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

Rozważmy belkę stożkową OB zamocowaną na jednym końcu i poddawaną obciążeniu rozłożonemu.
Określ równoważną siłę wypadkową zmiennego obciążenia i określ jego położenie na belce.
Najpierw podziel rozłożone obciążenie na dwa trójkątne obszary.
Następnie wielkość równoważnego obciążenia wypadkowego lewego i prawego obszaru trójkąta jest równa powierzchni każdego trójkąta.
Każde wynikowe obciążenie działa na centroidy, znajdujące się w jednej trzeciej długości podstawy od pionowego boku AD trójkąta.
Równoważne obciążenie wypadkowe można określić, dodając indywidualne obciążenie wypadkowe każdego obszaru trójkątnego.
Moment względem punktu O można wyznaczyć, dodając pojedynczy moment działający na każde obciążenie wypadkowe.
Przypomnijmy sobie zasadę momentu, która mówi, że moment równoważnego obciążenia wynikowego wokół punktu O jest równy iloczynowi równoważnego obciążenia wynikowego i odległości od punktu O.
Podstawiając wartości w równaniu, można określić położenie równoważnego obciążenia wynikowego.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall, s. 194-195</li>
</ol>

rozkłady obciążeń: rozwiązywanie problemów

Belki są elementami konstrukcyjnymi powszechnie stosowanymi w aplikacjach inżynieryjnych, które wymagają różnych zdolności nośnych. Pierwszym krokiem przy analizie belki pod obciążeniem rozkładanym jest uproszczenie problemu, dzieląc obciążenie na mniejsze obszary, co pozwala rozpatrzyć każdy obszar oddzielnie i obliczyć wartość równoważnego obciążenia skupionego, które działa na każdej części belki. Wartość równoważnego obciążenia skupionego dla każdego obszaru można obliczyć, obliczając pole powierzchni odpowiednich obszarów, które reprezentują siłę wywieraną przez obciążenie w każdym obszarze.

Następnie należy zlokalizować pozycję każdego równoważnego obciążenia na belce. Można to zrobić, znajdując środki ciężkości obszarów, które są punktami, w których masy obszarów można skoncentrować. Indywidualne równoważne obciążenia działają w tych środkach ciężkości, wywierając swoją siłę w określonych punktach na belce.

Równoważne obciążenie całej belki można obliczyć przy pomocy wartości i pozycji ustalonych indywidualnych obciążeń skupionych. Wymaga to dodania indywidualnych obciążeń skupionych z różnych obszarów, aby uzyskać ogólne równoważne obciążenie działające na belkę.

Kolejnym krokiem jest określenie momentu względem określonego punktu, zazwyczaj końca zamocowanego belki. Moment mierzy efekt obrotowy siły działającej na belkę. Równoważny moment można obliczyć przez dodanie indywidualnych momentów działających na każde obciążenie. Moment każdego obciążenia jest równy iloczynowi siły i jej odległości od wyznaczonego punktu.

<img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;" />

Przywołując zasadę momentu, moment równoważnego obciążenia względem określonego punktu jest równy iloczynowi równoważnego obciążenia i odległości od tego punktu.

<img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;" />

Poprzez przestawienie równania i podstawienie terminów można określić położenie równoważnego obciążenia względem belki.

<img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;" />

Rozkłady obciążeń: Rozwiązywanie problemów

Belki są elementami konstrukcyjnymi powszechnie stosowanymi w zastosowaniach inżynierskich wymagających różnych nośności. Pierwszym krokiem w analizie ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Force System Resultants

wypadkowe układu sił

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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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distributed loads: problem solving

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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