There are many reasons why the hoop longitudinal stress relationship does not always work. One reason is that the hoop stress is calculated using the assumption that the material is homogeneous and isotropic. However, many materials are not homogeneous and isotropic, and therefore the hoop stress may not be accurate. Additionally, the hoop stress relationship assumes that the material is in a state of plane stress. However, many materials are not in a state of plane stress, and therefore the hoop stress may not be accurate. Finally, the hoop stress relationship assumes that the material is linearly elastic. However, many materials are not linearly elastic, and therefore the hoop stress may not be accurate.

**Summary**Close

There can be many reasons why the hoop longitudinal stress relationship does not always work. Some possible reasons include: the material properties of the pipe may not be constant throughout the entire length of the pipe (e.g. different grades of pipe may be used in different sections); the wall thickness of the pipe may not be constant throughout its length; the pipe may not be perfectly round (e.g. it may be oval-shaped); or the pipe may not be perfectly straight. Additionally, the relationship may not work in all cases because it is only an approximate relationship and is not always accurate.

## What is the relationship between hoop and longitudinal stress?

Pipes are often subjected to both hoop stress and longitudinal stress. Hoop stress is generated when a cylinder is under internal pressure and is twice that of longitudinal stress. This means that longitudinal joints of a pipe carry twice as much stress compared to circumferential joints.

When a vessel has closed ends, the internal pressure acts on them to develop a force along the axis of the cylinder. This is known as the axial or longitudinal stress and is usually less than the hoop stress.

### On what factor longitudinal stress depends on

Yes, longitudinal stress depends upon area. The larger the area, the greater the stress. This is because the larger the area, the more force is required to deform the material.

The above equation states that the average value of the product of two random variables is equal to the product of their means. This is known as the law of averages.

## What is the nature of hoop stress and longitudinal stress?

The hoop stress and longitudinal stress induced in a thick cylinder by radial pressure will both be tensile in nature. Radial pressure is compressive in nature, but the stresses it induces in the cylinder will both tend to increase the length of the cylinder.

In a thin shell, circumferential stress is σc = Pd^2t and longitudinal stress will be half of the circumferential stress ie σl = Pd^4t. Hoop stress σh = Pd^2t = σ1.

## What does hoop stress tell you?

The hoop stress, or tangential stress, is the stress around the circumference of the pipe due to a pressure gradient. The maximum hoop stress always occurs at the inner radius or the outer radius depending on the direction of the pressure gradient.

As shown in Equations 121 and 122, the hoop stress is twice as large as the axial stress. This is because the hoop stress is caused by the pressure difference between the inside and outside of the pipe, while the axial stress is caused by the weight of the fluid in the pipe.

### What is the difference between longitudinal stress and circumferential stress

Circumferential stress is a type of stress that acts along the circumferential direction. This stress is generally tensile in nature, meaning that it tends to pull things apart. Longitudinal stress is another type of stress that acts along the length of an object. This stress is also tensile in nature, meaning that it too tends to pull things apart. Radial stress is a third type of stress that acts in the direction of the radius. This stress is compressive in nature, meaning that it tends to push things together.

The volume of a wire remains constant, when subjected to tensile stress is applied on it. If the percentage change in lateral strain is 2 %, then percentage change in longitudinal strain is 1 %.

## Is longitudinal stress an elastic constant?

Longitudinal stress is the deformation that occurs in a body when a force is applied to it. This deformation can cause the body to become elongated. Within the elastic limit, the ratio of longitudinal stress to force applied remains constant. Beyond the elastic limit, the body will deform permanently.

This is a brief note on longitudinal strain. Longitudinal strain is the stretching of an object along its length. This can only occur in solids, as they are the only medium which can maintain a constant length. This is due to the solid’s molecules being tightly packed together, meaning that they can withstand being stretched without breaking apart. liquids and gases are not able to undergo longitudinal strain as their molecules are not held together as tightly, meaning that they would break apart if force was applied to them.

### Which stress is responsible for the failure in cylindrical pressure vessel

As can be seen in Figure 2, longitudinal stress can cause failure in thin cylindrical shells. This is due to the stress being exerted along the length of the cylinder (represented by σx in Equation 4). When this stress becomes too great, the cylinder will buckle and collapse.

Hoop stress occurs when a cylindrical object is under axial compression. The hoop stress is highest at the inner radius and lowest at the outer radius.

## What are the assumptions in the analysis of thin cylinders?

Thin cylinders are usually thin-walled and are often subjected to internal pressure. In order to calculate the stresses and strains in such cylinders, a few assumptions are made. Firstly, it is assumed that the diameter of the cylinder is more than 20 times the thickness of the shell. This means that the cylinder is relatively thin and its walls are not very thick. Secondly, it is assumed that the stresses are uniformly distributed through the thickness of the wall. This means that the stresses are not concentrated in any one particular area of the wall but are evenly distributed throughout. These assumptions allow for the derivation of expressions for the stresses and strains in thin cylinders.

Circumferential stress, or hoop stress, is a normal stress in the tangential (azimuthal) direction. Axial stress is a normal stress parallel to the axis of cylindrical symmetry, and radial stress is a normal stress in directions coplanar with but perpendicular to the symmetry axis.

## Warp Up

There are a few reasons why the hoop longitudinal stress relationship does not always work. One reason is that the hoop stress is only valid for circular sections. If the cross-section is not perfectly circular, the hoop stress will be inaccurate. Additionally, the hoop stress relationship only applies to homogeneous, isotropic materials. If the material has any sort of inhomogeneity or anisotropy, the relationship will not be accurate. Finally, the relationship only applies to linear elastic materials. If the material is nonlinear or has plastic behavior, the relationship will not be valid.

Hoop stress is the term used to describe the stress that is exerted on a material when it is bent or deformed. The amount of hoop stress that is exerted on a material is dependent on the material’s cross-sectional shape, its modulus of elasticity, and the radius of the curve. While the hoop stress relationship is a good guide for estimating the amount of stress that will be exerted on a material, it is not always accurate. There are many factors that can affect the accuracy of the hoop stress relationship, such as the material’s microstructure, the type of loading, and the amount of deformation.