Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

Stellen Sie sich einen konischen Balken-OB vor, der an einem Ende befestigt und einer verteilten Last ausgesetzt ist.
Bestimmen Sie die äquivalente resultierende Kraft der variierenden Last und lokalisieren Sie ihre Position auf dem Träger.
Teilen Sie zunächst die verteilte Last in zwei dreieckige Bereiche auf.
Als nächstes ist die Größe der äquivalenten resultierenden Last des linken und rechten dreieckigen Bereichs gleich der Fläche jedes Dreiecks.
Jede resultierende Last wirkt an Schwerpunkten, die sich in einem Drittel der Basislänge von der vertikalen Seite AD des Dreiecks befinden.
Die äquivalente resultierende Last kann bestimmt werden, indem die individuelle resultierende Last jedes dreieckigen Bereichs addiert wird.
Das Moment um den Punkt O kann bestimmt werden, indem das einzelne Moment addiert wird, das aufgrund jeder resultierenden Last wirkt.
Erinnern Sie sich an das Momentenprinzip, das besagt, dass das Moment der äquivalenten resultierenden Last um den Punkt O gleich dem Produkt aus der äquivalenten resultierenden Last und dem Abstand vom Punkt O ist.
Durch Einsetzen der Werte in der Gleichung kann die Position der äquivalenten resultierenden Last bestimmt werden.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall, S. 194-195</li>
</ol>

verteilte lasten: problemlösung

Balken sind Strukturelemente, die in der Ingenieurwissenschaft häufig verwendet werden und unterschiedliche Lastkapazitäten aufweisen. Der erste Schritt bei der Analyse eines Balkens unter einer verteilen Last besteht darin, das Problem zu vereinfachen, indem die Last in kleinere Bereiche aufgeteilt wird. Dadurch kann jeder Bereich einzeln betrachtet werden, und die Größe der äquivalenten resultierenden Last, die auf jeden Teil des Balkens wirkt, kann berechnet werden. Die Größe der äquivalenten resultierenden Last für jeden Bereich kann bestimmt werden, indem die Fläche der jeweiligen Bereiche berechnet wird, die die von der Last in jedem Bereich ausgeübte Kraft repräsentiert. Als nächstes müssen die Positionen der einzelnen resultierenden Lasten auf dem Balken ermittelt werden. Dies kann erreicht werden, indem die Schwerpunkte der Bereiche gefunden werden, an denen sich die Masse der Bereiche konzentriert betrachten lässt. Die einzelnen resultierenden Lasten wirken an diesen Schwerpunkten und üben ihre Kraft an bestimmten Punkten entlang des Balkens aus. Die äquivalente resultierende Last für den gesamten Balken kann mithilfe der Größe und Position der ermittelten einzelnen resultierenden Lasten berechnet werden. Dies erfordert das Hinzufügen der einzelnen resultierenden Lasten der verschiedenen Bereiche, um die insgesamt äquivalente resultierende Last zu bekommen, die auf den Balken wirkt. Der nächste Schritt besteht darin, das Moment an einem bestimmten Punkt, normalerweise dem festen Ende des Balkens, zu bestimmen. Das Moment misst die rotierende Wirkung der auf den Balken wirkenden Kraft. Das resultierende Moment kann bestimmt werden, indem die einzelnen Momente addiert werden, die durch jede Last verursacht werden. Das Moment jeder Last entspricht dem Produkt aus der Kraft und ihrem Abstand von dem angegebenen Punkt. <img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;"> Indem das Momentprinzip angewendet wird, entspricht das Moment der äquivalenten resultierenden Last um den angegebenen Punkt dem Produkt aus der äquivalenten resultierenden Last und dem Abstand von diesem Punkt. <img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;"> Durch Umstellen der Gleichung und Einsetzen der Terme kann die Position der äquivalenten resultierenden Last entlang des Balkens bestimmt werden. <img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;">

Verteilte Lasten: Problemlösung

Träger sind Strukturelemente, die häufig in technischen Anwendungen eingesetzt werden, die unterschiedliche Tragfähigkeiten erfordern. Der erste Schritt bei der Analyse eines ...

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Distributed Loads: Problem Solving

equivalent resultant loads on beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined.

The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

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Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on Beams | JoVE K12

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Equivalent Resultant Loads on Beams

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