Name: truss member force analysis by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

トラス構造を考えてみましょう。力 F1 と F2 は点 B と D で作用しています。
セクションの方法は、トラスのいくつかの部材に作用する力を決定するために使用されます。これは、平衡状態のトラスがその各セグメントを平衡状態にあるという原則に基づいています。
トラスの自由体図は、メンバーEF、DC、およびDFに作用する力を計算するために考慮されます。
点Aの周りのモーメントの平衡方程式を使用して、点Eでのサポート反力を計算できます。
これで、最大 3 つの部材と交差する断面平面に沿ってカットが行われます。
未知の力を引張りと仮定した断面の自由体図が描画されます。
D に関するモーメントを合計すると、EF に作用する力の解が得られます。
未知の傾斜力は、水平成分と垂直成分に分解されます。
水平方向と垂直方向に沿って加えられる力の平衡状態は、2つの方程式になります。
連立方程式を解くと、DCとDFに沿った力を計算できます。

<ol>
	<li>R. C., Hibbeler Engineering Mechanics Statics, ピアソン. pp. 291-293</li>
	<li>F.P. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, B.P. Self, Vector Mechanics For Engineers Statics and Dynamics Engineering Mechanics Statics, Mc Graw-Hill Education. pp. 217</li>
</ol>

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断面法

図に示されるようなトラス構造を考えます。

<img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

関節Bと関節Dで力F_1とF_2が働いています。トラスの特定の部材（EF、DC、DFなど）に働く力を求めるために、断面法を用いることができます。この手法は、静力学の原理に基づいており、平衡状態にあるトラスは、それぞれのセグメントも平衡状態にあるということです。

<img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

これらの部材に働く力を計算するためには、トラスの自由物体図を考慮します。関節A周りのモーメントの平衡方程式を適用して、点Eでの支持反力を推定することができます。

<img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

切断面を選び、それが最大で3つの部材（EF、DC、DF）と交差するようにします。次に、切断断面の右側の自由体図を描きますが、未知の力を引張力として仮定します。

<img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

部材EFに作用する力の解を、関節D周りのモーメントの合計として得ることができます。

未知の傾斜力F_DCとF_DFは、水平および垂直成分に分解されます。水平および垂直方向の力に対する平衡条件を適用すると、2つの別々の方程式を得ることができます。

<img alt="Equation 3" src="/files/ftp_upload/14285/14285_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 4" src="/files/ftp_upload/14285/14285_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

これらの連立方程式を解くことで、部材DCおよびDFに作用する力を推定することができます。

図に示すように、トラス構造を考えてみましょう。

力F1とF2は、それぞれジョイントBとDで作用します。セクションの方法は、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Structural Analysis

構造解析

KEY TERMS AND CONCEPTS

主要用語と概念

Method of Sections

truss member force analysis by sections

Truss member force analysis by sections finds the force in selected members of a truss. In this problem, forces F1 and F2 act at joints B and D. The goal is to determine the forces in members EF, DC, and DF.

The method uses the idea that a truss in equilibrium also has each of its sections in equilibrium. A free-body diagram of the whole truss is drawn first. The moment equation about joint A is then used to estimate the support reaction at point E.

Next, a cut is made along a sectional plane that passes through no more than three members. Here, the cut intersects EF, DC, and DF. A free-body diagram of the right side of the cut section is then drawn, and the unknown member forces are assumed to be tensile, or pulling away from the cut.

The force in member EF is found by summing moments about joint D. The inclined forces in members DC and DF are then split into horizontal and vertical parts. Finally, equilibrium in the horizontal and vertical directions gives two equations, and solving them gives the forces in DC and DF.

Truss Member Force Analysis by Sections

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key terms and concepts

Learn how the method of sections uses free-body diagrams, moments, and force balance to find unknown forces in truss members EF, DC, and DF.

Truss Member Force Analysis by Sections | JoVE K12

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mechanical engineering

Truss Member Force Analysis by Sections

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