Name: beam deflection from loads and supports
Uploaded: 2024-05-23T13:00:01.000Z
Duration: 1 min 15 s
Channel: JoVE

Un componente crucial en el diseño de vigas es la identificación y medición de la deflexión. Es necesario una comprensión completa de las deflexiones cuando se trata de vigas indeterminadas.
Considere una viga en voladizo que soporta dos cargas concentradas. Las reacciones en los apoyos se calculan analizando el diagrama de cuerpo libre de la viga.
Con el diagrama de cuerpo libre y los soportes de reacción, se construye un diagrama de momento flector, que representa cómo se dobla la viga.
El diagrama de momento flector muestra que la viga se curva hacia arriba entre el comienzo y un punto específico debido a un momento flector positivo, y se curva hacia abajo desde ese punto hasta el final de la viga debido a un momento flector negativo.
El valor más grande de la curva o el radio de curvatura más pequeño ocurre en el soporte donde el momento de flexión está en su punto más alto.
Para un análisis y diseño detallado de una viga, es crucial tener datos precisos sobre la deflexión y la pendiente de la viga en varios puntos, con un enfoque especial en la comprensión de la deflexión máxima.

deformación de una viga bajo carga transversal

Comprender la deflexión de la viga, particularmente para vigas indeterminadas con segmentos sobresalientes y múltiples cargas concentradas, es crucial para garantizar la integridad estructural y la funcionalidad. El proceso comienza con la construcción de un diagrama de cuerpo libre preciso, que ayuda a identificar las fuerzas y momentos que actúan sobre la viga. Este diagrama es vital para visualizar cómo los momentos flectores varían a lo largo de la viga, influyendo en su curvatura.

Los conocimientos del diagrama de momento flector se extienden al análisis de la curvatura de la viga. La curvatura de la viga se correlaciona con los momentos flectores a lo largo de la viga y está inversamente relacionada con la rigidez y la sección transversal de la viga. Los momentos de flexión más altos dan como resultado una mayor curvatura, lo cual es esencial para comprender el perfil de deflexión de la viga.

En particular, la atención se centra en la deflexión máxima, ya que una deflexión excesiva puede provocar problemas estructurales o incluso fallos. Esta deflexión máxima generalmente ocurre donde la curvatura es mayor, a menudo cerca de los soportes o directamente debajo de los puntos donde se aplican las cargas. Identificar esta deflexión máxima es crucial para garantizar que los diseños de vigas cumplan con los estándares de seguridad y cumplan con los requisitos funcionales. Al realizar análisis exhaustivos utilizando diagramas de cuerpo libre y de momento flector, se pueden diseñar eficazmente estructuras que sean seguras y adecuadas para condiciones de carga y requisitos arquitectónicos específicos.

Deformación de una viga bajo carga transversal

Un componente crucial en el diseño de vigas es la identificación y medición de la deflexión. Es necesaria una comprensión integral de las deflexiones ...

deformation-of-a-beam-under-transverse-loading

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Deflection of Beams

Deflexión de vigas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Deformation of a Beam under Transverse Loading

beam deflection from loads and supports

Beam deflection depends on the loads on a beam and the support conditions at its ends. For indeterminate beams, especially those with overhanging parts and multiple concentrated loads, careful analysis is needed to predict how the beam will bend.

The first step is to draw an accurate free-body diagram. A free-body diagram shows the forces and moments acting on the beam. It helps reveal how the bending moment changes along the beam length.

The bending moment diagram also shows how the beam will curve. Beam curvature is related to the bending moment and is affected by the beam’s stiffness and cross-section. When the bending moment is higher, the curvature is greater, so the deflection profile becomes easier to evaluate.

The main goal is to find the maximum deflection. Too much deflection can cause structural problems or even failure. This largest deflection often appears where curvature is greatest, such as near supports or directly under applied loads. Using free-body and bending moment diagrams helps engineers design beams that stay safe and meet functional requirements under specific loading conditions.

Beam Deflection from Loads and Supports

deformation of a beam under transverse loading

Beam deflection depends on the loads on a beam and the support conditions at its ends. For indeterminate beams, especially those with overhanging parts and multiple concentrated loads, careful analysis is needed to predict how the beam will bend. The first step is to draw an accurate free-body diagram. A free-body diagram shows the forces and moments acting on the beam. It helps reveal how the bending moment changes along the beam length. The bending moment diagram also shows how the beam...

equation of the elastic curve

Beam Deflection and Boundary Conditions

Beam deflection and boundary conditions help describe how a beam bends under load. In structural engineering, the curvature of a plane curve shows how sharply the beam bends. That curvature is found from the curve’s first and second derivatives. A cantilever beam with a point load at its free end is a common example. A diving board works like this type of beam. When slopes are small, the beam’s elastic curve becomes the main shape used in the analysis. The governing equation connects bending...

elastic curve from the load distribution

Beam Deflection Under Distributed Load

Beam deflection under distributed load is a key part of beam analysis in engineering. It helps predict how a beam bends and reacts when a load is spread along its length. Engineers use this relationship to judge whether a structure will stay safe and functional. The analysis starts with the link between load, shear force, and bending moment. These quantities can be written in differential form. When beam flexibility is treated as constant, further differentiation leads to a higher-order...

deflection of a beam

Beam Slope and Deflection by Singularity

Beam slope and deflection can be found with singularity functions when beam loading is hard to write as one simple equation. This method is useful in structural engineering because it helps describe beams under several loads without breaking the problem into many separate cases. Singularity functions are mathematical tools for showing discontinuities in a load, shear force, or bending moment equation. They are especially helpful when a load acts at a single point or over a set interval. In the...

method of superposition

Beam Deflection Under Combined Loads

Beam deflection under combined loads can be found with the method of superposition. This structural engineering method is used to analyze how multiple loads affect a beam. It works by finding the slope and deflection from each load separately, then adding those results together. The method applies only when the beam stays within its elastic limit. In that range, the material deforms in a linearly elastic way. That makes it valid to combine the effects of separate loads without changing the...

moment-area theorems

Beam Deflection Using Moment-Area Rules

The moment-area theorems help describe beam bending in structural engineering. They are often used for building floor supports and other beams under load. The theorems use the elastic curve, which is the shape a beam takes as it deforms. The first theorem links slope change to area on an M/EI diagram. Here, M is the bending moment, E is the modulus of elasticity, and I is the moment of inertia. When M/EI is plotted along the beam length, the area under the curve gives the total rotation...

beams with symmetric loadings

Moment-Area Method for Cantilever Deflection

The moment-area method is used in structural engineering to find the slope and deflection of a beam under load. It is especially useful for a cantilever beam with a concentrated load and a moment at the free end. The analysis begins with a free-body diagram. This diagram helps calculate the reactions at the fixed end. After that, the bending moment diagram is drawn to show how the bending moment changes along the beam. Points where the bending moment is zero are important in this step. Next,...

beams with unsymmetric loadings

Beam Deflection and Level Points

Beam deflection and level points can be found for a supported beam under unsymmetrical loadings using moment-area theorems. This type of analysis helps show how a beam bends when forces are spread unevenly along it. It is an important part of structural engineering because it links load patterns to beam response. The first moment-area theorem is used to find the slope at any point on the beam. It states that the change in slope between two points equals the area under the moment diagram over...

maximum deflection

Locating the Beam’s Highest Deflection

Maximum deflection in a supported beam depends on where the load is placed. With an unsymmetrical load, such as a train moving across a bridge, the beam may bend most at a point that is not the midpoint. Finding that point is important for judging stress and deflection in the structure. The point of maximum deflection is called point O. At point O, the tangent to the deflection curve is horizontal. That means the slope is zero there. To locate point O, the slope at any point X along the beam...

key terms and concepts

Learn how free-body diagrams and bending moment diagrams help predict beam deflection, identify maximum deflection, and check structural safety under load.

Beam Deflection from Loads and Supports | 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.

mechanical engineering

Beam Deflection from Loads and Supports

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