Name: truss force analysis at joints a to e
Uploaded: 2023-09-22T11:49:24.000Z
Duration: 1 min 30 s
Channel: JoVE

Envisagez une structure en treillis avec des joints sans frottement fixés à un mur et un support à rouleaux au sol. Si une force de 150 N est appliquée à l’articulation A, déterminez les forces dans chaque membre de la ferme.
Les forces à chaque articulation peuvent être déterminées à l’aide de la méthode des articulations.
Tout d’abord, l’angle entre les membres AC et AB peut être déterminé comme l’inverse tan du rapport de la longueur de BC et AB.
Deuxièmement, dessinez un schéma de corps libre de l’articulation A et résolvez les forces en leurs composantes. En appliquant les équations d’équilibre, les forces inconnues peuvent être déterminées.
Ensuite, en dessinant les diagrammes à corps libre des articulations B et C, et en utilisant des équations d’équilibre, les forces inconnues aux articulations B et C peuvent être déterminées.
Enfin, dessinez un schéma du corps libre des articulations D et E. Pour les membres CD et EF, résolvez les forces en composantes horizontales et verticales. Les forces inconnues aux articulations D et E peuvent être déterminées à l’aide des équations d’équilibre.

<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 problèmes ii

Considérons une structure en treillis avec des joints sans friction fixés à un mur et un support à rouleaux. Si une force de 150 N est appliquée au joint A, les forces dans chaque élément du treillis peuvent être déterminées en utilisant la méthode des nœuds.

<img alt="Figure 1" src="/files/ftp_upload/14283/14283_PT_Fig_1v2.svg" style="text-align: center; height: 350px;">

L'angle entre les éléments AC et AB peut être trouvé en prenant la tangente inverse du rapport des longueurs de BC et AB, et le résultat obtenu est de 67.38°. Un diagramme des forces appliquées sur le joint A est considéré, et toutes les forces inconnues sont résolues en leurs composantes respectives.

La condition d'équilibre des forces verticales peut ensuite être utilisée pour calculer la force agissant sur l'élément CA, qui est égale à 173.08 N.

<img alt="Equation 1" src="/files/ftp_upload/14283/14283_PT_Equation_1v2.svg" style="text-align: center; height: 15px;">

De même, la condition d'équilibre des forces horizontales peut être utilisée pour trouver la force FAB qui est égale à 161.54 N.

<img alt="Equation 2" src="/files/ftp_upload/14283/14283_PT_Equation_2v2.svg" style="text-align: center; height: 15px;">

Des diagrammes des forces appliquées sur les joints B et C sont considérés, et les conditions d'équilibre des forces verticales et horizontales sont appliquées pour calculer les forces inconnues FBD, FCD et FEC. Les valeurs obtenues pour FBD, FCD et FEC sont respectivement de 161.53 N, 173.08 N et 207.70 N.

Finalement, des diagrammes des forces appliquées sur les joints D et E sont considérés, et les conditions d'équilibre des forces verticales et horizontales sont appliquées. Cela donne les valeurs de FED et FDF qui sont respectivement de 138.46 N et 265.39 N.

Méthode des nœuds: Résolution de problèmes II

Considérez une structure en treillis avec des joints sans frottement fixés à un mur et un support à rouleaux. Si une force de 150 N est appliquée à l’articulation A, les forces dans chaque ...

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Method of Joints: Problem Solving II

truss force analysis at joints a to e

Truss force analysis at joints A to E uses the method of joints to find the force in each member. The truss has frictionless joints, a wall support, and a roller support. A 150 N force is applied at joint A, and the member forces are solved from joint to joint.

First, the angle between members AC and AB is found using the inverse tangent of the ratio of BC to AB. This gives an angle of 67.38°. A free-body diagram of joint A is then drawn, and each unknown force is split into vertical and horizontal components.

The vertical force equilibrium equation is used to find the force in member CA, which is 173.08 N. The horizontal force equilibrium equation gives the force in member AB as 161.54 N. Free-body diagrams for joints B and C are then used to continue the calculation.

At joints B and C, the vertical and horizontal equilibrium conditions are applied again. This gives FBD = 161.53 N, FCD = 173.08 N, and FEC = 207.70 N. Free-body diagrams of joints D and E are used last, and the same equilibrium steps give FED = 138.46 N and FDF = 265.39 N.

Truss Force Analysis at Joints A to E

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key terms and concepts

Use the method of joints to solve truss forces at joints A to E. Find member forces from free-body diagrams, angles, and equilibrium equations.

Truss Force Analysis at Joints A to E | JoVE K12

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Truss Force Analysis at Joints A to E

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