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

Stellen Sie sich eine beliebige Fachwerkstruktur vor, die aus diagonalen, vertikalen und horizontalen Elementen besteht, die an der Wand befestigt sind.
Mit der Methode der Querschnitte kann die Kraft berechnet werden, die auf die Stäbe CB, GB und GH wirkt.
Dabei sind die Lasten und die Längen der horizontalen und vertikalen Stäbe die bekannten Parameter.
Es wird ein Schnitt entlang einer Ebene vorgenommen, die CB-, GB- und GH-Stäbe schneidet, und es wird ein Freikörperdiagramm des rechten Seitenabschnitts gezeichnet.
Die Momentengleichgewichtsgleichung um den Punkt G ergibt die Kraft entlang CB. Das positive Vorzeichen zeigt Spannungen im Stab an. 
Jetzt kann FGB mit einem Steigungsdreieck in BCG ausgedrückt werden, während FGH mit einem Steigungsdreieck in CEG ausgedrückt werden kann.
Unter Berücksichtigung der Summierung von vertikalen und horizontalen Kräften können die Kraftgleichgewichtsgleichungen geschrieben werden.
Der Wert von FCB wird substituiert. Die Kraftgleichgewichtsgleichungen werden gleichzeitig gelöst, um die Kraft entlang der GH- und GB-Stäbe zu erhalten.
Das negative Vorzeichen von FGH zeigt an, dass es sich um eine Druckkraft handelt, während das positive Vorzeichen von FGB die Zugkraft angibt.

<ol>
	<li>R. C., Hibbeler Technische Mechanik Statik, Pearson. S. 291-293</li>
	<li>F.P. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, B.P. Self, Vektormechanik für Ingenieure Statik und Dynamik Technische Mechanik Statik, Mc Graw-Hill Bildung. S. 217</li>
</ol>

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methode der schnitte: problemlösung ii

Betrachten Sie eine beliebige Fachwerkstruktur, bestehend aus diagonalen, vertikalen und horizontalen Elementen, die an der Wand befestigt sind. Um die auf die Elemente CB, GB, und GH wirkenden Kräfte zu berechnen, kann die Methode der Schnitte verwendet werden. Die Lasten und Längen der horizontalen und vertikalen Elemente sind bekannte Parameter, wie in der Abbildung gezeigt. <img alt="Figure 1" src="/files/ftp_upload/14287/14287_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> Um zu beginnen, wird ein Schnitt entlang einer Ebene gemacht, die die Elemente CB, GB, und GH schneidet, und es wird eine Freikörperdiagramm des rechten Abschnitts erstellt. <img alt="Figure 2" src="/files/ftp_upload/14287/14287_PT_Fig_2v2.svg" style="text-align: center; height: 350px;"> Die Momentengleichung um den Punkt G wird angewendet. <img alt="Equation 1" src="/files/ftp_upload/14287/14287_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> Das Ergebnis gibt die Kraft entlang des Elements CB als 4 kN an, wobei das positive Vorzeichen auf eine Zugkraft im Element hinweist. Nun kann FCB mithilfe eines Steigungsdreiecks in BCG ausgedrückt werden, während FGH mithilfe eines Steigungsdreiecks in CEG ausgedrückt werden kann. Unter Berücksichtigung der Summe der vertikalen und horizontalen Kräfte können die Kräftegleichgewichtsgleichungen wie folgt geschrieben werden: <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;"> Die Wert von FCB wird eingesetzt, und die Kräftegleichgewichtsgleichungen werden gleichzeitig gelöst. Das Ergebnis ergibt die Kraft FGH als -7.454 kN und FGB als 3.772 kN. Das negative Vorzeichen von FGH zeigt an, dass die Kraft drückend ist, während das positive Vorzeichen für die Kraft FGB die Zugkraft anzeigt.

Methode der Schnitte: Problemlösung II

Stellen Sie sich eine beliebige Fachwerkstruktur vor, die aus diagonalen, vertikalen und horizontalen Elementen besteht, die an der Wand befestigt sind. Um die auf Stäbe wirkende Kraft zu berechnen ...

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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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Truss Member Force Analysis by Sections

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