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

Considérez une structure en treillis. Les forces F1 et F2 agissent aux points B et D.
La méthode des sections est utilisée pour déterminer les forces agissant sur quelques membres d’une ferme. Il est basé sur le principe qu’une ferme en équilibre a chacun de ses segments en équilibre.
On considère qu’un schéma à corps libre de la poutre permet de calculer les forces agissant sur les membres EF, DC et DF.
L’équation d’équilibre pour les moments autour du point A peut être utilisée pour calculer la réaction de support au point E.
Maintenant, une coupe est effectuée le long d’un plan de section coupant un maximum de trois membres.
Un schéma à corps libre de la section, en supposant que les forces inconnues sont en traction, est dessiné.
La somme des moments autour de D donne une solution pour la force agissant sur EF.
Les forces inclinées inconnues sont résolues en composantes horizontales et verticales.
La condition d’équilibre pour les forces appliquées le long des directions horizontale et verticale aboutit à deux équations.
En résolvant les équations simultanées, la force le long du courant continu et du facteur de fréquence peut être calculée.

<ol>
	<li>R. C., Hibbeler Engineering Mechanics Statics, Pearson, p. 291 à 293</li>
	<li>F.P. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, B.P. Self, Mécanique vectorielle pour les ingénieurs Statique et dynamique Génie mécanique Statique, Mc Graw-Hill Éducation. pp. 217</li>
</ol>

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méthode des sections

Considérez une structure en treillis, comme indiqué dans la figure. <img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> Forces F1 et F2 agissent aux articulations B et D, respectivement. La méthode des sections peut être utilisée pour déterminer les forces agissant sur des membres spécifiques du treillis, tels que EF, DC et DF. Cette approche est basée sur le principe qu'un treillis en équilibre a également chacun de ses segments en équilibre. Pour calculer les forces agissant sur ces membres, on considère un diagramme de corps libre du treillis. L'équation d'équilibre pour les moments autour de l'articulation A peut être appliquée pour estimer la réaction de support au point E. <img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> Une coupe est faite le long d'un plan de section qui intersecte au maximum trois membres : EF, DC et DF. Ensuite, un diagramme de corps libre de la moitié droite de la section coupée est dessiné, en supposant que les forces inconnues sont de tension. <img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;"> Une solution pour la force agissant sur le membre EF peut être obtenue en additionnant les moments autour de l'articulation D. <img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> Les forces inclinées inconnues, FDC et FDF, sont résolues en composantes horizontales et verticales. L'application de la condition d'équilibre pour les forces le long des directions horizontale et verticale donne deux équations distinctes. <img alt="Equation 3" src="/files/ftp_upload/14285/14285_PT_Equation_3v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 4" src="/files/ftp_upload/14285/14285_PT_Equation_4v2.svg" style="text-align: center; height: 13px;"> Les forces le long des membres DC et DF peuvent être estimées en résolvant ces équations simultanées.

Méthode des Sections

Considérons une structure en treillis, comme illustré sur la figure.

Les forces F1 et F2 agissent respectivement au niveau des articulations B et D. La méthode des sections peut être utilisée pour ...

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Method of Sections

truss member force analysis by sections

Truss member force analysis by sections finds the force in selected members of a truss. In this problem, forces F1 and F2 act at joints B and D. The goal is to determine the forces in members EF, DC, and DF.

The method uses the idea that a truss in equilibrium also has each of its sections in equilibrium. A free-body diagram of the whole truss is drawn first. The moment equation about joint A is then used to estimate the support reaction at point E.

Next, a cut is made along a sectional plane that passes through no more than three members. Here, the cut intersects EF, DC, and DF. A free-body diagram of the right side of the cut section is then drawn, and the unknown member forces are assumed to be tensile, or pulling away from the cut.

The force in member EF is found by summing moments about joint D. The inclined forces in members DC and DF are then split into horizontal and vertical parts. Finally, equilibrium in the horizontal and vertical directions gives two equations, and solving them gives the forces in DC and DF.

Truss Member Force Analysis by Sections

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Learn how the method of sections uses free-body diagrams, moments, and force balance to find unknown forces in truss members EF, DC, and DF.

Truss Member Force Analysis by Sections | JoVE K12

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Truss Member Force Analysis by Sections

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