Name: finding zero-force members in trusses
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 30 s
Channel: JoVE

Un élément de poutrelle qui ne subit aucune contrainte dans des conditions de charge est appelé un élément à force nulle.
Pour un assemblage de treillis avec deux éléments non colinéaires et sans charge externe ou réaction de support, les deux membres doivent être des éléments à force nulle.
Un schéma de corps libre est dessiné pour cette articulation. La somme des forces le long de la direction verticale est égale à zéro, ce qui rend la force le long de BA nulle. En utilisant l’équation d’équilibre le long de la direction horizontale, la force le long de BC est égale à zéro.
Pour une articulation à trois éléments, dont deux éléments colinéaires, le troisième élément est un élément à force nulle, à condition qu’aucune charge externe ou réaction d’appui ne soit appliquée à cet assemblage.
Encore une fois, en dessinant un diagramme de corps libre et en appliquant les conditions d’équilibre statique, on prouve que la force le long de CA est nulle.
Considérons une ferme avec un support de rouleau et de goupille et une charge externe au niveau du joint E.
Les articulations à trois membres, dont deux membres colinéaires, sont identifiées. La condition de force nulle au niveau de ces articulations implique que FG, EH et FD sont des membres à force nulle.
Cependant, ED ne peut pas être un membre à force nulle en raison de la charge externe.

<ol>
	<li>R. C., Hibbeler Engineering Mechanics Statics, Pearson. p. 282</li>
</ol>

Aucun conflit d’intérêts n’a été déclaré.

membre à force nulle

Un treillis est une structure composée de membres minces reliés à leurs extrémités par des joints. Les treillis sont largement utilisés en génie et en architecture pour stabiliser et renforcer des structures telles que des ponts, des toits et des tours. Les membres du treillis sont conçus pour supporter des charges par tension et compression, permettant ainsi au treillis de résister aux forces externes. Un concept essentiel dans la conception d'un treillis est l'idée de membres à force nulle. Cela fait référence à un membre du treillis qui ne subit aucune contrainte dans des conditions de charge. Lors de l'analyse d'un treillis, certains membres peuvent avoir une force nulle, indiquant qu'ils ne contribuent pas à la capacité portante globale de la structure. Identifier les membres à force nulle est essentiel pour optimiser la conception des structures en treillis. Il existe deux conditions pour l'existence de membres à force nulle. Premièrement, si deux membres non colinéaires forment un joint de treillis et qu'aucune charge externe ou réaction de soutien n'est appliquée à un joint, les deux membres doivent être des membres à force nulle. Deuxièmement, si trois membres forment un joint de treillis et que deux sont colinéaires, le troisième membre est un membre à force nulle, à condition qu'aucune force externe ou réaction de soutien n'ait une composante qui agit le long de ce membre. <img alt="Figure 1" src="/files/ftp_upload/14284/14284_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> Considérons un treillis avec un appui à rouleau et un appui à pivot et une charge externe au niveau du joint E. Ici, les joints H et G sont des joints à trois membres avec deux membres colinéaires. En appliquant la deuxième condition, EH et FG sont des membres à force nulle. En utilisant la condition de force nulle sur le joint F, DF est un membre à force nulle. Cependant, en raison de la charge externe, ED ne peut pas être un membre à force nulle. Les membres à force nulle sont essentiels pour maintenir la stabilité et l'équilibre du treillis, optimiser la conception structurale et réduire les coûts de matériaux et de construction.

Membre à force nulle

Une ferme est un cadre composé d’éléments minces reliés à leurs extrémités par des joints. Les fermes sont largement utilisées dans l’ingénierie et l’architecture pour ...

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Zero-Force Member

finding zero-force members in trusses

Trusses are frameworks made of slender members that connect at their ends by joints. Engineers and architects use them to stabilize and strengthen structures such as bridges, roofs, and towers. Truss members carry loads through tension and compression so the structure can handle external forces.

A key part of truss analysis is spotting zero-force members. A zero-force member is a truss member that carries no stress under loading conditions. During analysis, some members may show zero force, which means they do not add to the load-bearing capacity of the structure. Finding these members helps improve the design of truss structures.

There are two common conditions for zero-force members. If only two non-collinear members meet at a joint, and no external load or support reaction acts on that joint, both members are zero-force members. If three members meet at a joint and two are collinear, the third member is a zero-force member, as long as no external force or support reaction has a component along that member.

A truss with a roller and pin support and an external load at joint E shows how these rules work. Joints H and G each have three members with two collinear members, so EH and FG are zero-force members. At joint F, the same idea makes DF a zero-force member. ED is not a zero-force member because the external load affects it.

Zero-force members are important for truss stability and equilibrium. They also help optimize structural design. In many cases, identifying them can reduce material use and construction cost.

Finding Zero-Force Members in Trusses

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Trusses are frameworks made of slender members that connect at their ends by joints. Engineers and architects use them to stabilize and strengthen structures such as bridges, roofs, and towers. Truss members carry loads through tension and compression so the structure can handle external forces. A key part of truss analysis is spotting zero-force members. A zero-force member is a truss member that carries no stress under loading conditions. During analysis, some members may show zero force,...

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key terms and concepts

Learn how to identify zero-force members in trusses using joint rules, with a worked example that shows how they affect design and cost.

Finding Zero-Force Members in Trusses | 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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Finding Zero-Force Members in Trusses

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