Name: finding the resultant of distributed loads
Uploaded: 2023-09-22T11:49:32.000Z
Duration: 1 min 13 s
Channel: JoVE

Bei technischen Anwendungen ist es wichtig, die Lastverteilung entlang der Strecke zu berücksichtigen.
Die Nettokraft, die aufgrund der verteilten Last ausgeübt wird, wird als einzelner Vektor dargestellt, der als resultierende Kraft bezeichnet wird.
Stellen Sie sich eine beliebig geformte flache Platte vor, die gleichmäßig belastet wird.
Die Kraft, die auf eine unendlich kleine Fläche auf der Platte wirkt, hat eine Größe, die dem Differentialvolumenelement entspricht.
Die resultierende Kraft, die auf die Platte wirkt, wird berechnet, indem alle Differenzkräfte, die auf die gesamte Plattenoberfläche wirken, addiert werden.
Die Integration über die Fläche der Platte gibt uns einen Ausdruck für die Berechnung der Größe der resultierenden Kraft, die auch gleich dem Gesamtvolumen unter dem Diagramm der verteilten Belastung ist.
Der Ort der resultierenden Kraft wird bestimmt, indem die Momente der resultierenden Kraft mit denen aller Differenzkräfte um ihre jeweiligen Achsen verglichen werden.
Die erhaltenen Ausdrücke implizieren, dass die Wirkungslinie der Kraft durch das geometrische Zentrum oder den Schwerpunkt des Volumens unter dem Diagramm der verteilten Belastung verläuft.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik: Statik. Vierzehnte Auflage, New Jersey: Pearson. Abschnitt 9.4, S. 511.</li>
	<li>Bier, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. und Self, B.P. (2016). Vektormechanik für Ingenieure. Elfte Auflage, New York: McGraw-Hill Education. Abschnitt 5.3, S. 262.</li>
</ol>

resultierende einer allgemeinen verteilten belastung

Resultant of a General Distributed Loading

Beim Entwurf von Strukturen, die ungleichmäßigen Belastungen ausgesetzt sind, ist es entscheidend, die resultierende Kraft und ihre Position zu berücksichtigen. Diese resultierende Kraft ist ein einziger Vektor, der die Gesamtkraft aufgrund der verteilten Last darstellt. Beispiele für Lastverteilung aufgrund von Wind und Lastverteilung auf einer Brücke veranschaulichen, wie dieses Konzept verwendet wird, um sichere und zuverlässige Strukturen unter variablen Lastbedingungen zu analysieren und zu entwerfen. Die meisten Strukturen wie Wohngebäude, Brücken und Türme sind so konzipiert, dass sie Windbelastungen standhalten, die mit der Windgeschwindigkeit und -richtung variieren. Ebenso sind Brücken so konzipiert, dass sie das Gewicht der darüber fahrenden Fahrzeuge aushalten können. Jedoch ist die Gewichtsverteilung der Fahrzeuge nicht gleichmäßig, und einige Teile der Brücke können mehr Stress und Dehnung erfahren als andere. Es ist notwendig, die resultierende Kraft zu berechnen, die auf die Gebäude oder Brücken wirkt, was ein Problem der ungleichmäßigen Lastverteilung darstellt. Um diese Kraft zu bestimmen, muss die Größe jeder differentiellen Kraft, die auf infinitesimalen Flächen wirkt, summiert und über die belastete Oberfläche integriert werden. Die Größe dieser resultierenden Kraft entspricht dem Gesamtvolumen unter dem Diagramm der verteilten Belastung. Die Position dieser resultierenden Kraft kann bestimmt werden, indem ihre Momente mit den Momenten aller differentiellen Kräfte um ihre jeweiligen Achsen verglichen werden. Dies bedeutet, dass die Wirkungslinie dieser Kraft durch den geometrischen Schwerpunkt oder das Schwerpunktzentrum des betrachteten Volumens verlaufen wird. Zu wissen, wo und wie viel Kraft auf eine Struktur ausgeübt wird, ermöglicht es den Ingenieuren, ausreichende Festigkeit und Steifigkeit für die Struktur sicherzustellen, um ihrem Zweck zu dienen. Diese Werte können sich auch aufgrund variabler Lastbedingungen ändern, daher ist es wichtig, diese potenziellen Änderungen zu berücksichtigen, um eine sichere und solide Struktur zu entwerfen.

Resultierende einer allgemeinen verteilten Belastung

Bei der Konstruktion von Strukturen, die ungleichmäßigen Belastungen ausgesetzt sind, ist es entscheidend, die resultierende Kraft und ihre Position zu berücksichtigen. Diese resultierende Kraft ist eine einzige ...

resultant-of-a-general-distributed-loading

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finding the resultant of distributed loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load.

This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel more stress and strain than others.

To find the resultant force, the small forces acting on tiny areas are added together with integration over the load-bearing surface. The size of the resultant force equals the total area under the distributed-loading diagram. Its location is found by comparing moments, which means the turning effects of the force about an axis.

The line of action of the resultant passes through the geometric center, or centroid, of the volume under the load diagram. Knowing both the size and location of the force helps engineers judge whether a structure has enough strength and rigidity. Because loading can change, these calculations help support safe and reliable design for buildings, bridges, and other structures.

Finding the Resultant of Distributed Loads

finding-the-resultant-of-distributed-loads

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resultant of a general distributed loading

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

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A submerged flat plate experiences fluid pressure that changes with depth. This pressure can create effects such as drag and buoyancy. To study a flat plate with variable width, the pressure distribution across the plate must be analyzed first. The force on a small strip of the plate is found by multiplying the pressure by the strip’s differential area. The pressure can also be written using the fluid’s specific weight and the depth of that strip below the surface. To find the total, or...

key terms and concepts

Learn how engineers combine non-uniform loads into one resultant force, find its location with moments, and apply the idea to bridges and buildings.

Finding the Resultant of Distributed Loads | JoVE K12

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Finding the Resultant of Distributed Loads

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