Name: sizing beams for safe bending loads
Uploaded: 2024-05-23T12:59:46.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

Design of Prismatic Beams for Bending

Le processus de conception des poutres prismatiques soumises à la flexion commence par la détermination de la contrainte admissible pour le matériau choisi.
La contrainte admissible est généralement obtenue à partir d’un tableau des propriétés des matériaux ou des spécifications de conception. Alternativement, il peut être calculé en divisant la résistance finale du matériau par un facteur de sécurité approprié.
Ensuite, les diagrammes de force de cisaillement et de moment de flexion correspondant aux conditions de charge spécifiées sont dessinés.
Ensuite, la valeur absolue maximale du moment de flexion est calculée à l’aide du diagramme de force de cisaillement.
Le module de section minimum admissible est ensuite calculé à l'aide de la valeur absolue du moment de flexion et de la contrainte admissible de la poutre.
Lorsqu’une poutre en bois est conçue, le rapport caractérisant la forme de sa section transversale est généralement spécifié. Les dimensions inconnues sont identifiées à l’aide de la relation entre les dimensions de la poutre et le module de section.
Lors de la conception d’une poutre en acier laminé, un tableau contenant les propriétés de la poutre en acier laminé est référencé, et seules les sections de poutre dont le module de section est supérieur ou égal au module de section minimum requis sont prises en compte.

conception de poutres prismatiques pour le pliage

La conception des poutres prismatiques, éléments structurels à section transversale uniforme, vise à garantir la sécurité et l’intégrité structurelle sous charge. Le processus de conception commence par déterminer la contrainte admissible, soit à partir des tableaux de propriétés des matériaux, soit en divisant la résistance ultime du matériau par un facteur de sécurité. Ce facteur de sécurité est essentiel pour tenir compte des incertitudes et varie en fonction du matériau (bois, acier ou béton), chacun ayant des caractéristiques de résistance et de contrainte uniques. Sa valeur dépendra du matériau choisi et de l’usage prévu de la structure.

Ensuite, tracez des diagrammes de force de cisaillement et de moment de flexion pour visualiser la répartition des charges et identifier les points de contrainte de flexion maximale. Cette visualisation est essentielle pour optimiser les dimensions de la poutre afin de maximiser la sécurité et l'efficacité de la poutre.

Enfin, calculez le module de section minimum qui permettra à la poutre de résister aux contraintes de flexion. Des modules plus élevés indiquent une plus grande résistance. Pour les poutres en bois, le concepteur spécifie un rapport de forme de section transversale qui produira le module souhaité. Pour les poutres en acier, le concepteur sélectionne parmi les sections préexistantes, garantissant que le module de la poutre dépasse le minimum calculé. Cette sélection garantit que la poutre peut résister aux forces de flexion, tout en maintenant la sécurité et la stabilité structurelles.

Cette approche systématique combine les considérations de sécurité avec l'analyse des matériaux et des charges, garantissant que la poutre choisie maintient l'intégrité et la fiabilité de la structure sous les charges anticipées, garantissant ainsi les performances structurelles à long terme.

Conception de poutres prismatiques pour le pliage

Le processus de conception des poutres prismatiques soumises à la flexion commence par la détermination de la contrainte admissible pour le matériau choisi.
La contrainte admissible est de ...

Education

Enseignement

JoVE Core

Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Analysis and Design of Beams for Bending

Analyse et conception des poutres soumises à la flexion

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

sizing beams for safe bending loads

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable.

The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material and the intended use of the structure.

Timber, steel, and concrete each have different strength and stress behavior, so the design method depends on the material. After selecting the material, the designer plots shear force and bending moment diagrams. These diagrams show how the load is distributed and help locate the points where bending stress is highest.

The final step is to calculate the minimum section modulus needed to resist bending stress. A higher section modulus means greater resistance to bending. For timber beams, the designer chooses a cross-section shape ratio that gives the needed modulus. For steel beams, the designer selects a standard section whose modulus is at least as large as the calculated minimum. This process helps the beam carry bending forces safely and maintain structural integrity over time.

Sizing Beams for Safe Bending Loads

design of prismatic beams for bending

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable. The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material...

prismatic beams: problem solving

Timber Beam Design Under Distributed Load

Timber beam design under a distributed load uses the beam’s size and the wood’s properties to keep the structure safe. The beam’s length and width are known at the start. The timber’s grade and species also matter because they affect the allowable stress, which is the highest stress the material can safely handle. The first step is to treat the beam as a free body. A free-body diagram shows the forces and moments acting on the beam. From this, the support reactions can be found by balancing...

singularity functions for shear

Beam Shear Diagrams with Macaulay Brackets

Beam shear diagrams can be written with singularity functions when the load changes suddenly along the beam. In structural analysis, these functions help show discontinuous shear force with one mathematical expression, even when the loading is complex. They make it easier to describe how shear changes from one point to the next. The method starts with a free-body diagram of the beam. Then the beam is cut at specific points to check the shear force in each section. For a beam with width W and...

singularity functions for bending moment

Beam Load Modeling with Singularity Functions

Singularity functions help model beam loads and bending moments when the loading changes along the beam. They make it possible to write the bending moment with one mathematical expression instead of separate equations for each section. In this method, Macaulay’s brackets are often used to show where a load starts or stops. For a simply supported beam AB, the load is uniform from the midpoint M to the right support B. To find the bending moment, the beam is cut at different points. A cut...

key terms and concepts

Learn how prismatic beams are sized for bending by finding allowable stress, using shear and moment diagrams, and choosing the right section modulus.

Sizing Beams for Safe Bending Loads | JoVE K12

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Sizing Beams for Safe Bending Loads

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