# Difference between Linear and Cubic Deformation in Bending?

• olski1
In summary, the difference between linear and cubic displacement deformation functions in beam bending lies in their shape and the resulting bending behavior, with the choice depending on the material properties of the beam.
olski1
I do not really understand this as you can probably tell, but What is the difference bewteen Linear and Cubic displacement deformation functions in beam bending? For example why would one be used over another to model or calculate beam bending? or how does either type effect what bending behaviour will occur?

All my notes just state we will assume linear or cubic for each example, so is it just the intrinsic properties of the material that determine the deformation function. For example is steel more likely to have a cubic relationship and wood a linear one?

Last edited:
The difference between linear and cubic displacement deformation functions in beam bending has to do with the shape of the function itself and the resulting bending behavior. In a linear displacement deformation function, the amount of displacement increases linearly with the applied force. This means that the displacement is proportional to the applied force, and the shape of the function will be a straight line. With a cubic displacement deformation function, the amount of displacement increases at a higher rate than linear displacement. This means that the displacement is proportional to the cube of the applied force, and the shape of the function will be a curved line. The choice of which deformation function to use in beam bending depends on the material properties of the beam. Steel, for example, is known to have a higher stiffness than wood, so it would typically require a cubic displacement deformation function. Wood, on the other hand, is usually softer and would require a linear displacement deformation function. The type of deformation function used will affect the bending behavior of the beam, with a cubic deformation function resulting in more pronounced bending behavior.

## 1. What is the difference between linear and cubic deformation in bending?

Linear deformation refers to a uniform and proportional change in shape or size of a material when subjected to a bending force. On the other hand, cubic deformation occurs when the material undergoes a non-uniform change in shape or size, resulting in a curved or distorted shape.

## 2. How does the type of material affect the deformation in bending?

The type of material plays a crucial role in the deformation during bending. Materials with high elasticity, such as rubber, tend to exhibit more linear deformation, while materials with lower elasticity, such as metals, are more likely to undergo cubic deformation.

## 3. What causes linear and cubic deformation in bending?

The primary factor that causes deformation in bending is the applied force or load. When a material is subjected to a bending force, the internal stresses and strains within the material cause it to deform. The magnitude and direction of the force can determine whether the deformation will be linear or cubic.

## 4. How do we measure the amount of deformation in bending?

The amount of deformation in bending can be measured using various methods, such as strain gauges, extensometers, and displacement sensors. These tools measure the change in length or displacement of the material and provide a numerical value for the deformation.

## 5. What are the practical applications of understanding the difference between linear and cubic deformation in bending?

Understanding the behavior of materials under bending forces is crucial in designing and constructing structures, such as bridges, buildings, and aircraft. It also has applications in the manufacturing industry, where precise control of deformation is necessary to produce high-quality products.

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