Name: cantilever beam yield and failure
Uploaded: 2024-05-23T12:59:50.000Z
Duration: 1 min 19 s
Channel: JoVE

Una viga en voladizo, cuando se somete a una carga en su extremo libre, desarrolla el máximo momento flector en su extremo fijo.
Hasta que el momento flector supere el límite elástico de la viga, la tensión normal permanece por debajo del límite elástico. Más allá de este punto, el rendimiento se inicia desde el extremo fijo.
El límite entre las zonas elástica y plástica se puede obtener midiendo el espesor medio del núcleo elástico.
Cuando la carga alcanza un cierto umbral, la sección cerca del extremo fijo se vuelve completamente plástica, formando una bisagra de plástico. Esta bisagra representa la carga máxima que puede soportar la viga.
En una sección parcialmente plástica, las tensiones normales en las caras se distribuyen uniformemente y son iguales al límite elástico.
La fuerza de corte en la cara inferior es cero, lo que da como resultado un valor promedio cero de la tensión de corte. El corte vertical se distribuye completamente sobre la parte elástica de la sección transversal.
A medida que disminuye el área de la porción elástica, el esfuerzo cortante máximo aumenta y finalmente alcanza el límite elástico, lo que contribuye a la falla final de la viga.

deformaciones plásticas

Plastic Deformations

La deformación plástica representa un concepto fundamental en la ciencia de los materiales, que explica el cambio irreversible en la forma de un material cuando experimenta tensiones más allá de su capacidad elástica. Este fenómeno es importante en ingeniería estructural, especialmente en el diseño y análisis de vigas en voladizo (estructuras que están fijadas de forma segura en un extremo y soportan cargas en el extremo opuesto). Cuando estas vigas se someten a cargas dentro de su rango elástico, volverán a su forma original cuando se retire la carga, demostrando la propiedad de elasticidad. Sin embargo, superar este límite elástico conduce a la deformación plástica, que se inicia en el extremo fijo debido al momento de flexión máximo y se manifiesta como una curvatura permanente conocida como "bisagra plástica".

A medida que aumenta la carga, la bisagra plástica se extiende progresivamente hacia el extremo libre de la viga, marcando la transición de una deformación reversible a una irreversible. Este cambio también altera la distribución de tensiones dentro de la viga desde un patrón uniforme, directamente proporcional a la carga aplicada, a una disposición más compleja que define el límite elástico del material. La carga continua resultará en la fractura de la viga.

Comprender el concepto de deformación plástica es vital a la hora de diseñar estructuras que deben ser seguras y económicamente viables. Es crucial garantizar que estas estructuras puedan soportar las cargas previstas.

Deformaciones Plásticas

Una viga en voladizo, cuando se somete a una carga en su extremo libre, desarrolla el máximo momento flector en su extremo fijo.
Hasta que el momento de flexión supera el ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Shearing Stresses in Beams and Thin-Walled Members

Esfuerzos cortantes en vigas y elementos de pared delgada

shearing-stresses-in-beams-and-thin-walled-members

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

cantilever beam yield and failure

Cantilever beams show how a material bends, yields, and can eventually fail under load. A cantilever beam is fixed firmly at one end and loaded at the other end. When the load stays within the elastic range, the beam returns to its original shape after the load is removed. That reversible behavior is called elasticity.

If the load goes beyond the elastic limit, the beam begins plastic deformation. Plastic deformation means the shape change is permanent. In a cantilever beam, this change starts at the fixed end because the bending moment is greatest there. The bent region at that point is called a plastic hinge.

As the load increases, the plastic hinge spreads toward the free end of the beam. This marks the shift from reversible deformation to irreversible deformation. The stress pattern in the beam also changes. It no longer stays uniform and directly proportional to the applied load, and this change helps define the yield point of the material.

If loading continues, the beam will fracture. Knowing how cantilever beams behave under stress is important in structural engineering. It helps engineers design structures that are safe and still economical. These structures must be able to handle the loads they are expected to carry.

Cantilever Beam Yield and Failure

shear on the horizontal face of a beam element

shear-on-the-horizontal-face-of-a-beam-element

Beam Shear Flow from Bending Moments

Beam shear flow comes from the horizontal shear that acts on a prismatic beam element. The element is also acted on by vertical shear forces and normal forces. To study this behavior, the beam is divided into upper and lower sections by the neutral axis. The force balance on the small element is written with an equilibrium equation. That step reveals the horizontal shearing force. This force is tied to the bending moments and to the cross-section’s first moment of inertia. The same result is...

distribution of stresses in a narrow rectangular beam

distribution-of-stresses-in-a-narrow-rectangular-beam

Shearing Stress Pattern in a Narrow Beam

Shearing stress in a narrow rectangular beam is found by studying a small elemental section of the beam. The average shearing stress on that face is calculated by dividing the shear by the surface area. This gives a simple way to describe how the load is spread through the beam. The shearing stresses on the beam&amp;#39;s transverse and horizontal planes match each other. That means the stress pattern is consistent in the upper region of the beam. Shearing stress is also absent at the top and...

shearing stresses in a beam: problem solving

shearing-stresses-in-a-beam-problem-solving

Beam Shear Stress Analysis and Safety Check

Beam shear stress analysis shows how loads create internal stress in a cantilever beam with a rectangular cross-section. The beam in this problem carries both a distributed load and a point load. The goal is to find the shearing stress at key points and check whether the beam stays within a safe limit. The first step is to identify all loads acting on the beam. Next, the reactions at the fixed end are found using equilibrium equations. The vertical reaction combines the distributed load and...

plastic deformations

Cantilever beams show how a material bends, yields, and can eventually fail under load. A cantilever beam is fixed firmly at one end and loaded at the other end. When the load stays within the elastic range, the beam returns to its original shape after the load is removed. That reversible behavior is called elasticity. If the load goes beyond the elastic limit, the beam begins plastic deformation. Plastic deformation means the shape change is permanent. In a cantilever beam, this change starts...

unsymmetric loading of thin-walled members

unsymmetric-loading-of-thin-walled-members

Shear Center in Thin-Walled Members

Thin-walled members with non-symmetrical cross-sections are widely used in engineering structures because they save material while still providing strength. Their shape helps with structural integrity, but it also makes load analysis more complex. When these members are loaded in an unsymmetrical way, the stress is not spread evenly. Unsymmetrical loading can make a member bend and twist at the same time. That combined action can lead to deformation or even structural failure. Engineers must...

unsymmetric loading of thin-walled members: problem solving

unsymmetric-loading-of-thin-walled-members-problem-solving

Finding the Shear Center of a Channel Section

Finding the shear center of a channel section starts with the member’s shear force and moments of inertia. A shear center is the point where a load must act so the section bends without twisting. For a channel with uniform thickness, height, and width, the distance to this point can be calculated from the section geometry. The first step is to compute the shear flow at a set distance from the end of the flange. Shear flow is the force per unit length along the wall of the section. It is found...

key terms and concepts

Learn how a cantilever beam bends under load, forms a plastic hinge at the fixed end, reaches yield, and can fracture if loading continues.

Cantilever Beam Yield and Failure | 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.

Cantilever Beam Yield and Failure

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