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

Si consideri un OB a trave rastremata fissata a un'estremità e soggetta a un carico distribuito.
Determinare la forza risultante equivalente del carico variabile e localizzare la sua posizione sulla trave.
Innanzitutto, dividere il carico distribuito in due regioni triangolari.
Successivamente, l'entità del carico risultante equivalente della regione triangolare sinistra e destra è uguale all'area di ciascun triangolo.
Ogni carico risultante agisce ai baridi, situati a un terzo della lunghezza della base dal lato verticale AD del triangolo.
Il carico risultante equivalente può essere determinato sommando il carico risultante individuale di ciascuna regione triangolare.
Il momento intorno al punto O può essere determinato sommando il singolo momento che agisce a causa di ciascun carico risultante.
Ricordiamo il principio del momento, che afferma che il momento del carico risultante equivalente attorno al punto O è uguale al prodotto del carico risultante equivalente e della distanza dal punto O.
Sostituendo i valori nell'equazione, è possibile determinare la posizione del carico risultante equivalente.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall, pp. 194-195</li>
</ol>

carichi distribuiti: risoluzione dei problemi

Le travi sono elementi strutturali comunemente impiegati in applicazioni ingegneristiche che richiedono diverse capacità di carico. Il primo passo nell'analisi di una trave sotto un carico distribuito è semplificare il problema dividendo il carico in regioni più piccole, il che consente di considerare separatamente ciascuna regione e calcolare la magnitudine del carico risultante equivalente che agisce su ogni porzione della trave. La magnitudine del carico risultante equivalente per ogni regione, può essere determinata calcolando l'area delle rispettive regioni, che rappresenta la forza esercitata dal carico in ciascuna regione.

Successivamente, si individua la posizione di ogni carico risultante sulla trave. Ciò può essere fatto trovando i centroidi delle regioni, che sono i punti in cui si può considerare concentrata la massa delle regioni. I carichi risultanti individuali agiscono su questi centroidi, esercitando la loro forza su punti specifici lungo la trave.

Il carico risultante equivalente per l'intera trave, può essere calcolato con le magnitudini e le posizioni dei carichi risultanti individuali determinati. Ciò comporta l'aggiunta dei carichi risultanti individuali delle diverse regioni, per ottenere il carico risultante equivalente complessivo che agisce sulla trave.

Il passo successivo è determinare il momento rispetto a un punto specifico, di solito l'estremità fissa della trave. Il momento misura l'effetto rotazionale della forza che agisce sulla trave. Il momento risultante può essere determinato aggiungendo i momenti individuali che agiscono a causa di ciascun carico. Il momento di ciascun carico è uguale al prodotto della forza e della sua distanza dal punto specificato.

<img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;" />

Ricordando il principio del momento, il momento del carico risultante equivalente rispetto al punto specificato, è uguale al prodotto del carico risultante equivalente e della distanza da quel punto.

<img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;" />

Riorganizzando l'equazione e sostituendo i termini, è possibile determinare la posizione del carico risultante equivalente lungo la trave.

<img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;" />

Carichi Distribuiti: Risoluzione dei Problemi

Le travi sono elementi strutturali comunemente impiegati in applicazioni ingegneristiche che richiedono diverse capacità di carico. Il primo passo nell'analisi di un ...

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Mechanical Engineering

Ingegneria Meccanica

Unit 1

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Force System Resultants

Risultanti dei sistemi di forze

KEY TERMS AND CONCEPTS

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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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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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