# Stresses in the bending of a thin walled cylinder

• mechE235
In summary, the conversation discusses the bending of a thin-walled cylinder about its neutral axis. The maximum stress at the outer fibers is Mr/I, but the speaker is looking for an expression for the load per unit circumference on a small element at the outer fibers. They ask if anyone has a solution for this, as they have forgotten a solution from a previous team member. The force required will depend on the degree and type of bending. For uniaxial bending, the stress at any point along the outside fibers is My/I, requiring the use of geometry and trigonometry to solve for a specific point or angle along the circumference.
mechE235
I am looking into the bending of a thin walled cylinder about it's neutral axis. Should be simple enough, it is just Mr/I. However, that is the maximum stress at the outer fibers of the cylinder and I want to find an approximate expression for the load per unit circumference on a small element at the outer fibers of the cylinder. Anyone have a solution for this? A member of a team where I used to work had a solution, but I forgot it.

Welcome to PF.
The force required will depend on the degree of bending, and on how you hold or apply the force to the thin walled tube. Do you want a temporary elastic bend, or will you make a permanent plastic bend?

berkeman and Bystander
For uniaxial bending, the stress at any point along the outside fibers of the circumference is My/I, where y is the perpendicular distance from the Neutral Axis to the point of interest. You’ll have to use a little geometry/ trig to solve
it in terms of a general point along the circumference, or the central angle from the center of the tube to that point.

## 1. What is a thin-walled cylinder?

A thin-walled cylinder is a type of hollow cylindrical structure with a relatively small thickness compared to its diameter. It is commonly used in engineering and construction, such as in pipes, tubes, and pressure vessels.

## 2. What are the main factors that affect stresses in the bending of a thin-walled cylinder?

The main factors that affect stresses in the bending of a thin-walled cylinder are the material properties (such as elasticity and yield strength), the dimensions of the cylinder (such as wall thickness and diameter), and the applied loads or forces.

## 3. How do you calculate stresses in the bending of a thin-walled cylinder?

The stress in the bending of a thin-walled cylinder can be calculated using the formula σ = My/I, where σ is the stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia of the cross-section of the cylinder.

## 4. What is the significance of stresses in the bending of a thin-walled cylinder?

Understanding the stresses in the bending of a thin-walled cylinder is crucial in designing and analyzing structures to ensure they can withstand the anticipated loads and forces. It also helps in identifying potential weak points or areas of failure.

## 5. How can the stresses in the bending of a thin-walled cylinder be reduced?

The stresses in the bending of a thin-walled cylinder can be reduced by increasing the wall thickness, decreasing the diameter, or using materials with higher elasticity and yield strength. Proper design and distribution of loads can also help to reduce stresses.

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