Name: truss joint force analysis by equilibrium
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 30 s
Channel: JoVE

Stellen Sie sich eine Fachwerkstruktur vor, bei der zwei Kräfte an den Verbindungen C und D wirken, die mit reibungsfreien Verbindungen verbunden sind. Bestimmen Sie die Kräfte in jedem Fachwerkstab und identifizieren Sie die Zug- oder Druckspannung in jedem Fachwerkstab.
Mit der Methode der Gelenke können alle Kräfte bestimmt werden, die an jedem Gelenk wirken.
Die Analyse beginnt mit Gelenk C, da es die geringsten unbekannten Kräfte aufweist.
Zeichnen Sie ein Freikörperdiagramm des Gelenks C. Mit Hilfe der Gleichgewichtsgleichungen können die unbekannten Kräfte bestimmt werden.
Der Winkel zwischen den Stäben BD und AD kann als Tan-Kehrwert des Verhältnisses der Länge von AB und AD bestimmt werden.
Betrachten Sie als Nächstes Gelenk D und zeichnen Sie ein Freikörperdiagramm. Das Gelenk D besteht aus zwei bekannten und zwei unbekannten Kräften.
Löst man die Kraft im Stab BD in ihre Bestandteile auf, so können mit Hilfe der Gleichgewichtsgleichung die unbekannten Kräfte bestimmt werden.
Stäbe, die die Kräfte spüren, die vom Gelenk weg zeigen, stehen unter Spannung, während die Stäbe, die Kräfte spüren, die auf das Gelenk zeigen, unter Druck stehen.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seiten 276-277.</li>
</ol>

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methode der knoten: problem lösung i

Die Methode der Knoten ist eine häufig verwendete Technik zur Analyse der Kräfte in Tragwerken. Die Methode basiert auf dem Prinzip des Gleichgewichts, das davon ausgeht, dass die Tragwerksmitglieder durch reibungsfreie Stifte verbunden sind. Die Kräfte an jedem Knoten können bestimmt werden, indem das Gleichgewicht der auf diesen Knoten wirkenden Kräfte betrachtet wird. Betrachten Sie eine Tragwerksstruktur mit zwei Kräften von 20 N und 10 N, die an den Knoten C und D wirken. Die Methode der Knoten kann verwendet werden, um die Kräfte FCB, FDC, FDB und FAD zu bestimmen. <img alt="Figure 1" src="/files/ftp_upload/14282/14282_PT_Fig1v2.svg" style="text-align: center; height: 350px;"> Um mit der Analyse zu beginnen, wird ein Freikörperdiagramm des Knotens C betrachtet und die Bedingungen des Kräftegleichgewichts angewendet. <img alt="Equation 1" src="/files/ftp_upload/14282/PT_14282_Equation_1v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 2" src="/files/ftp_upload/14282/PT_14282_Equation_2v2.svg" style="text-align: center; height: 13px;"> Die horizontale Kraftgleichgewichtsbedingung ergibt FCB als Null. Ebenso wird die vertikale Kraftgleichgewichtsbedingung angewendet, um FDC als 20 N zu berechnen. Als Nächstes wird ein Freikörperdiagramm des Knotens D betrachtet. Der Winkel zwischen den Mitgliedern BD und AD, der mithilfe des Tangens der Verhältnisses der Längen AB und AD berechnet wird, beträgt 36,87°. Die Kraft FDB kann in ihre horizontalen und vertikalen Komponenten aufgelöst werden. Durch Anwendung der vertikalen Kraftgleichgewichtsgleichung wird FDB zu 33,33 N berechnet. Darüber hinaus ergibt sich durch das horizontale Kräftegleichgewicht die Kraft FAD als 36,67 N. Da die Kraft FDB vom Knoten weg zeigt, ist sie zugbeansprucht. Die Kraft FDC ist druckbeansprucht, da sie zum Knoten C zeigt. Auch FAD zeigt zum Knoten D und ist druckbeansprucht.

Methode der Knoten: Problem Lösung I

Die Methode der Verbindungen ist eine häufig verwendete Technik zur Analyse der Kräfte in strukturellen Fachwerken. Die Methode basiert auf dem Gleichgewichtsprinzip, das ...

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Method of Joints: Problem Solving I

truss joint force analysis by equilibrium

The method of joints uses equilibrium to find forces in structural trusses. It treats the truss members as being joined by frictionless pins. For each joint, the forces acting there must balance. That balance makes it possible to solve for the member forces one joint at a time.

Here, a truss has 20 N acting at joint C and 10 N acting at joint D. The method of joints is used to find FCB, FDC, FDB, and FAD. The analysis starts with a free-body diagram of joint C. Free-body diagram means drawing only the forces acting on one joint.

At joint C, the horizontal force equilibrium gives FCB as zero. The vertical force equilibrium then gives FDC as 20 N. Next, a free-body diagram of joint D is used. The angle between members BD and AD is found with the inverse tangent of the ratio of AB to AD, which is 36.87°.

The force FDB is split into horizontal and vertical parts. Using the vertical force equilibrium equation, FDB is 33.33 N. The horizontal force equilibrium then gives FAD as 36.67 N. Because FDB points away from the joint, it is tensile. FDC points toward joint C, so it is compressive. FAD also points toward joint D, so it is compressive.

Truss Joint Force Analysis by Equilibrium

truss-joint-force-analysis-by-equilibrium

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key terms and concepts

Use equilibrium and free-body diagrams to solve truss joint forces. Find member forces, angles, and tension or compression in a sample truss problem.

Truss Joint Force Analysis by Equilibrium | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Truss Joint Force Analysis by Equilibrium

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