# Homework Help: Mechanical - Deflection and Slope, cantilever beam

1. Mar 27, 2014

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:

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,

2. Mar 27, 2014

### SteamKing

Staff Emeritus
Yes. Beams are subject to superposition for small deflections.

3. Mar 27, 2014

Okay, what does that mean?

Last edited: Mar 27, 2014
4. Mar 27, 2014

### SteamKing

Staff Emeritus
5. Mar 27, 2014

### Staff: Mentor

If the deflections add, then the slopes, which are their derivatives, must add also.

Chet

6. Mar 27, 2014