR amount, add your activity calories, then drag the calories from foods. If you eat over you burn (BMR + the business is 2000 plus you eat 2400 calories) we should gain fat. If you burn over you eat, you'll lose fat. |
| {{Mechanical_failure_modes}}
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| '''Structural analysis''' is the determination of the effects of [[structural load|load]]s on physical [[structure]]s and their [[Structural_engineering#Structural_elements|components]]. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, vehicles, machinery, furniture, attire, soil strata, prostheses and biological tissue. Structural analysis incorporates the fields of [[applied mechanics]], [[materials science]] and [[applied mathematics]] to compute a structure's [[deformation (engineering)|deformation]]s, internal [[force]]s, [[stress analysis|stress]]es, support reactions, accelerations, and [[structural stability|stability]]. The results of the analysis are used to verify a structure's fitness for use, often saving [[physical test]]s. Structural analysis is thus a key part of the [[structural engineering|engineering design of structures]].
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| ==Structures and Loads==
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| A [[structure]] refers to a body or system of connected parts used to support a load. Important examples related to [[Civil Engineering]] include buildings, bridges, and towers; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important. In order to design a structure, one must serve a specified function for public use, the engineer must account for its safety, aesthetics, and serviceability, while taking into consideration economic and environmental constraints. Other branches of [[engineering]] work on a wide variety of [[nonbuilding structure]]s.
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| ===Classification of structures===
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| A ''structural system'' is the combination of structural elements and their materials.
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| It is important for a structural engineer to be able to classify a structure by either its form or its function, by recognizing the various [[Structural_engineering#Structural_elements|elements]] composing that structure.
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| The structural elements guiding the systemic forces through the materials are not only such as a connecting rod, a truss, a beam, or a column, but also a cable, an arch, a cavity or channel, and even an angle, a surface structure, or a frame.
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| ===Loads===
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| {{main|Structural load}}
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| Once the dimensional requirement for a structure have been defined, it becomes necessary to determine the loads the structure must support. In order to design a structure, it is therefore necessary to first specify the loads that act on it. The design loading for a structure is often specified in [[building codes]]. There are two types of codes: general building codes and design codes, engineer must satisfy all the codes requirements for a reliable structure.
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| There are two types of loads that structure engineering must encounter in the design. First type of load is called Dead loads that consist of the weights of the various structural members and the weights of any objects that are permanently attached to the structure. For example, columns, beams, girders, the floor slab, roofing, walls, windows, plumbing, electrical fixtures, and other miscellaneous attachments. Second type of load is Live Loads which vary in their magnitude and location. There are many different types of live loads like building loads, highway bridge Loads, railroad bridge Loads, impact loads, wind loads, snow loads, earthquake loads, and other natural loads.
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| ==Analytical methods==
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| To perform an accurate analysis a structural engineer must determine such information as [[structural load]]s, [[List of structural elements|geometry]], support conditions, and materials properties. The results of such an analysis typically include support reactions, [[Stress (physics)|stresses]] and [[Displacement (vector)|displacements]]. This information is then compared to criteria that indicate the conditions of failure. Advanced structural analysis may examine [[dynamic response]], [[buckling|stability]] and [[non-linear]] behavior.
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| There are three approaches to the analysis: the [[Strength of materials|mechanics of materials]] approach (also known as strength of materials), the [[3-D elasticity|elasticity theory]] approach (which is actually a special case of the more general field of [[continuum mechanics]]), and the [[finite element]] approach. The first two make use of analytical formulations which apply mostly to simple linear elastic models, lead to closed-form solutions, and can often be solved by hand. The finite element approach is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials. However, the finite-element method depends heavily on the processing power of computers and is more applicable to structures of arbitrary size and complexity.
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| Regardless of approach, the formulation is based on the same three fundamental relations: [[mechanical equilibrium|equilibrium]], [[Constitutive equation|constitutive]], and [[Compatibility (mechanics)|compatibility]]. The solutions are approximate when any of these relations are only approximately satisfied, or only an approximation of reality.
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| ''Limitations''. | |
| Each method has noteworthy limitations. The method of mechanics of materials is limited to very simple structural elements under relatively simple loading conditions. The structural elements and loading conditions allowed, however, are sufficient to solve many useful engineering problems. The theory of elasticity allows the solution of structural elements of general geometry under general loading conditions, in principle. Analytical solution, however, is limited to relatively simple cases. The solution of elasticity problems also requires the solution of a system of partial differential equations, which is considerably more mathematically demanding than the solution of mechanics of materials problems, which require at most the solution of an ordinary differential equation. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other structural theories (such as the other two discussed here) for equations to solve. It does, however, make it generally possible to solve these equations, even with highly complex geometry and loading conditions, with the restriction that there is always some numerical error. Effective and reliable use of this method requires a solid understanding of its limitations.
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| ==Strength of materials methods (classical methods)==
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| The simplest of the three methods here discussed, the mechanics of materials method is available for simple structural members subject to specific loadings such as axially loaded bars, prismatic [[Beam (structure)|beams]] in a state of [[pure bending]], and circular shafts subject to torsion. The solutions can under certain conditions be superimposed using the [[superposition principle]] to analyze a member undergoing combined loading. Solutions for special cases exist for common structures such as thin-walled pressure vessels.
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| For the analysis of entire systems, this approach can be used in conjunction with statics, giving rise to the ''method of sections'' and ''method of joints'' for [[truss]] analysis, [[moment distribution method]] for small rigid frames, and ''portal frame'' and ''cantilever method'' for large rigid frames. Except for moment distribution, which came into use in the 1930s, these methods were developed in their current forms in the second half of the nineteenth century. They are still used for small structures and for preliminary design of large structures.
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| The solutions are based on linear isotropic infinitesimal elasticity and Euler–Bernoulli beam theory. In other words, they contain the assumptions (among others) that the materials in question are elastic, that stress is related linearly to strain, that the material (but not the structure) behaves identically regardless of direction of the applied load, that all [[deformation (engineering)|deformation]]s are small, and that beams are long relative to their depth. As with any simplifying assumption in engineering, the more the model strays from reality, the less useful (and more dangerous) the result.
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| ===Example===
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| There are 2 commonly used methods to find the truss element forces, namely the Method of Joints and the Method of Sections. Below is an example that is solved using both of these methods.
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| The first diagram below is the presented problem for which we need to find the truss element forces. The second diagram is the loading diagram and contains the reaction forces from the joints.
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| :[[Image:Truss Structure Analysis, Full Figure2.jpg|center|border|750x450px]]
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| Since there is a pin joint at A, it will have 2 reaction forces. One in the x direction and the other in the y direction. At point B, we have a roller joint and hence we only have 1 reaction force in the y direction. Let us assume these forces to be in their respective positive directions (if they are not in the positive directions like we have assumed, then we will get a negative value for them).
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| :[[Image:Truss Structure Analysis, FBD2.jpg|center|border|750x450px]]
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| Since the system is in static equilibrium, the sum of forces in any direction is zero and the sum of moments about any point is zero.
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| Therefore, the magnitude and direction of the reaction forces can be calculated.
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| :<math>\sum M_A=0=-10*1+2*R_B \Rightarrow R_B=5</math>
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| :<math>\sum F_y=0=R_{Ay}+R_B-10 \Rightarrow R_{Ay}=5</math>
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| :<math>\sum F_x=0=R_{Ax}</math>
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| ====Method of Joints====
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| This method uses the force balance in the x and y directions at each of the joints in the truss structure.
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| :[[Image:Truss Structure Analysis, Method of Joints2.png|border|350x450px]]
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| At A,
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| :<math>\sum F_y=0=R_{Ay}+F_{AD}\sin(60)=5+F_{AD}\frac{\sqrt{3} }{2} \Rightarrow F_{AD}=-\frac{10}{\sqrt{3}}</math>
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| :<math>\sum F_x=0=R_{Ax}+F_{AD}\cos(60)+F_{AB}=0-\frac{10}{\sqrt{3} }\frac{1}{2}+F_{AB} \Rightarrow F_{AB}=\frac{5}{\sqrt{3}}</math>
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| At D,
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| :<math>\sum F_y=0=-10-F_{AD}\sin(60)-F_{BD}\sin(60)=-10-\left(-\frac{10}{\sqrt{3}}\right)\frac{\sqrt{3} }{2}-F_{BD}\frac{\sqrt{3}}{2} \Rightarrow F_{BD}=-\frac{10}{\sqrt{3}}</math>
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| :<math>\sum F_x=0=-F_{AD}\cos(60)+F_{BD}\cos(60)+F_{CD}=-\frac{10}{\sqrt{3}}\frac{1}{2}+\frac{10}{\sqrt{3} }\frac{1}{2}+F_{CD} \Rightarrow F_{CD}=0</math>
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| At C,
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| :<math>\sum F_y=0=-F_{BC} \Rightarrow F_{BC}=0</math>
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| Although we have found the forces in each of the truss elements, it is a good practice to verify the results by completing the remaining force balances.
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| :<math>\sum F_x=-F_{CD}=-0=0 \Rightarrow verified</math>
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| At B,
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| :<math>\sum F_y=R_B+F_{BD}\sin(60)+F_{BC}=5+\left(-\frac{10}{\sqrt{3}}\right)\frac{\sqrt{3} }{2}+0=0 \Rightarrow verified</math>
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| :<math>\sum F_x=-F_{AB}-F_{BD}\cos(60)=\frac{5}{\sqrt{3}}-\frac{10}{\sqrt{3}}\frac{1}{2}=0 \Rightarrow verified</math>
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| ====Method of Sections====
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| This method can be used when the truss element forces of only a few members wants to be known. This method is used by introducing a single straight line cutting through the member whose force wants to be calculated. However this method has a limit in that the cutting line can pass through a maximum of only 3 members of the truss structure. This restriction is because this method uses the force balances in the x and y direction and the moment balance, which gives us a maximum of 3 equations to find a maximum of 3 unknown truss element forces through which this cut is made.
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| Let us try to find the forces FAB, FBD and FCD in the above example
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| =====Method 1: Ignore the right side=====
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| :[[Image:Truss Structure Analysis, Method of Sections Left2.jpg|border|550x450px]]
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| :<math>\sum M_D=0=-5*1+\sqrt{3}*F_{AB} \Rightarrow F_{AB}=\frac{5}{\sqrt{3} }</math>
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| :<math>\sum F_y=0=R_{Ay}-F_{BD}\sin(60)-10=5-F_{BD}\frac{\sqrt{3}}{2}-10 \Rightarrow F_{BD}=-\frac{10}{\sqrt{3}}</math> | |
| :<math>\sum F_x=0=F_{AB}+F_{BD}\cos(60)+F_{CD}=\frac{5}{\sqrt{3}}-\frac{10}{\sqrt{3}}\frac{1}{2}+F_{CD} \Rightarrow F_{CD}=0</math>
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| =====Method 2: Ignore the left side=====
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| :[[Image:Truss Structure Analysis, Method of Sections Right2.jpg|border|600x450px]]
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| :<math>\sum M_B=0=\sqrt{3}*F_{CD} \Rightarrow F_{CD}=0</math>
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| :<math>\sum F_y=0=F_{BD}\sin(60)+R_B=F_{BD}\frac{\sqrt{3}}{2}+5 \Rightarrow F_{BD}=-\frac{10}{\sqrt{3}}</math>
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| :<math>\sum F_x=0=-F_{AB}-F_{BD}\cos(60)-F_{CD}=-F_{AB}-\left(-\frac{10}{\sqrt{3}}\right)\frac{1}{2}-0 \Rightarrow F_{AB}=\frac{5}{\sqrt{3}}</math>
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| The truss elements forces in the remaining members can be found by using the above method with a section passing through the remaining members.
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| ==Elasticity methods==
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| Elasticity methods are available generally for an elastic solid of any shape. Individual members such as beams, columns, shafts, plates and shells may be modeled. The solutions are derived from the equations of [[linear elasticity]]. The equations of elasticity are a system of 15 partial differential equations. Due to the nature of the mathematics involved, analytical solutions may only be produced for relatively simple geometries. For complex geometries, a numerical solution method such as the finite element method is necessary.
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| ==Methods using numerical approximation==
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| It is common practice to use approximate solutions of differential equations as the basis for structural analysis. This is usually done using numerical approximation techniques. The most commonly used numerical approximation in structural analysis is the [[Finite Element Method]].
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| The finite element method approximates a structure as an assembly of elements or components with various forms of connection between them. Thus, a continuous system such as a plate or shell is modeled as a discrete system with a finite number of elements interconnected at finite number of nodes. The behaviour of individual elements is characterised by the element's stiffness or flexibility relation, which altogether leads to the system's stiffness or flexibility relation. To establish the element's stiffness or flexibility relation, we can use the ''mechanics of materials'' approach for simple one-dimensional bar elements, and the ''elasticity approach'' for more complex two- and three-dimensional elements. The analytical and computational development are best effected throughout by means of [[matrix (mathematics)|matrix algebra]], solving [[partial differential equation]]s.
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| Early applications of matrix methods were for articulated frameworks with truss, beam and column elements; later and more advanced matrix methods, referred to as "[[finite element method in structural mechanics|finite element analysis]]," model an entire structure with one-, two-, and three-dimensional elements and can be used for articulated systems together with continuous systems such as a [[pressure vessel]], plates, shells, and three-dimensional solids. Commercial computer software for structural analysis typically uses matrix finite-element analysis, which can be further classified into two main approaches: the displacement or [[stiffness method]] and the force or [[flexibility method]]. The stiffness method is the most popular by far thanks to its ease of implementation as well as of formulation for advanced applications. The finite-element technology is now sophisticated enough to handle just about any system as long as sufficient computing power is available. Its applicability includes, but is not limited to, linear and non-linear analysis, solid and fluid interactions, materials that are isotropic, orthotropic, or anisotropic, and external effects that are static, dynamic, and environmental factors. This, however, does not imply that the computed solution will automatically be reliable because much depends on the model and the reliability of the data input.
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| ==Timeline==
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| *1452–1519 [[Leonardo da Vinci]] made many contributions
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| *1638: [[Galileo Galilei]] published the book "[[Two New Sciences]]" in which he examined the failure of simple structures
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| *1660: [[Hooke's law]] by [[Robert Hooke]]
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| *1687: [[Isaac Newton]] published "[[Philosophiae Naturalis Principia Mathematica]]" which contains the [[Newton's laws of motion]]
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| *1750: [[Euler–Bernoulli beam equation]]
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| *1700–1782: [[Daniel Bernoulli]] introduced the principle of [[virtual work]]
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| *1707–1783: [[Leonhard Euler]] developed the theory of [[buckling]] of columns
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| *1826: [[Claude-Louis Navier]] published a treatise on the elastic behaviors of structures
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| *1873: [[Carlo Alberto Castigliano]] presented his dissertation "Intorno ai sistemi elastici", which contains [[Castigliano's method|his theorem]] for computing displacement as partial derivative of the strain energy. This theorem includes the method of ''least work'' as a special case
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| *1936: [[Hardy Cross]]' publication of the moment distribution method which was later recognized as a form of the relaxation method applicable to the problem of flow in pipe-network
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| *1941: [[Alexander Hrennikoff]] submitted his D.Sc thesis in [[Massachusetts Institute of Technology|MIT]] on the discretization of plane elasticity problems using a lattice framework
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| *1942: [[Richard Courant|R. Courant]] divided a domain into finite subregions
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| *1956: J. Turner, [[Ray W. Clough|R. W. Clough]], H. C. Martin, and L. J. Topp's paper on the "Stiffness and Deflection of Complex Structures" introduces the name "finite-element method" and is widely recognized as the first comprehensive treatment of the method as it is known today
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| ==See also==
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| * [[Structural integrity and failure]]
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| * [[Stress–strain analysis]]
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| ==External links==
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| {{wikibooks}}
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| {{wikiversity}}
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| *[http://impact.sourceforge.net Impact - Dynamic Finite Element Program Suite, for dynamic events like crashes, written in Java, GNU license]
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| *[http://www.colorado.edu/engineering/CAS/Felippa.d/FelippaHome.d/Publications.d/Report.CU-CAS-00-13.pdf A Historical Outline of Matrix Structural Analysis: A Play in Three Acts]
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| *[http://en.wikiversity.org/wiki/Probabilistic_Assessment_of_Structures Probabilistic assessment of structures using Monte Carlo simulation] by [http://www.pro-eng.com Jan Hlavacek]
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| *[http://www.eng.fea.ru/ANSYS_LSDYNA_AviGallery.html FEM Applications in Structural Analysis. AVI-gallery at CompMechLab site, St.Petersburg State Polytechnical University, Russia]
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| *[http://frame3dd.sourceforge.net/ Frame3DD open source 3D structural analysis program]
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| *[http://ocframe.sourceforge.net/ Ocframe open source 2D structural analysis in GNU Octave]
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| [[Category:Structural analysis|*]]
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| * [http://www.VCmaster.com/ www.VCmaster.com] – Technical word processing for structural calculations
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This Halloween, make a new tradition. Instead of it being a day, or days, of indulging inside a favorite sugary treats, create it a day for creating healthy resolutions.
There are very a few sites which make it truly simple to obtain out how many calories you require for weight repair and weight reduction. Just type bmr calculator into a look engine plus follow the procedures they provide we. BMR stands for basal metabolic rate, plus acquiring this number usually enable provide we an idea of how various calories you need to consume for your specific goals. You'll be asked to answer several issues about a activity level and possibly even the degree of weight reduction you wish to achieve. Some BMR calculators might go thus far as to supply you with the amounts of proteins, carbohydrates and fats you need to consume also. They're a very useful tool!
Do you know a basal metabolic rate or BMR? BMR is the resting metabolic rate. This is the total number of calories needed to maintain your current fat in the event you are completely sedentary. There are several kinds of online calculators that could give we this rate and the calculators could fluctuate as it is very based on several factors including weight, age, and gender. Different calculators employ different methods to determine the rate. BMR refuses to consider the calories expended through exercise and other daily activities. As an example, if your BMR is 2100 kcals plus the exercise for the day burns 500 kcals, you'd end the day with 1600 kcals.
A low calorie diet may do we more damage than wise. If you are wanting more calories, this usually in turn affect a metabolism. Where might the body receive the stamina it demands? It could really get power from the muscle mass, because there are no food reserves available. When this occurs, it may be highly detrimental to a wellness, because the proper method to lose fat is to gain muscle mass, not take it away.
Another advantage of gaining lean muscle mass is that metabolically this kind of tissue needs more energy so a bmr actually increases because a outcome of having greater lean muscle. Burning more calories whilst at rest does not sound too bad, does it?
To calculate a activity level, see this free online calculator: http://exercise.about.com/cs/fitnesstools/l/blcalorieburn.htm which usually use your weight, the kind of exercise, and the amount of time you are able to afford to spend doing that exercise to tell you how numerous calories you're going to burn. Take note of the results - when you utilize this calculator realistically, you are able to plug it right into the BMR results.
Add it up. Take the BMR amount, add your activity calories, then drag the calories from foods. If you eat over you burn (BMR + the business is 2000 plus you eat 2400 calories) we should gain fat. If you burn over you eat, you'll lose fat.