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

壁に固定された対角線、垂直、および水平の部材で構成される任意のトラス構造を考えてみましょう。
セクションの方法を使用して、メンバーCB、GB、およびGHに作用する力を計算できます。
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。
CB、GB、GHメンバーと交差する平面に沿って切り込みを行い、右側の断面のフリーボディ図を描きます。
点Gの周りのモーメント平衡方程式は、CBに沿った力を与えます。正の符号は、部材の張力を示します。 
現在、BCGではFGBをスロープ三角形で表現し、CEGではFGHをスロープ三角形で表現できるようになりました。
垂直方向と水平方向の力の合計を考慮すると、力の平衡方程式を書くことができます。
FCB の値を代入します。力の平衡方程式を同時に解いて、GH と GB のメンバーに沿った力を求めます。
FGHの負の符号は力が圧縮されていることを示し、FGBの正の符号は引張力を示します。

<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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断面法：問題解決ii

任意の斜め、垂直、水平部分が壁に固定されたトラス構造を考えます。部分CB、GB、およびGHに作用する力を計算するために、断面法を使用することができます。水平および垂直部分の荷重と長さは既知のパラメーターです。

<img alt="Figure 1" src="/files/ftp_upload/14287/14287_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

以下に示す図のように、まず、CB、GB、およびGHの部分に交わる平面で切り込みを入れ、右側の断面の自由物体図を描きます。

<img alt="Figure 2" src="/files/ftp_upload/14287/14287_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

G点に関してのモーメント平衡の方程式を適用します。

<img alt="Equation 1" src="/files/ftp_upload/14287/14287_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

結果として、部分CBに沿って作用する力は4 kNであり、正の符号は部分の張力を示します。

今度は、BCGの傾斜三角形を使用してF_CBを表現し、CEGの傾斜三角形を使用してFGHを表現することができます。垂直および水平力の総和を考慮して、力の平衡方程式は以下のように書くことができます。

<img alt="Equation 2" src="/files/ftp_upload/14287/14287_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

<img alt="Equation 3" src="/files/ftp_upload/14287/14287_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

F_HGの値が代入され、力の平衡方程式が同時に解かれます。その結果、F_HGは-7.454 kN、F_GBは3.772 kNとなります。F_HGの負の符号は圧縮力を示し、F_GBの正の符号は引張力を示します。

断面法：問題解決II

壁に固定された斜めの部材、垂直部材、水平部材で構成される任意のトラス構造を考えてみましょう。部材に作用する力を計算するには...

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: Problem Solving II

truss member force analysis by sections

Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH.

A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the positive sign shows that CB is in tension.

The force in CB is then written with a slope triangle in triangle BCG. The force in GH is written with a slope triangle in triangle CEG. After that, the sums of vertical and horizontal forces are set equal to zero. The equation for CB is substituted, and the remaining equations are solved at the same time.

The final values are FGH = -7.454 kN and FGB = 3.772 kN. The negative sign for GH means the member is in compression. The positive sign for GB means the member is in tension.

Truss Member Force Analysis by Sections

truss-force-analysis-using-method-of-sections

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Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH. A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the...

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key terms and concepts

Learn how the method of sections isolates a truss cut, uses moment and force balance, and identifies tension or compression in members CB, GB, and GH.

Truss Member Force Analysis by Sections | JoVE K12

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mechanical engineering

Truss Member Force Analysis by Sections

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