# Slope of deflection of beam at center

• fonseh
In summary, the slope of deflection of a beam at its center is a measure of how much the beam deviates from its original position when loaded. It can be calculated using the Euler-Bernoulli beam theory or numerical methods such as the finite element method. Factors such as material properties, dimensions, and loading conditions affect the slope of deflection. It is important in beam design as it can impact structural integrity and stability. The slope of deflection can be controlled through proper design, material selection, and support conditions.
fonseh

## Homework Statement

in the first photo , it's stated that the dy/dx at center = 0 , however , in the second photo (website) , it's stated that the dy/dx at the boundary = 0 ,which is correct ? I'm confused now
http://www.geom.uiuc.edu/education/calc-init/static-beam/support.html

## The Attempt at a Solution

#### Attachments

• 444.PNG
15.9 KB · Views: 386
• 445.PNG
30 KB · Views: 420
Bump

## What is the slope of deflection of a beam at its center?

The slope of deflection of a beam at its center is the measure of how much the beam deviates from its original position at the point where it is loaded. It is usually expressed in radians or degrees.

## How is the slope of deflection of a beam at its center calculated?

The slope of deflection at the center of a beam can be calculated using the Euler-Bernoulli beam theory, which takes into account the material properties, dimensions, and loading conditions of the beam. It can also be calculated using numerical methods such as the finite element method.

## What factors affect the slope of deflection of a beam at its center?

The slope of deflection of a beam at its center is affected by several factors, including the material properties of the beam, its dimensions, the type and magnitude of the load applied, and the support conditions. Higher load and longer beam length tend to result in a larger slope of deflection.

## Why is the slope of deflection important in beam design?

The slope of deflection is an important factor to consider in beam design because it can affect the structural integrity and stability of the beam. A large slope of deflection can lead to excessive stress and potentially cause failure of the beam. It is also important for ensuring that the beam can support the intended load without excessive deformation.

## Can the slope of deflection of a beam at its center be controlled?

Yes, the slope of deflection of a beam at its center can be controlled through proper beam design and selection of materials and support conditions. For example, increasing the beam's width or using a stiffer material can reduce the slope of deflection. Additionally, adding support or using different loading configurations can also help control the slope of deflection.

Replies
1
Views
1K
Replies
1
Views
2K
Replies
5
Views
3K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
18
Views
3K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
2
Views
3K