Cantilever Beam Deflection with Concentrated Loads

In summary, the conversation was about a question involving a cantilever beam with concentrated masses and its deflection under a load applied at its tip. The person was stuck because they did not know much about cantilever beams. They also mentioned needing to find the equation of cantilever deflection and the flexibility matrix. Someone else asked about the relation between the second derivative of deflection and the moment.
  • #1
parmz_11
5
0
hi guys was doing one of the questions sort of stuck as i don't know much about cantilever beams. I've got this question here:

Consider a cantilever beam of length L carrying concentrated masses at both of its mid-lenght and at its tip. the cantilever may be assumed to have negligible mass:
find the equation of cantilever deflection solely under a concentrated load applied at its tip as a function of a positive variable measured relative to the fixed end and also the flexibility matrix of a cantilever system equation abpve, matrix element 1,1 1,2 2,1 2,2

thanks guys
 
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  • #2
What's the relation between the second derivative of deflection and the moment?
 

1. What is a cantilever beam?

A cantilever beam is a type of structural element that is supported at only one end, with the other end being free to deflect under load. It is commonly used in construction and engineering projects where a long, unsupported span is needed.

2. How do concentrated loads affect the deflection of a cantilever beam?

Concentrated loads, also known as point loads, are forces that are applied at specific points along the length of a cantilever beam. These loads can cause the beam to deflect or bend at the point of application, resulting in a change in the beam's shape and position.

3. What is the equation for calculating deflection of a cantilever beam with concentrated loads?

The equation for calculating deflection of a cantilever beam with concentrated loads is: D = (PL^3)/(3EI), where D is the deflection, P is the applied load, L is the length of the beam, E is the Young's modulus of the material, and I is the moment of inertia of the beam.

4. How does the position of the concentrated load affect the deflection of a cantilever beam?

The position of the concentrated load along the length of a cantilever beam can greatly affect the beam's deflection. If the load is applied at the end of the beam, the deflection will be at its maximum. As the load is moved closer to the support, the deflection decreases.

5. What are some factors that can affect the deflection of a cantilever beam with concentrated loads?

Some factors that can affect the deflection of a cantilever beam with concentrated loads include the magnitude and position of the load, the length and cross-sectional shape of the beam, and the material properties of the beam. Temperature changes, moisture, and external forces can also affect the deflection of a cantilever beam.

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