# Airys stress function -- structures

• praveenpandiyan
In summary, the conversation discusses the stress function for a simply supported beam with a concentrated load at the mid-span. The loading condition for the stress function is satisfied and the concentrated load is treated as a shear stress and integrated to determine the value of the stress function. The boundary conditions for the stress function are specified as (sigma)yy=0 for y=h to -h and (tou)xy=0 at y=(-h, h). One more boundary condition is needed to remove constants in the stress function.

## Homework Statement

For (fi)= (b/6) x*y3 +C*xy show that simply supported beam of 2L loaded concentrated load at mid span.,the stress function satisfy loading condition is (fi) .treat concentrated load as shear stress suitably distributed to shoot this function. so that intergtal of limit (h to -h) for stress stress (tou)xy= (-W/2) ..

see attachment

## The Attempt at a Solution

boundary conditions 1. (sigma)yy=0 for y =h to -h
to remove constants in stress function i need one more boundary condition .. ?? any help ll be apreciated . thanks

#### Attachments

• WP_20150113_001.jpg
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i found other boundary condition too ..beam shear stess (tou)xy=o at y=(-h &=+h)..thanks anyway ..

## 1. What is Airys stress function and how is it used in structural analysis?

Airys stress function is a mathematical function used in structural analysis to represent the state of stress in a two-dimensional region. It is a solution to the governing equations of elasticity and is used to determine the stress components in a structure.

## 2. How is the Airys stress function related to the strain energy of a structure?

The Airys stress function is related to the strain energy of a structure through the principle of minimum potential energy. This principle states that the stress function must be chosen in a way that minimizes the total potential energy of the structure.

## 3. Can the Airys stress function be used for three-dimensional structures?

No, the Airys stress function is only applicable to two-dimensional structures. It cannot be extended to three-dimensional structures due to the complexity of the governing equations of elasticity in three dimensions.

## 4. How is the Airys stress function solved for in structural analysis?

The Airys stress function is typically solved for using the boundary conditions and compatibility equations of the structure. These equations can be derived from the equilibrium equations and the constitutive relationships of the material.

## 5. What are the advantages and limitations of using the Airys stress function in structural analysis?

The main advantage of using the Airys stress function is that it provides a convenient and efficient way to solve for stress components in a structure. However, it is limited to two-dimensional structures and cannot account for stress concentrations or material nonlinearities.