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

Considere um guindaste de lança com uma carga externa da polia.
Se as dimensões dos membros do guindaste são conhecidas, quais são as forças de reação nas juntas dos pinos, considerando que as polias não têm atrito?
O sistema é uma estrutura de quadro, consistindo em um membro BD de duas forças e um membro ABC de várias forças.
Considerando um diagrama de corpo livre e aplicando as condições de equilíbrio de força para a seção inferior da polia, a tensão no cabo pode ser obtida.
Considerando o ponto C, a tensão no cabo vertical é direcionada para baixo, enquanto para o cabo horizontal, é direcionada para a junta A.
Na barra DB, a força FBD pode ser expressa usando um triângulo de inclinação.
A condição de equilíbrio de momento na junta A dá a força ao longo de BD.
Aplicando as condições de equilíbrio de força, as forças de reação horizontal e vertical na junta A são calculadas.
Agora, considerando o diagrama de corpo livre para o membro BD, as condições de equilíbrio de força podem ser aplicadas na junta D para obter as forças de reação horizontal e vertical em D.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 305.</li>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. pág. 330</li>
	<li>Meriam, J.L., Kraige, L.G., e Bolton, J.N. (2020). Engenharia Mecânica \u2012 Estática. Hoboken, Nova Jersey: John Wiley. pág. 200</li>
</ol>

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armações: resolução de problemas i

Frames: Problem Solving I

Considere uma ponte rolante com uma carga externa suspensa pela polia. As dimensões dos membros da ponte são mostradas na figura. Uma análise sistemática da estrutura da estrutura é necessária para determinar as forças de reação nas articulações de pino, assumindo que as polias são sem atrito.

<img alt="Figure 1" src="/files/ftp_upload/14291/14291_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

O sistema tem dois componentes estruturais principais: um membro bi-force BD e um membro multi-força ABC. O membro bi-force BD refere-se a um elemento reto sujeito apenas a forças em suas duas extremidades, B e D, sem forças adicionais atuando ao longo de seu comprimento. Essas forças são iguais em magnitude, mas opostas em direção, resultando no membro estar em puro tensionamento ou compressão. Por outro lado, o membro multi-força ABC é sujeito a mais de duas forças distribuídas ao longo de seu comprimento. Essas forças podem incluir cargas externas, forças de reação nas articulações de pino e a força exercida pelo cabo. Devido às múltiplas forças agindo no membro ABC, ele experimenta uma distribuição de tensão mais complexa em comparação ao membro bi-força BD mais simples.

<img alt="Figure 2" src="/files/ftp_upload/14291/14291_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Considerando a seção da polia inferior, o peso da carga equilibra a tensão nos cabos, resultando em uma tensão ascendente de 10 kN para cada cabo. Agora, considerando a seção da polia superior, a tensão T no cabo vertical é direcionada para baixo, enquanto aponta para a junção A para o cabo horizontal. A tensão no cabo vertical também é de 10 kN, pois faz parte do mesmo sistema contínuo de cabos.

No membro DB, a força F_BD pode ser resolvida em seus componentes horizontais e verticais usando um triângulo de inclinação. A condição de equilíbrio do momento na junção A dá F_BD como 50 kN.

A condição de equilíbrio da força horizontal pode ser aplicada à junção A.

<img alt="Equation 1" src="/files/ftp_upload/14291/14291_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Substituindo os valores do comprimento AB, AC e raio da polia C, a força F_BD é obtida como 50 kN.

A condição de equilíbrio da força horizontal dá a força de reação em A como 40 kN.

<img alt="Equation 2" src="/files/ftp_upload/14291/14291_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

Da mesma forma, usando a condição de equilíbrio da força vertical, a força de reação vertical em A é estimada como -20 kN.

<img alt="Equation 3" src="/files/ftp_upload/14291/14291_PT_Equation_3v2.svg" style="text-align: center; height: 15px;" />

As condições de equilíbrio de forças podem ser aplicadas na junção D para obter as forças de reação horizontal e vertical em 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;" />

Os resultados obtidos indicam que as forças de reação horizontal e vertical no ponto D são -30 kN e 40 kN, respectivamente.

Armações: Resolução de Problemas I

Considere um guindaste de lança com uma carga externa suspensa na polia. As dimensões dos membros do guindaste são mostradas na figura. Uma análise sistemática ...

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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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frames: problem solving i

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...

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key terms and concepts

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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