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

Considérons une structure en treillis où deux forces agissent au niveau des joints C et D, reliées par des joints sans frottement. Déterminez les forces dans chaque élément de treillis et identifiez la tension ou la compression dans chaque élément de treillis.
La méthode des assemblages peut être utilisée pour déterminer toutes les forces agissant sur chaque articulation.
L’analyse commence par l’articulation C car elle a le moins de forces inconnues.
Dessinez un schéma du corps libre de l’articulation C. À l’aide des équations d’équilibre, les forces inconnues peuvent être déterminées.
L’angle entre les éléments BD et AD peut être déterminé comme l’inverse tangueux du rapport de la longueur de AB et AD.
Ensuite, considérez l’articulation D et dessinez un schéma de corps libre. L’articulation D se compose de deux forces connues et de deux forces inconnues.
Résolvez la force dans l’élément BD en ses composantes, et en utilisant l’équation d’équilibre, les forces inconnues peuvent être déterminées.
Les éléments subissant les forces pointant vers l’opposé de l’articulation sont en tension, tandis que les éléments subissant des forces pointant vers l’articulation sont en compression.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 276 et 277.</li>
</ol>

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méthode des nœuds : résolution de problème i

La méthode des nœuds est une technique couramment utilisée pour analyser les forces dans les treillis structuraux. La méthode est basée sur le principe d'équilibre, qui suppose que les membres du treillis sont reliés par des pivots sans frottement. Les forces à chaque nœud peuvent être déterminées en considérant l'équilibre des forces agissant sur ce nœud. Considérons une structure de treillis avec deux forces de 20 N et 10 N agissant respectivement sur les nœuds C et D. La méthode des nœuds peut être utilisée pour déterminer les forces FCB, FDC, FDB et FAD. <img alt="Figure 1" src="/files/ftp_upload/14282/14282_PT_Fig1v2.svg" style="text-align: center; height: 350px;"> Pour commencer l'analyse, on considère un diagramme de corps libre du nœud C , et les conditions d'équilibre des forces sont appliquées. <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;"> La condition d'équilibre des forces horizontales donne FCB égal à zéro. De même, la condition d'équilibre des forces verticales est appliquée pour calculer FDC comme étant de 20 N. Ensuite, on considère un diagramme de corps libre du nœud D. L'angle entre les membres BD et AD, calculé à l'aide de la tangente inverse du rapport des longueurs de AB et AD, est de 36.87°. La force FDB peut être décomposée en ses composantes horizontale et verticale. En appliquant l'équation d'équilibre des forces verticales, FDB est calculée à 33.33 N. De plus, l'équilibre des forces horizontales donne une force FAD de 36.67 N. Comme la force FDB pointe loin du nœud, elle est de tension. La force FDC est compressive car elle pointe vers le nœud C. De même, FAD pointe vers le nœud D et est compressive.

Méthode des nœuds : Résolution de problème I

La méthode des joints est une technique couramment utilisée pour analyser les forces dans les fermes structurelles. La méthode est basée sur le principe de l’équilibre, qui ...

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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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method of joints: problem solving i

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...

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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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