Mechanical - Deflection and Slope, cantilever beam

[Sadlercomfrot]

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,

 

[SteamKing]

Yes. Beams are subject to superposition for small deflections.

 

[Sadlercomfrot]

Okay, what does that mean?

I add the deflections together? What about the slopes?

 

[SteamKing]

Brush up on beam basics:

http://www.assakkaf.com/courses/enes220/lectures/lecture19.pdf

 

[Chestermiller]

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

 

[Sadlercomfrot]

Nice source, thanks guys