Name: pipe wall thickness and bending strength
Uploaded: 2024-05-23T12:59:43.000Z
Duration: 1 min 9 s
Channel: JoVE

Considérons deux tuyaux métalliques ayant un rayon intérieur de 1,5 cm et 1 cm, respectivement, et un rayon extérieur de 1,8 cm. Si les deux tuyaux peuvent résister à une contrainte maximale de 100 mégapascals, quel sera le rapport de la valeur maximale du couple qui peut être appliqué à chaque tuyau ?
Ici, le moment d’inertie du tuyau est proportionnel à la différence entre le rayon extérieur élevé à la quatrième puissance et le rayon intérieur élevé à la quatrième puissance. Le moment d’inertie de chaque tuyau est calculé en substituant les rayons donnés.
Le moment de couple maximal autorisé requis est lié à la contrainte maximale autorisée via le moment d’inertie et la distance perpendiculaire entre l’élément le plus à l’extérieur du tuyau et l’axe neutre, qui est le rayon extérieur de chaque tuyau.
En substituant les valeurs connues, le couple maximal autorisé pour chaque tuyau peut être calculé.
La division des moments de couple maximum pour chaque tuyau donne le rapport requis.

flexion d'un matériau : résolution de problèmes

Dans cette leçon, déterminez le rapport des moments de flexion maximum appliqués à deux tuyaux métalliques, étant donné que les deux tuyaux peuvent résister à une contrainte maximale de 100 MPa. Les deux tuyaux ont un rayon extérieur de 1,8 cm. Le tuyau A, a un rayon intérieur de 1,5 cm et le tuyau B a un rayon intérieur de 1 cm. Le rapport du moment de flexion maximal appliqué à deux tuyaux métalliques, chacun ayant un rayon intérieur et extérieur différent, est déterminé en considérant leurs dimensions. Le rayon intérieur du premier tuyau est de 1,5 cm et celui du deuxième tuyau est de 1 cm.

Le moment d'inertie est donné par l'équation suivante. À l'aide de ces valeurs, calculez le moment d'inertie de chaque tuyau.

<img alt="Equation 1" src="/files/ftp_upload/15629/15629_Equation_1a.svg" style="text-align: center; height: 36px;">

<img alt="Equation 2" src="/files/ftp_upload/15629/15629_Equation_1b.svg" style="text-align: center; height: 36px;">

Le moment de flexion maximal admissible pour chaque tuyau est directement lié à la contrainte maximale, au moment d'inertie et au rayon extérieur, qui sert de distance entre l'axe neutre et la fibre externe extrême du tuyau, comme indiqué dans l'équation suivante :

<img alt="Equation 3" src="/files/ftp_upload/15629/15629_Equation_2a.svg" style="text-align: center; height: 42px;">

<img alt="Equation 4" src="/files/ftp_upload/15629/15629_Equation_2b.svg" style="text-align: center; height: 42px;">

Ensuite, le moment de flexion maximum pour chaque tuyau sera déterminé à l'aide de ces valeurs calculées. Enfin, le rapport de ces moments de flexion maximaux pour les deux tuyaux est calculé. Ce rapport indique la résistance à la torsion et la résilience comparatives de chaque tuyau sous une contrainte maximale admissible. Il met également en évidence l’effet de l’épaisseur de la paroi du tuyau sur le moment de flexion maximal dans cette situation.

Flexion d'un matériau : résolution de problèmes

Considérons deux tuyaux métalliques ayant un rayon intérieur de 1,5 cm et 1 cm, respectivement, et un rayon extérieur de 1,8 cm. Si les deux tuyaux peuvent résister à un maximum ...

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Bending of Material: Problem Solving

pipe wall thickness and bending strength

Pipe wall thickness and bending strength are compared by finding the ratio of the maximum bending moments for two metal pipes. Both pipes can withstand a maximum stress of 100 MPa. Each pipe has the same outer radius of 1.8 cm, but Pipe A has an inner radius of 1.5 cm and Pipe B has an inner radius of 1 cm.

The first step is to calculate the moment of inertia for each pipe. The moment of inertia depends on the pipe dimensions and is found using the given equation for a hollow circular section. Because the two pipes have different inner radii, they will have different moment of inertia values even though their outer radii are the same.

Next, the maximum allowable bending moment is determined from the maximum stress, the moment of inertia, and the outer radius. The outer radius gives the distance from the neutral axis to the extreme outer fiber of the pipe. Using the calculated values, the maximum bending moment for each pipe is found.

Finally, the ratio of the two maximum bending moments is calculated. This ratio shows how the pipes compare in bending strength under the same stress limit. It also shows how wall thickness affects the maximum bending moment, since the pipe with the different inner radius responds differently under maximum permissible stress.

Pipe Wall Thickness and Bending Strength

bending

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Pure bending describes how a beam bends under equal and opposite moments. It is a key idea in structural mechanics. Engineers use it to study how prismatic members, such as beams, deform under symmetrical loads without direct forces on the member. In pure bending, the beam experiences bending without axial force or shear force. This makes it possible to predict the stress pattern across the cross-section. The bending stress depends on the bending moment, the moment of inertia of the...

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Bending stress in a symmetric member comes from a prismatic member that is loaded by two couples acting in opposite directions. A couple is made of two equal and opposite forces. It creates a moment, but it does not create a resultant force. To keep the member in equilibrium, internal forces appear at any section cut. These internal forces must balance the external couples. They are resolved into normal stress and shear stress components. Normal stress acts perpendicular to the...

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Neutral Axis and Strain in Bending

A symmetric prismatic member in bending shows how neutral surfaces, strain, and stress work together. When equal and opposite couples bend the member, the straight lines on its wider faces become circular arcs centered at Point C. That curved shape helps show how deformation changes across the section. If the member is divided into tiny cubic elements, the main stress inside it is normal stress. This creates uniaxial stress conditions at any point. The bending pattern also reveals a neutral...

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bending of material: problem solving

Pipe wall thickness and bending strength are compared by finding the ratio of the maximum bending moments for two metal pipes. Both pipes can withstand a maximum stress of 100 MPa. Each pipe has the same outer radius of 1.8 cm, but Pipe A has an inner radius of 1.5 cm and Pipe B has an inner radius of 1 cm. The first step is to calculate the moment of inertia for each pipe. The moment of inertia depends on the pipe dimensions and is found using the given equation for a hollow circular section.

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Plastic Bending and the Neutral Axis

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Unsymmetrical Bending and Neutral Axis

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Curved Beam Bending and the Neutral Axis

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Curved Beam Stress and Neutral Axis

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key terms and concepts

Compare two metal pipes with different inner radii and find the ratio of their maximum bending moments using stress, moment of inertia, and outer radius.

Pipe Wall Thickness and Bending Strength | JoVE K12

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Pipe Wall Thickness and Bending Strength

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