Deflection and Slope, cantilever beam

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 got so far:

For the point load
dy/dx [COLOR=#545454][FONT=arial]= (FL^2) / 2EI

[/FONT][/COLOR]dy/dx [COLOR=#545454][FONT=arial]= 61.25x10^-6


y = (FL^3) / 3EI
[/FONT][/COLOR][COLOR=#545454][FONT=arial]y = 285.83[/FONT][/COLOR][COLOR=#545454][FONT=arial]μm
[/FONT][/COLOR][COLOR=#545454][FONT=arial]
For the udl:
[/FONT][/COLOR]dy/dx [COLOR=#545454][FONT=arial]= (wL^3) / 6EI

[/FONT][/COLOR]dy/dx [COLOR=#545454][FONT=arial]=214.4x10^-6


y = (wL^4) / 8EI
[/FONT][/COLOR][COLOR=#545454][FONT=arial]y = 1.12m[/FONT][/COLOR][COLOR=#545454][FONT=arial]m
[/FONT][/COLOR][COLOR=#545454][FONT=arial]
[/FONT][/COLOR][COLOR=#545454][FONT=arial]Now what? Do i add them?
Thanks,



[/FONT][/COLOR]

As long as the sum of the stresses of the two loadings does not exceed the elastic limit of the beam material, i.e remains within the elastic limit of the material, then you can combine the two loading values.