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

考虑一个滑轮施加外部载荷的悬臂起重机。
如果已知起重机各构件的尺寸，且滑轮无摩擦，那么销接点处的反作用力是多少？
该系统为框架结构，由二力构件 BD 和多力构件 ABC 组成。
通过分析受力图并应用下部滑轮部分的力平衡条件，可求得缆绳中的张力。
考虑点 C，垂直缆索中的张力方向向下，而水平缆索中的张力方向指向铰接点 A。
在构件 DB 中，力&#160; FBD 可通过斜率三角形表示。
节点 A 的力矩平衡条件给出了沿 BD 方向的力。
根据力的平衡条件，计算铰链 A 处的水平和竖直方向的支座反力。
现在，考虑构件 BD 的受力分析图，可在节点 D 处应用力的平衡条件，以求得 D 点的水平和竖直方向的支座反力。

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	<li>比尔，F.P.;约翰斯顿，ER;马祖克，DF;克伦威尔，PJ 和塞尔夫，BP（2019 年）。工程师的矢量力学 \u2012 静力学和动力学。纽约:麦格劳-希尔。页码 330</li>
	<li>Meriam， JL、Kraige， LG 和 Bolton， JN （2020）。工程力学 \u2012 静力学。新泽西州霍博肯:约翰·威利。页码 200</li>
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框架：问题求解 i

Frames: Problem Solving I

假设有一台悬臂起重机，其外部负载悬挂在滑轮上。起重机构件的尺寸如图所示。假设滑轮是无摩擦的，需要对框架结构进行系统分析，以确定销关节处的反作用力。 <img alt="Figure 1" src="/files/ftp_upload/14291/14291_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> 系统由两个主要的结构组件组成：双力杆BD和多力杆ABC。双力杆BD指的是一个直线元素，并受到两端的力所产生的作用，并在其长度上没有额外的力。这些力的大小相等且方向相反，从而导致杆件处于纯拉力状态或压缩状态。另一方面，多力杆ABC受到分布在其长度上多个力所产生的作用。这些力可能包括外部负载、销钉连接处的反力以及缆绳所施加的力。由于多个力作用在杆件 ABC 上，它的应力分布比简单的双力杆 BD 更加复杂。 <img alt="Figure 2" src="/files/ftp_upload/14291/14291_PT_Fig_2v2.svg" style="text-align: center; height: 350px;"> 考虑下部滑轮部分，负载的重量平衡了缆绳的拉力，每根缆绳向上的拉力为10千牛。现在，考虑上部的滑轮部分，垂直缆绳的张力T是向下的，而水平缆绳则指向关节A。垂直缆绳的张力也为10千牛，因为它是同一个连续缆绳系统中的一部分。 在杆件DB中，力FBD可以使用斜三角形来将其分解为水平方向和垂直方向的分量。关节A的力矩平衡条件给出了50千牛的力FBD。 水平力的平衡条件可以应用于关节A。 <img alt="Equation 1" src="/files/ftp_upload/14291/14291_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> 代入长度AB、AC以及滑轮半径C的值，能够得到力FBD为50千牛。 水平力的平衡条件给出了关节A的反力为40千牛。 <img alt="Equation 2" src="/files/ftp_upload/14291/14291_PT_Equation_2v2.svg" style="text-align: center; height: 15px;"> 类似地，使用垂直力平衡条件，可以得出关节A在垂直方向上的反作用力为-20千牛。 <img alt="Equation 3" src="/files/ftp_upload/14291/14291_PT_Equation_3v2.svg" style="text-align: center; height: 15px;"> 力平衡的条件可以应用于关节D，以获得关节D的水平和垂直反力。 <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;"> 得到的结果表明了，位于关节D处在水平方向和垂直方向反作用力分别为-30千牛和40千牛。

框架：问题求解 I

考虑一台悬臂起重机，其滑轮上悬挂有外部载荷。起重机各构件的尺寸如图所示。系统性分析……

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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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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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