Name: truss member force calculation by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 27 s
Channel: JoVE

垂直、斜め、および水平の部材で構成される対称的な屋根トラス構造を考えてみましょう。
自由体図を描き、断面法を使用してDCおよびHCメンバーにかかる力を解析します。
ここでは、水平および垂直メンバーの荷重と長さが既知のパラメータです。
まず、点Aの周りのモーメントを合計して、Eでの反力を計算します。
また、トラスに対する力平衡条件を用いて、Aにおける反力を求める。
トラスの対称性により、両方の反力が等しくなります。
ここで、DC、HC、HGメンバーと交差する平面に沿ってカットが行われ、小さい方のセクションのフリーボディ図が描画されます。
Hに関するモーメントの総和を取ると、DCに沿った力が得られます。正の符号は引張力を示します。
HCに沿った力は、その正弦成分と余弦成分に分解され、三角法を使用して角度θを推定します。
Eでのモーメント平衡状態はHCに力を生じさせ、負の符号は圧縮力を示します。

<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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断面の方法：問題解決 i

対称な屋根トラス構造を考えます。垂直、対角、水平のメンバーで構成されています。各水平メンバーの長さは4mです。垂直メンバーFBとHDの長さは4mであり、メンバーGCの長さは6mです。ジョイントF、G、Hでの負荷は2kNであり、ジョイントAとEでの負荷は1kNです。

<img alt="Figure 1" src="/files/ftp_upload/14286/14286_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

断面法を使用してメンバーDCおよびHCに作用する力を計算します。モーメントの平衡条件はポイントAに適用され、既知の力と距離の値がモーメント方程式に代入されます。

<img alt="Equation 1" src="/files/ftp_upload/14286/14286_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

これにより、ポイントEの推定反力は4kNになります。次に、ポイントAでの垂直力の平衡条件により、ポイントAでの反力も4kNであることがわかります。

<img alt="Equation 2" src="/files/ftp_upload/14286/14286_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

トラスの対称性により、ポイントAとEの反力は等しいです。

反力を把握した後、メンバーDCとHCに作用する力を求めることができます。断面の切断は、メンバーDC、HC、およびHGと交差する面に沿って行われ、小さなセクションの自由物体図が考慮されます。

<img alt="Figure 2" src="/files/ftp_upload/14286/14286_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

ポイントHを中心にモーメントを合計することで、DCに沿った力は正の3kNであり、引張力を示しています。

<img alt="Equation 3" src="/files/ftp_upload/14286/14286_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

CHに沿った力は、そのサインとコサイン成分に分解されます。三角法を使用して、メンバーCHと水平軸との間の角度を45°と求めます。最後に、ポイントEでのモーメントの平衡条件を適用することで、FCHの力は-1.41kNとなります。

<img alt="Equation 4" src="/files/ftp_upload/14286/14286_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

この場合、負の結果はメンバーCHに作用する圧縮力を示しています。

断面の方法：問題解決 I

垂直、斜め、および水平の部材で構成される対称的な屋根トラス構造を考えてみましょう。各水平部材の長さは4mです。

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: Problem Solving I

truss member force calculation by sections

Truss member forces can be found with the method of sections in a symmetrical roof truss. The structure here includes vertical, diagonal, and horizontal members. Each horizontal member is 4 m long. The vertical members FB and HD are 4 m long, and member GC is 6 m long.

The roof truss carries loads at several joints. Joints F, G, and H each have a 2 kN load. Joints A and E each have a 1 kN load. To start the analysis, moment equilibrium is used at point A. The force and distance values are placed into the moment equation, which gives a reaction force of 4 kN at point E.

Next, vertical force equilibrium at point A gives the reaction force at A as 4 kN. Because the truss is symmetrical, the reactions at A and E are equal. Once the reactions are known, the forces in members DC and HC can be found. A section is cut through members DC, HC, and HG, and a free-body diagram is drawn for the smaller part.

Moments about point H are then summed to solve for the force in DC. The result is 3 kN, which is positive and shows tension. The force in CH is handled with trigonometry. The angle between member CH and the horizontal axis is found to be 45°. Using moment equilibrium at point E gives FCH = -1.41 kN. The negative sign means member CH is in compression.

Truss Member Force Calculation by Sections

truss-member-force-calculation-by-sections

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key terms and concepts

Learn how the method of sections is used on a symmetrical roof truss to find support reactions and member forces, including tension and compression.

Truss Member Force Calculation by Sections | JoVE K12

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mechanical engineering

Truss Member Force Calculation by Sections

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