Name: jib crane reaction forces in frames
Uploaded: 2023-09-22T11:49:25.000Z
Duration: 1 min 24 s
Channel: JoVE

Si consideri una gru a bandiera con un carico esterno dalla puleggia.
Se le dimensioni degli elementi della gru sono note, quali sono le forze di reazione ai giunti dei perni, considerando che le pulegge sono prive di attrito?
Il sistema è una struttura a telaio, costituita da un membro BD a due forze e da un membro ABC a più forze.
Considerando un diagramma a corpo libero e applicando le condizioni di equilibrio della forza per la sezione inferiore della puleggia, si può ottenere la tensione nel cavo.
Considerando il punto C, la tensione nel cavo verticale è diretta verso il basso, mentre per il cavo orizzontale è diretta verso il giunto A.
Nell'asta DB, la forza FBD può essere espressa utilizzando un triangolo di pendenza.
La condizione di equilibrio del momento al giunto A fornisce la forza lungo BD.
Applicando le condizioni di equilibrio delle forze, vengono calcolate le forze di reazione orizzontali e verticali al giunto A.
Ora, considerando il diagramma di corpo libero per l'asta BD, le condizioni di equilibrio delle forze possono essere applicate al giunto D per ottenere le forze di reazione orizzontali e verticali in D.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 305.</li>
	<li>Birra, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. e Self, B.P. (2019). Meccanica vettoriale per ingegneri \u2012 Statica e dinamica. New York: McGraw-Hill. pagine 330</li>
	<li>Meriam, JL, Kraige, LG e Bolton, JN (2020). Ingegneria Meccanica \u2012 Statica. Hoboken, New Jersey: John Wiley. pagine 200</li>
</ol>

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telai: risoluzione dei problemi i

Frames: Problem Solving I

Considera una gru a cavalletto con un carico esterno sospeso dalla puleggia. Le dimensioni dei membri della gru sono mostrate nella figura. Per determinare le forze di reazione ai giunti a perno, assumendo che le pulegge siano prive di attrito, è necessaria un'analisi sistematica della struttura del telaio.

<img alt="Figure 1" src="/files/ftp_upload/14291/14291_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Il sistema ha due componenti strutturali principali: un membro a due forze BD e un membro a molte forze ABC. Il membro a due forze BD si riferisce a un elemento diritto soggetto solo a forze alle due estremità, B e D, senza forze aggiuntive che agiscono lungo la sua lunghezza. Queste forze hanno la stessa intensità ma direzioni opposte, risultando nell'elemento sia in una pura tensione che in una compressione. D'altra parte, il l'elemento a molte forze ABC è soggetto a più di due forze distribuite lungo la sua lunghezza. Queste forze possono includere carichi esterni, forze di reazione ai giunti a perno e la forza esercitata dal cavo. A causa delle forze multiple che agiscono su di esso, ABC, sperimenta una distribuzione di stress più complessa rispetto al più semplice BD.

<img alt="Figure 2" src="/files/ftp_upload/14291/14291_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Considerando la sezione inferiore della puleggia, il peso del carico bilancia la tensione nei cavi risultando in una tensione verso l'alto di 10 kN per ogni cavo. Ora, considerando la sezione superiore della puleggia, la tensione T nel cavo verticale è diretta verso il basso, mentre punta verso il giunto A per il cavo orizzontale. La tensione nel cavo verticale è anche di 10 kN poiché fa parte del sistema di cavi continuo.

 Nel membro DB, la forza FBD può essere risolta nei suoi componenti orizzontali e verticali utilizzando un triangolo di pendenza. La condizione di equilibrio del momento al giunto A fornisce FBD pari a 50 kN.

 La condizione di equilibrio della forza orizzontale può essere applicata al giunto A.

<img alt="Equation 1" src="/files/ftp_upload/14291/14291_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Sostituendo i valori della lunghezza AB, AC e il raggio della puleggia C, la forza FBD ottenuta è pari a 50 kN.

La condizione di equilibrio della forza orizzontale, fornisce la forza di reazione al giunto A di 40 kN.

<img alt="Equation 2" src="/files/ftp_upload/14291/14291_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

Allo stesso modo, utilizzando la condizione di equilibrio della forza verticale, la forza di reazione verticale al punto A è stimata di -20 kN.

<img alt="Equation 3" src="/files/ftp_upload/14291/14291_PT_Equation_3v2.svg" style="text-align: center; height: 15px;" />

Le condizioni di equilibrio della forza, possono essere applicate al giunto D per ottenere le forze di reazione orizzontali e verticali rispetto al punto D.

<img alt="Equation 4" src="/files/ftp_upload/14291/14291_PT_Equation_4v2.svg" style="text-align: center; height: 15px;" />

<img alt="Equation 5" src="/files/ftp_upload/14291/14291_PT_Equation_5v2.svg" style="text-align: center; height: 15px;" />

I risultati ottenuti indicano che le forze di reazione orizzontali e verticali rispetto al punto D sono rispettivamente -30 kN e 40 kN.

Telai: Risoluzione dei problemi I

Si consideri una gru a bandiera con un carico esterno sospeso alla puleggia. Le dimensioni dei membri della gru sono mostrate nella figura. Un'analisi sistematica ...

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jib crane reaction forces in frames

Jib crane reaction forces in frames are found by analyzing the pin joints, the cable tension, and the load carried by the pulley. The structure in this problem has an external load suspended from the pulley, and the member sizes are shown in the figure. Because the pulleys are frictionless, the force balance can be worked out step by step.

The frame has two main parts. Member BD is a two-force member, which means it is a straight part loaded only at its two ends, D and B. Those end forces are equal in size and opposite in direction, so the member is in either tension or compression. Member ABC is a multi-force member, so it carries more than two forces along its length. These forces include the pin reactions, the external load, and the cable force, which makes its stress state more complex.

The lower pulley section shows that the load weight is balanced by the cable tension. That gives an upward tension of 10 kN in each cable. In the upper pulley section, the tension T in the vertical cable points downward, while the horizontal cable tension points toward joint A. The vertical cable tension is also 10 kN because it is part of the same continuous cable system.

To solve member DB, the force FBD is split into horizontal and vertical parts with a slope triangle. A moment balance at joint A gives FBD as 50 kN. The horizontal force balance at A then uses the lengths AB and AC and the pulley radius at C to confirm this value. From that balance, the reaction at A is 40 kN in the horizontal direction, and the vertical reaction at A is -20 kN. The force balance at joint D gives the reaction forces there as -30 kN horizontally and 40 kN vertically.

Jib Crane Reaction Forces in Frames

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Analyze a jib crane frame with a frictionless pulley, two-force member BD, and multi-force member ABC to find reaction forces at joints A and D.

Jib Crane Reaction Forces in Frames | JoVE K12

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Jib Crane Reaction Forces in Frames

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