Name: critical load and structure stability
Uploaded: 2024-05-23T13:00:07.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Stability of structures

Considérons deux tiges reliées au point O par une goupille et un ressort de torsion de constante k. Les extrémités des deux tiges sont reliées par des broches.
Si les deux tiges sont parfaitement alignées et que deux charges se trouvent le long de la même ligne d’action, le système reste en équilibre.
Maintenant, si le point O est légèrement déplacé, en faisant un petit angle par rapport à la position verticale, alors deux couples agissent sur les tiges.
La première est due à la charge appliquée agissant au point O, provoquant l’éloignement de la tige de la verticale.
Le deuxième couple est dû à la constante du ressort de torsion, qui tente de ramener la tige vers la position verticale.
Si l’intensité des moments de ces deux couples est la même, une expression de charge critique est formulée.
La stabilité du système dépend de la comparaison entre la charge appliquée et la charge critique.
Si la charge appliquée dépasse la charge critique, le système devient instable. À l’inverse, si la charge appliquée est inférieure à la charge critique, le système est stable.

stabilité des structures

En génie mécanique, la stabilité des systèmes soumis à diverses forces est essentielle à la conception de structures durables et efficaces. Une manière fondamentale d'explorer ces concepts consiste à analyser des systèmes tels que deux tiges reliées en un point de pivotement, O, avec un ressort de torsion de constante de raideur k au point de pivotement. Ce système ressemble en apparence à un cric ciseaux utilisé pour changer les pneus d’une voiture. Dans ce cas, les bras du mécanisme (équivalent aux tiges de ce système) sont entièrement verticaux, correspondant au cas où le véhicule a été soulevé aussi haut que possible.

Ces tiges sont initialement positionnées verticalement et sont empêchées de pivoter sous l’action du ressort. Si deux charges externes F et F’, d’amplitude égale et de direction opposée, sont appliquées au système de telle manière qu’elles partagent la même ligne d’action sur la longueur des tiges, alors le système reste en équilibre. Cet alignement garantit qu’il n’y a pas de moment ou de couple net agissant pour déplacer le système de son état d’équilibre.

Cependant, si le point de pivotement O est légèrement déplacé latéralement, ce mouvement entraîne une légère déviation angulaire des tiges par rapport à la verticale. Cela fait tourner les extrémités de chaque tige par rapport à leurs points de pivotement, introduisant des couples dans le système. Le premier couple résulte du support de réaction au point O. Cette force, agissant désormais selon un angle, tente de déplacer davantage la tige de son orientation verticale initiale, l'éloignant ainsi de l'équilibre. Le deuxième couple, résultant de la résistance du ressort de torsion, exerce une force de rappel pour ramener la tige dans sa position verticale d'origine. Le système atteint un point de charge critique F_cr lorsque ces deux moments sont égaux. Si la charge appliquée dépasse la charge critique, le système devient instable ; si elle est inférieure à la charge critique, le système reste stable.

Ce principe est universellement applicable dans les systèmes structurels et est largement utilisé dans les conceptions mécaniques, notamment pour la stabilisation des bâtiments, des véhicules et des machines.

Stabilité des structures

Considérons deux tiges reliées au point O par une goupille et un ressort de torsion de constante k. Les extrémités des deux tiges sont reliées par des broches.
Si les deux tiges sont ...

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critical load and structure stability

Structural stability is an important idea in mechanical engineering. It helps engineers design buildings, vehicles, and machines that stay safe and efficient under load. A simple model for studying this behavior uses two rods joined at a pivot point O with a torsional spring, which is a spring that resists twisting, at the pivot.

The setup is similar to a scissor jack used to lift a car. In the example, the linkage arms are vertical, which matches the case where the vehicle has been raised as far as possible. The rods are held in that vertical position by the spring. When two equal and opposite forces, F and F', act along the same line as the rods, the system stays in equilibrium because there is no net moment, or turning effect, to move it away from that state.

If point O shifts slightly sideways, the rods tilt a little from vertical. That small change makes each rod rotate about its pin connection and creates couples, which are pairs of forces that cause rotation. One couple comes from the support reaction at O, and it pushes the rod farther from the original position. The other couple comes from the torsional spring, and it acts as a restoring force that tries to bring the rods back to vertical.

The critical load Fcr is the load at which these two moments are equal. If the applied load is below this value, the system remains stable. If the load rises above it, the system becomes unstable. This idea is useful in many structural systems and helps explain why stability matters in engineering design.

Critical Load and Structure Stability

stability of structures

Structural stability is an important idea in mechanical engineering. It helps engineers design buildings, vehicles, and machines that stay safe and efficient under load. A simple model for studying this behavior uses two rods joined at a pivot point O with a torsional spring, which is a spring that resists twisting, at the pivot. The setup is similar to a scissor jack used to lift a car. In the example, the linkage arms are vertical, which matches the case where the vehicle has been raised as...

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Critical Load and Structure Stability

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