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About: Mohr's circle
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Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so." /> <meta property="og:site_name" content="DBpedia" /> <!-- /OpenGraph--> </head> <body about="http://dbpedia.org/resource/Mohr's_circle"> <!-- navbar --> <nav class="navbar navbar-expand-md navbar-light bg-light fixed-top align-items-center"> <div class="container-xl"> <a class="navbar-brand" href="http://wiki.dbpedia.org/about" title="About DBpedia" style="color: #2c5078"> <img class="img-fluid" src="/statics/images/dbpedia_logo_land_120.png" alt="About DBpedia" /> </a> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#dbp-navbar" aria-controls="dbp-navbar" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="collapse navbar-collapse" 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</div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so.</p> </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Mohr_Circle.svg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ca" >La Circumferència de Mohr (Incorrectament anomenada Cercle de Mohr , ja que no es treballa amb una àrea sinó amb el perímetre) és una tècnica usada en enginyeria i geofísica per un tensor simètric (de 2x2 o de 3x3) i calcular amb ella moments d'inèrcia, deformacions i tensions, adaptant els mateixos a les característiques d'una circumferència (radi, centre, etc.). També és possible el càlcul de l'esforç tallant màxim absolut i la deformació màxima absoluta. Aquest mètode va ser desenvolupat cap 1882 per l'enginyer civil alemany (1835-1918).</span><small> (ca)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ar" >دائرة مور(بالإنجليزية: Mohr's circle) هي تمثيل بياني للأسطح المعرضة للإجهادات؛ استخدمها أول مرة كريستيان أوتو مور في العام 1892. وتستخدم حاليا بوفرة في المجالات الهندسية المختلفة لحسابات الإجهادات، الانفعال، وعزوم المساحات.</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="cs" >Mohrova kružnice je diagram znázorňující stav napjatosti určitého bodu v rovině, pokud je známo hlavní napětí, nebo normálové a smykové napětí ve dvou navzájem kolmých rovinách. Mohrova kružnice umožňuje znázornit dvou- i třírozměrné napětí. Na abscise (ose x) je v grafu znázorňováno (σ – sigma) a na ordinátě (ose y) je znázorněno (tangenciální) napětí (τ – tau). Konstrukce Mohrovy kružnice umožňuje rychlé grafické odhady vlastních hodnot a vlastních vektorů, což je vhodné zejména pro ověřování analytických výsledků. Metodu Mohrovy kružnice je možno použít i pro libovolný symetrický tenzor v rovině.</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="de" >Mohr’sche Spannungskreis oder kurz Mohr’sche Kreis, benannt nach Christian Otto Mohr, ist eine Möglichkeit, den 2D-Spannungszustand in einem Punkt eines Körpers zu veranschaulichen oder zu untersuchen, siehe Abbildung 1. Seine Gleichung lautet im Spannungsraum, wo auf der Abszisse die Normalspannungen und auf der Ordinate die Schubspannungen aufgetragen sind: mit und Darin ist * {σxx, σyy, σxy} ein gegebener Spannungszustand in der xy-Ebene, die zur Drehachse ê senkrecht ist, wie zum Beispiel im ebenen Spannungszustand mit Drehachse senkrecht zu seiner Ebene, * {σuu, σvv, σuv} ist der Spannungszustand im uv-Koordinatensystem, dessen u- und v-Achsen wie in um den Winkel α um ê gegenüber den x- bzw. y-Achsen verdreht sind, * M der Mittelpunkt des Kreises auf der Abszisse und * R der Radius des Kreises. Am Kreis kann abgelesen werden, in welchem Winkel β zur x-Achse die Hauptschubspannung τI und in welchem Winkel γ die Hauptspannungen σI,II auftreten, siehe dazu den Abschnitt . Neben dem Cauchy-Spannungstensor können auch andere symmetrische Tensoren mit dem Mohr’schen Kreis veranschaulicht oder untersucht werden, z. B. der Verzerrungstensor und der Trägheitstensor. Neben dem Mohr’schen Kreis gibt es auch andere Verfahren zur Veranschaulichung symmetrischer Tensoren, z. B. Ellipsoide oder , je nachdem der Tensor positiv definit ist oder nicht. Mohr führte den Spannungskreis 1882 ein.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="es" >El círculo de Mohr es una técnica usada en ingeniería y geofísica para representar gráficamente un tensor simétrico (de 2x2 o de 3x3) y calcular con ella momentos de inercia, deformaciones y tensiones, adaptando los mismos a las características de una circunferencia (radio, centro, etc.). También es posible el cálculo del esfuerzo cortante máximo absoluto y la deformación máxima absoluta. Este método fue desarrollado hacia 1882 por el ingeniero civil alemán Christian Otto Mohr (1835-1918).</span><small> (es)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so. After performing a stress analysis on a material body assumed as a continuum, the components of the Cauchy stress tensor at a particular material point are known with respect to a coordinate system. The Mohr circle is then used to determine graphically the stress components acting on a rotated coordinate system, i.e., acting on a differently oriented plane passing through that point. The abscissa and ordinate of each point on the circle are the magnitudes of the normal stress and shear stress components, respectively, acting on the rotated coordinate system. In other words, the circle is the locus of points that represent the state of stress on individual planes at all their orientations, where the axes represent the principal axes of the stress element. 19th-century German engineer Karl Culmann was the first to conceive a graphical representation for stresses while considering longitudinal and vertical stresses in horizontal beams during bending. His work inspired fellow German engineer Christian Otto Mohr (the circle's namesake), who extended it to both two- and three-dimensional stresses and developed a failure criterion based on the stress circle. Alternative graphical methods for the representation of the stress state at a point include the Lamé's stress ellipsoid and Cauchy's stress quadric. The Mohr circle can be applied to any symmetric 2x2 tensor matrix, including the strain and moment of inertia tensors.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >Le cercle de Mohr est une représentation graphique des états de contrainte à deux dimensions, proposée par Christian Otto Mohr en 1882. Dans un graphique où l'axe horizontal représente l'amplitude de la contrainte normale et l'axe vertical représente l'amplitude de la contrainte de cisaillement, le cercle de Mohr est le lieu des états de contrainte en un point P lorsque le plan de coupe tourne autour du point P. Il s'agit d'un cercle centré sur l'axe horizontal dont les intersections avec l'axe horizontal correspondent aux deux contraintes principales au point P. Ce cercle se construit à partir de la connaissance des efforts extérieurs auxquels est soumise la pièce. Il permet de déterminer : * les directions principales , ainsi que les contraintes principales σI, σII et σIII ; * la direction pour laquelle on a la cission τ maximale, qui est donc la direction de rupture probable (l'orientation du faciès de rupture), ainsi que la valeur de cette contrainte.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="it" >Il circolo di Mohr è una rappresentazione grafica dello stato piano di tensione interna in un punto, proposta dall'ingegnere tedesco Otto Mohr nel 1882. La rappresentazione è costruita riportando su un opportuno piano (il piano di Mohr), le componenti normali e tangenziali dello stato di tensione su una generica giacitura passante per il punto. Al variare della giacitura nel piano del problema, i punti rappresentativi dello stato tensionale descrivono nel piano di Mohr una circonferenza che costituisce il perimetro di quello che viene detto, appunto, cerchio di Mohr. La conoscenza del cerchio di Mohr permette di ricostruire lo stato tensionale su una qualsiasi giacitura passante per il punto e, in particolare, di individuare le tensioni principali e le direzioni principali del problema piano di tensione.</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ja" >モールの応力円（モールのおうりょくえん、Mohr's stress circle）とは、物体内の応力状態を図示するときに現れる円である。名称はにちなむ。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="nl" >De cirkel van Mohr (genoemd naar de Duitse mechanicus Otto Mohr (1835 - 1918)) is een grafisch diagram waarin een mechanische spanningstoestand wordt weergegeven. In een tweedimensionale ruimte tussen schuifspanning en normaalspanning plot de spanning als een cirkel. De kleinste en grootste principiële hoofdspanningen zijn de snijpunten met de as van de normaalspanning en het middelpunt van de cirkel ligt op deze as. De tweedimensionale tensorweergave (de ) van de spanning is: Waarin met de normaalspanningen en met de schuifspanningen zijn aangegeven. De principiële spanningsrichtingen ( en ) zijn per definitie de richtingen waarin geen schuifspanning werkt. Dit zijn wiskundig gezien de eigenwaardes van de spanningstensor, zodat ze als volgt te berekenen zijn: Het eerste deel van deze formules is grafisch een translatie in de normaalspanningsrichting, het tweede deel is een cirkel. Als er sprake is van drie dimensies, zijn er drie principiële spanningsrichtingen . In drie dimensies kan de spanning dan als een ellipsoïde worden weergegeven, maar dit is voor de analyse van schuifspanning niet nodig. De grootste schuifspanning heerst namelijk tussen de grootste en de kleinste ( en ), zodat alleen deze twee richtingen geanalyseerd hoeven te worden. In dat geval kan weer een Mohrcirkel worden getekend met als snijpunten van de horizontale (normaalspannings-) as de waarden van en .</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pt" >O círculo de Mohr, denominado em memória de seu idealizador, Christian Otto Mohr, é um método gráfico bidimensional representativo da lei de transformação do tensor tensão de Cauchy. Após realizar uma análise de tensões em um corpo material assumido como um meio contínuo, as componentes do tensor tensão de Cauchy em um determinado ponto do corpo são conhecidas em relação a um sistema de coordenadas. O círculo de Mohr é então usado para determinar graficamente as componentes de tensão em relação a um sistema rotacionado, isto é, agindo sobre um plano de orientação diferente passando sobre o ponto. A abscissa e a ordenada de cada ponto do círculo são as magnitudes da tensão normal e da tensão cisalhante atuando sobre um sistema de coordenadas rotacionado. Em outras palavras, o círculo é o locus dos pontos que representam o estado de tensão sobre planos individuais em todas as suas orientações, onde os eixos representam os eixos principais dos elementos de tensão. Karl Culmann foi o primeiro a conceber uma representação gráfica para tensões, considerando tensões normais e cisalhantes em vigas horizontais sob flexão. A contribuição de Mohr estendeu o uso desta representação para estados de tensão bi e tridimensional e desenvolveu um critério de falha baseado sobre o círculo de tensão. O círculo de Mohr pode ser aplicado a qualquer matriz simétrica 2x2, incluindo os tensores deformação e momento de inércia.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pl" >Koło Mohra (koło naprężeń) – graficzna reprezentacja (rys. 1) stanu naprężenia, opracowana przez niemieckiego inżyniera Christiana Mohra.</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="sv" >Mohrs cirkel är inom hållfasthetslära en tvådimensionell geometrisk representation av spänningstillstånd eller töjning i en punkt. Denna mekanikartikel saknar väsentlig information. Du kan hjälpa till genom att lägga till den.</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ru" >Круг Мора — графическое представление нормальных напряжений и касательных напряжений, разработанное профессором Отто Мором (1835—1918).. Круг Мора также можно использовать для нахождения главных плоскостей и главных напряжений в графическом представлении, и это один из самых простых способов сделать это.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="uk" >Круг Мора (круг напружень) — графічний метод визначення напружень при складному . Розроблений Мором О. Х. для більш наочного розв'язання задач з теорії напруженого стану. Круг Мора використовують для розв'язання прямої та оберненої задачі.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="zh" >莫爾圓（Mohr's circle）得名自德國土木工程師，是一種用二維方式表示柯西应力张量轉換關係的圖。 先針對假設為連續的物體進行，之後特定一點的柯西应力张量分量會和坐標系有關。莫爾圓是用圖形的方法去確認一個旋轉坐標系上的應力分量，也就是在同一點上，但是作用在不同方向平面上的分量。 圓上每一個點的橫坐標及縱坐標都是在這個旋轉坐標系統上某一個方向的正應力及剪應力。換句話說，莫爾圓表示了在所有方向平面上應力狀態的軌跡，而X軸和Y軸為應力元素的主軸。 是第一個想到用圖形來表示應力的人，他是在分析水平樑承受彎曲時的縱向應力及垂直應力時所想到的。莫爾的貢獻不止是用莫爾圓表示二維及三維的應力，他也根據莫爾圓發展了結構失效判定的準則。 其他表示應力狀態的方式有及柯西應力二次曲線（Cauchy's stress quadric）。 莫爾圓可以擴展到對稱的 2x2 張量，包括應變及轉動慣量張量。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail"><small>dbo:</small>thumbnail</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Mohr_Circle.svg?width=300" 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text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ca" >La Circumferència de Mohr (Incorrectament anomenada Cercle de Mohr , ja que no es treballa amb una àrea sinó amb el perímetre) és una tècnica usada en enginyeria i geofísica per un tensor simètric (de 2x2 o de 3x3) i calcular amb ella moments d'inèrcia, deformacions i tensions, adaptant els mateixos a les característiques d'una circumferència (radi, centre, etc.). També és possible el càlcul de l'esforç tallant màxim absolut i la deformació màxima absoluta. Aquest mètode va ser desenvolupat cap 1882 per l'enginyer civil alemany (1835-1918).</span><small> (ca)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ar" >دائرة مور(بالإنجليزية: Mohr's circle) هي تمثيل بياني للأسطح المعرضة للإجهادات؛ استخدمها أول مرة كريستيان أوتو مور في العام 1892. وتستخدم حاليا بوفرة في المجالات الهندسية المختلفة لحسابات الإجهادات، الانفعال، وعزوم المساحات.</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="cs" >Mohrova kružnice je diagram znázorňující stav napjatosti určitého bodu v rovině, pokud je známo hlavní napětí, nebo normálové a smykové napětí ve dvou navzájem kolmých rovinách. Mohrova kružnice umožňuje znázornit dvou- i třírozměrné napětí. Na abscise (ose x) je v grafu znázorňováno (σ – sigma) a na ordinátě (ose y) je znázorněno (tangenciální) napětí (τ – tau). Konstrukce Mohrovy kružnice umožňuje rychlé grafické odhady vlastních hodnot a vlastních vektorů, což je vhodné zejména pro ověřování analytických výsledků. Metodu Mohrovy kružnice je možno použít i pro libovolný symetrický tenzor v rovině.</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="es" >El círculo de Mohr es una técnica usada en ingeniería y geofísica para representar gráficamente un tensor simétrico (de 2x2 o de 3x3) y calcular con ella momentos de inercia, deformaciones y tensiones, adaptando los mismos a las características de una circunferencia (radio, centro, etc.). También es posible el cálculo del esfuerzo cortante máximo absoluto y la deformación máxima absoluta. Este método fue desarrollado hacia 1882 por el ingeniero civil alemán Christian Otto Mohr (1835-1918).</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ja" >モールの応力円（モールのおうりょくえん、Mohr's stress circle）とは、物体内の応力状態を図示するときに現れる円である。名称はにちなむ。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pl" >Koło Mohra (koło naprężeń) – graficzna reprezentacja (rys. 1) stanu naprężenia, opracowana przez niemieckiego inżyniera Christiana Mohra.</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="sv" >Mohrs cirkel är inom hållfasthetslära en tvådimensionell geometrisk representation av spänningstillstånd eller töjning i en punkt. Denna mekanikartikel saknar väsentlig information. Du kan hjälpa till genom att lägga till den.</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ru" >Круг Мора — графическое представление нормальных напряжений и касательных напряжений, разработанное профессором Отто Мором (1835—1918).. Круг Мора также можно использовать для нахождения главных плоскостей и главных напряжений в графическом представлении, и это один из самых простых способов сделать это.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="uk" >Круг Мора (круг напружень) — графічний метод визначення напружень при складному . Розроблений Мором О. Х. для більш наочного розв'язання задач з теорії напруженого стану. Круг Мора використовують для розв'язання прямої та оберненої задачі.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="zh" >莫爾圓（Mohr's circle）得名自德國土木工程師，是一種用二維方式表示柯西应力张量轉換關係的圖。 先針對假設為連續的物體進行，之後特定一點的柯西应力张量分量會和坐標系有關。莫爾圓是用圖形的方法去確認一個旋轉坐標系上的應力分量，也就是在同一點上，但是作用在不同方向平面上的分量。 圓上每一個點的橫坐標及縱坐標都是在這個旋轉坐標系統上某一個方向的正應力及剪應力。換句話說，莫爾圓表示了在所有方向平面上應力狀態的軌跡，而X軸和Y軸為應力元素的主軸。 是第一個想到用圖形來表示應力的人，他是在分析水平樑承受彎曲時的縱向應力及垂直應力時所想到的。莫爾的貢獻不止是用莫爾圓表示二維及三維的應力，他也根據莫爾圓發展了結構失效判定的準則。 其他表示應力狀態的方式有及柯西應力二次曲線（Cauchy's stress quadric）。 莫爾圓可以擴展到對稱的 2x2 張量，包括應變及轉動慣量張量。</span><small> (zh)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="de" >Mohr’sche Spannungskreis oder kurz Mohr’sche Kreis, benannt nach Christian Otto Mohr, ist eine Möglichkeit, den 2D-Spannungszustand in einem Punkt eines Körpers zu veranschaulichen oder zu untersuchen, siehe Abbildung 1. Seine Gleichung lautet im Spannungsraum, wo auf der Abszisse die Normalspannungen und auf der Ordinate die Schubspannungen aufgetragen sind: mit und Darin ist Am Kreis kann abgelesen werden, in welchem Winkel β zur x-Achse die Hauptschubspannung τI und in welchem Winkel γ die Hauptspannungen σI,II auftreten, siehe dazu den Abschnitt . Mohr führte den Spannungskreis 1882 ein.</span><small> (de)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >Le cercle de Mohr est une représentation graphique des états de contrainte à deux dimensions, proposée par Christian Otto Mohr en 1882. Dans un graphique où l'axe horizontal représente l'amplitude de la contrainte normale et l'axe vertical représente l'amplitude de la contrainte de cisaillement, le cercle de Mohr est le lieu des états de contrainte en un point P lorsque le plan de coupe tourne autour du point P. Il s'agit d'un cercle centré sur l'axe horizontal dont les intersections avec l'axe horizontal correspondent aux deux contraintes principales au point P.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="it" >Il circolo di Mohr è una rappresentazione grafica dello stato piano di tensione interna in un punto, proposta dall'ingegnere tedesco Otto Mohr nel 1882. La rappresentazione è costruita riportando su un opportuno piano (il piano di Mohr), le componenti normali e tangenziali dello stato di tensione su una generica giacitura passante per il punto. Al variare della giacitura nel piano del problema, i punti rappresentativi dello stato tensionale descrivono nel piano di Mohr una circonferenza che costituisce il perimetro di quello che viene detto, appunto, cerchio di Mohr. La conoscenza del cerchio di Mohr permette di ricostruire lo stato tensionale su una qualsiasi giacitura passante per il punto e, in particolare, di individuare le tensioni principali e le direzioni principali del problema</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="nl" >De cirkel van Mohr (genoemd naar de Duitse mechanicus Otto Mohr (1835 - 1918)) is een grafisch diagram waarin een mechanische spanningstoestand wordt weergegeven. In een tweedimensionale ruimte tussen schuifspanning en normaalspanning plot de spanning als een cirkel. De kleinste en grootste principiële hoofdspanningen zijn de snijpunten met de as van de normaalspanning en het middelpunt van de cirkel ligt op deze as. De tweedimensionale tensorweergave (de ) van de spanning is: Waarin met de normaalspanningen en met de schuifspanningen zijn aangegeven.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pt" >O círculo de Mohr, denominado em memória de seu idealizador, Christian Otto Mohr, é um método gráfico bidimensional representativo da lei de transformação do tensor tensão de Cauchy. Após realizar uma análise de tensões em um corpo material assumido como um meio contínuo, as componentes do tensor tensão de Cauchy em um determinado ponto do corpo são conhecidas em relação a um sistema de coordenadas. O círculo de Mohr é então usado para determinar graficamente as componentes de tensão em relação a um sistema rotacionado, isto é, agindo sobre um plano de orientação diferente passando sobre o ponto.</span><small> (pt)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ar" >دائرة مور</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ca" >Cercle de Mohr</span><small> (ca)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="cs" >Mohrova kružnice</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="de" >Mohrscher Spannungskreis</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="es" >Círculo de Mohr</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Cercle de Mohr</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="it" >Cerchio di Mohr</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ja" >モールの応力円</span><small> (ja)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >Mohr's circle</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="nl" >Cirkel van Mohr</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pt" >Círculo de Mohr</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pl" >Koło Mohra</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ru" >Круг Мора</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="sv" >Mohrs cirkel</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="uk" >Круг Мора</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="zh" >莫爾圓</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.02p45kz" 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