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

プーリーから外部負荷がかかるジブクレーンを考えてみましょう。
クレーン部材の寸法がわかっている場合、プーリーが摩擦がないことを考えると、ピンジョイントの反力はどれくらいですか?
システムは、2フォースメンバーBDとマルチフォースメンバーABCからなるフレーム構造です。
フリーボディ図を考慮し、下部プーリー部分に力平衡条件を適用すると、ケーブルの張力を得ることができます。
点Cを考慮すると、垂直ケーブルの張力は下向きですが、水平ケーブルの場合、ジョイントAに向けられます。
部材DBでは、力FBDは傾斜三角形で表すことができます。
ジョイントAでのモーメント平衡状態は、BDに沿った力を与えます。
力の平衡条件を適用して、ジョイントAの水平反力と垂直反力が計算されます。
ここで、メンバーBDの自由体図を考えると、ジョイントDに力平衡条件を適用して、Dでの水平および垂直反力を求めることができます。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。ニュージャージー州ホーボーケン:ピアソンプレンティスホール。305ページ。</li>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。330ページ</li>
	<li>メリアム、JL、クレイジ、LG、およびボルトン、JN(2020)。エンジニアリングメカニクス \u2012 静力学。ニュージャージー州ホーボーケン:ジョン・ワイリー。200ページ</li>
</ol>

利益相反は宣言されていません。

フレーム：問題解決i

Frames: Problem Solving I

クレーンに外部の荷重が滑車から吊るされているとします。クレーン部分の寸法は図に示されています。滑車は摩擦のないものと仮定し、ピンジョイントでの反力を求めるために、フレーム構造の系統的な分析が必要です。

<img alt="図1" src="/files/ftp_upload/14291/14291_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

このシステムには、2つの主要な構造部品があります：2力部分BDと多力部分ABCです。2力部分BDとは、その両端BとDでの力だけが作用する直線要素を指します。これらの力は大きさは同じですが、方向は逆であり、その結果、部分は純粋な張力または圧縮になります。一方、多力部分ABCは、その長さに沿って2つ以上の力が分布している状態になります。これらの力には、外部荷重、ピンジョイントの反力、およびケーブルによって生じる力が含まれる場合があります。部分ABCには複雑な応力分布が生じるため、より複雑な応力分布が生じます。

<img alt="図2" src="/files/ftp_upload/14291/14291_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

下部滑車セクションを考慮すると、荷重の重さはケーブルの張力をバランスさせ、各ケーブルに10 kNの上向きの張力が発生します。さらに、上部滑車セクションを考慮すると、垂直なケーブルの張力Tは下向きに向かい、水平なケーブルの張力はジョイントAに向かっています。垂直なケーブルの張力も10 kNであり、それは同じ連続したケーブルシステムの一部です。

部分DBでは、力FBDは、傾斜三角形を使用して水平方向と垂直方向の成分に分解することができます。ジョイントAでのモーメントの平衡条件により、力FBDは50 kNとなります。

水平力の平衡条件は、ジョイントAに適用することができます。

<img alt="式1" src="/files/ftp_upload/14291/14291_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

長さAB、AC、および滑車の半径Cの値を代入すると、力FBDが50 kNとなります。

水平力の平衡条件から、ジョイントAの反力は40 kNとなります。

<img alt="式2" src="/files/ftp_upload/14291/14291_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

同様に、垂直力の平衡条件を使用して、ジョイントAの垂直な反力は-20 kNと推定されます。

<img alt="式3" src="/files/ftp_upload/14291/14291_PT_Equation_3v2.svg" style="text-align: center; height: 15px;" />

力の平衡条件をジョイントDに適用して、ジョイントDの水平および垂直な反力を求めることができます。

<img alt="式4" src="/files/ftp_upload/14291/14291_PT_Equation_4v2.svg" style="text-align: center; height: 15px;" />

<img alt="式5" src="/files/ftp_upload/14291/14291_PT_Equation_5v2.svg" style="text-align: center; height: 15px;" />

得られた結果から、ポイントDにおける水平および垂直な反力は、それぞれ-30 kNと40 kNです。

フレーム：問題解決I

プーリーから外部荷重が吊り下げられたジブクレーンを考えてみましょう。クレーン部材の寸法を図に示します。体系的な分析...

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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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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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