Mechanical - Deflection and Slope, cantilever beam

In summary, the conversation discusses calculating the deflection and slope at the free end of a cantilever beam with a point load and UDL. The calculations for both are provided, and it is confirmed that the deflections should be added together due to superposition. It is also noted that the slopes, being derivatives of the deflections, should also be added together. A source for further information on beam basics is also mentioned.
  • #1
Sadlercomfrot
4
0
Hi guys, I have been a question to solve this week to do with deflections and slopes at the free end of a cantilever beam. I have calculated the deflection and slope for the point load and UDL, but I'm not sure whether to add them together or not?.. as they're both acting on the beam?

A cantilever beam with a length of 7meters, has a 2KN point load at the free end and a UDL of 3KN/m along its length. Calculate the deflection and slope at the free end. *Assume the flexural stiffness [EI]is 800MPa.


This is what I've calculated so far, some steps have been omitted:

For the point load
dy/dx = (FL^2) / 2EI

dy/dx = 61.25x10^-6


y = (FL^3) / 3EI
y = 285.83μm

For the udl:
dy/dx = (wL^3) / 6EI

dy/dx =214.4x10^-6


y = (wL^4) / 8EI
y = 1.12mm

Now what? Do i add them?
Thanks,
 
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  • #2
Yes. Beams are subject to superposition for small deflections.
 
  • #3
Okay, what does that mean?

I add the deflections together? What about the slopes?
 
Last edited:
  • #5
Sadlercomfrot said:
Okay, what does that mean?

I add the deflections together? What about the slopes?
If the deflections add, then the slopes, which are their derivatives, must add also.

Chet
 
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  • #6
Nice source, thanks guys
 

FAQ: Mechanical - Deflection and Slope, cantilever beam

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 projecting out into space. It is commonly used in building and bridge construction.

How does deflection affect a cantilever beam?

Deflection is the amount of bending or displacement that a cantilever beam experiences when a load is applied. The greater the load, the greater the deflection. This can impact the structural integrity of the beam and must be carefully considered in design.

What factors influence the deflection and slope of a cantilever beam?

The deflection and slope of a cantilever beam are influenced by several factors, including the material properties of the beam (such as elasticity and density), the length and shape of the beam, and the magnitude and location of the applied load.

How is the deflection and slope of a cantilever beam calculated?

The deflection and slope of a cantilever beam can be calculated using mathematical equations based on the beam's material properties, dimensions, and applied load. Advanced analysis techniques, such as finite element analysis, may also be used to determine these values.

What are some common applications of cantilever beams?

Cantilever beams are commonly used in building and bridge construction, as well as in mechanical and aerospace engineering. They are also found in everyday objects such as diving boards, shelves, and diving platforms.

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