# Support reactions, castigliano's second.

• kantti
In summary, the conversation discusses determining the support reactions for a given structure using Castigliano's second theorem. The focus is on flexural deformations, with negligible axial deformations. The equations used involve differentiating with respect to displacement, and replacing it with support reactions. The conversation also mentions the importance of not assuming the right hand reaction to be P/2, as the structure is statically indeterminate. It is recommended to obtain all the reactions and check external equilibrium before attempting the integrals.
kantti

## Homework Statement

Determine the support reactions for the given structure(see attachment) due to flexural deformations using castigliano's second theorem. Axial deformations are considered negilible.

delta = dU / dP

## The Attempt at a Solution

See attachment. I could use some advice on how to continue. Thanks.

#### Attachments

• _DSC00022.jpg
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in such questions u don't have to differentiate with respect to force...do it with respect to displacement...n then by using relations replace it with the support reactions..

It would help if you didn't assume that the Right hand reaction was P/2. It is less than that because the encastre support at A attracts load to it, this being a statically indeterminate structure. Have you obtained all the reactions and checked external equilibrium before starting all those integrals?

## What is the concept of support reactions?

The concept of support reactions refers to the forces exerted by a structure's supports in order to keep it in equilibrium. These reactions are typically denoted as either vertical or horizontal forces, and they are essential in calculating the overall stability and strength of a structure.

## How are support reactions calculated?

Support reactions are typically calculated using equations of equilibrium, which state that the sum of all forces acting on a structure must equal zero. These equations take into account the geometry and material properties of the structure, as well as any external loads or forces.

## What is Castigliano's second theorem?

Castigliano's second theorem is a mathematical concept that allows engineers to calculate the deflection of a structure at a specific point by using the partial derivative of the strain energy with respect to the applied load. It is often used in conjunction with support reactions to determine the overall stability and strength of a structure.

## What are the assumptions made when using Castigliano's second theorem?

When using Castigliano's second theorem, it is assumed that the structure is linearly elastic, meaning that it follows Hooke's law. Additionally, the structure must be statically determinate, meaning that the number of unknown forces must be equal to the number of equilibrium equations.

## How is Castigliano's second theorem used in real-world applications?

Castigliano's second theorem is commonly used in structural engineering to determine the deflection of beams, frames, and other structures under various loads. It is also used in fields such as aerospace engineering and mechanical engineering to analyze the stability and strength of complex structures.

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