Name: shearing stress pattern in a narrow beam
Uploaded: 2024-05-23T12:59:49.000Z
Duration: 1 min 11 s
Channel: JoVE

Se considera una sección elemental de una viga para analizar la distribución de las tensiones. La magnitud de la fuerza cortante ejercida sobre la cara horizontal del elemento se obtiene a partir de la expresión de cortante horizontal.
El esfuerzo cortante promedio en esa cara se determina dividiendo el corte horizontal por el área de la cara.
Los esfuerzos cortantes en los planos transversal y horizontal de la sección de la viga son iguales, representando el esfuerzo medio a lo largo de la línea en la parte superior de la viga. Los esfuerzos cortantes son cero en las caras superior e inferior, ya que no se ejercen fuerzas.
En una viga rectangular estrecha, el esfuerzo cortante a lo largo del ancho de la sección de la viga varía menos del 0,8% del esfuerzo cortante promedio, ya que el ancho es menos de un cuarto de su profundidad.
Por lo tanto, la ecuación de esfuerzo cortante promedio se utiliza para determinar el esfuerzo cortante en cualquier punto a lo largo de su sección transversal.
En la sección transversal de la viga rectangular, los esfuerzos cortantes se distribuyen parabólicamente, con esfuerzos cero en la parte superior e inferior.

distribución de tensiones en una viga rectangular estrecha

Distribution of Stresses in a Narrow Rectangular Beam

Al estudiar la distribución de tensiones de una viga, es esencial examinar una sección elemental. Para determinar el esfuerzo cortante promedio en esta cara, el corte calculado se divide por el área de la superficie. Es importante destacar que los esfuerzos cortantes en los planos transversal y horizontal de la viga se reflejan entre sí, lo que indica una distribución consistente de los esfuerzos a lo largo de la región superior de la viga. En particular, los esfuerzos cortantes están ausentes en las superficies superior e inferior de la viga debido a la ausencia de fuerzas aplicadas en estas áreas.

Para vigas con una sección transversal rectangular estrecha, la variación del esfuerzo cortante a lo largo del ancho es mínima, menos del 0,8% del esfuerzo promedio. Esta variación menor se atribuye a que el ancho de la viga es significativamente menor que su profundidad, lo que hace que la ecuación del esfuerzo cortante promedio sea un método confiable para evaluar la tensión en cualquier punto de la sección transversal de la viga. En la sección transversal de la viga rectangular, los esfuerzos cortantes se distribuyen de forma parabólica. Esta distribución presenta tensión cero en los bordes superior e inferior de la viga, con una tensión que aumenta hacia el centro. Este perfil de tensiones parabólicas es esencial para comprender cómo las vigas gestionan las tensiones, asegurando su integridad estructural y la capacidad de soportar cargas sin comprometer la estabilidad.

Distribución de tensiones en una viga rectangular estrecha

Se considera una sección elemental de una viga para analizar la distribución de las tensiones. La magnitud de la fuerza de cizallamiento ejercida sobre la ...

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

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

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 bottom surfaces, because no applied forces act there.

For a narrow rectangular cross-section, the change in shearing stress across the width is very small. It is less than 0.8% of the average stress. Because the beam is much wider in depth than in width, the average shearing stress equation works well at any point in the cross-section.

Across the rectangular beam&amp;#39;s transverse section, the shearing stress follows a parabolic shape. A parabolic distribution curves upward from the edges to the center. Stress is zero at the top and bottom edges and rises toward the middle. This pattern helps explain how beams carry load while staying structurally stable.

Shearing Stress Pattern in a Narrow Beam

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

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 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...

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

Explore how shearing stress changes across a narrow rectangular beam, including zero stress at the edges and a parabolic distribution toward the center.

Shearing Stress Pattern in a Narrow Beam | 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.

Shearing Stress Pattern in a Narrow Beam

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