# Deflection of a beam

1. Jul 9, 2011

### wildleaf

1. The problem statement, all variables and given/known data
For the given beam (link), calculate the tip deflection for the given loadings. In addition to the applied load, the beam wt 2000 lbs/ ft.
E = 30 * 10^6 psi
I = 60 * 10^3 in^4

http://i52.tinypic.com/990xef.jpg

2. Relevant equations
deflection for the uniform load is: w= -p/ (24*E*I)* [(x^4) - (4*L*x^3) + (6*L^2*x^2)]

You use this to calculate the uniform load of 1000 lb/ft. I think you use this for the weight of the beam (2000 lb/ft) as well, but i am not too sure.
I have solved the deflection function by hand and have checked on sites and it is the correct case for uniform load.

3. The attempt at a solution
I know we have to use superposition, we have to separate them by uniform load of
1000 lb/ft, the 4000 lb load, 5000 lb load, and the weight of the beam itself... After I separate them, I solved for the deflection function for the uniform load of 1000 lb/ft.
I know that I need to do this for all four loads and then add them together at the end but I dont know how to calculate the deflection for the 4000 lb load, and 5000 lb load since they are not evenly spaced.

2. Jul 9, 2011

### SteamKing

Staff Emeritus
Check your deflection tables for a cantilever beam with a single load applied away from the end. You can calculate the deflection of the 4000# load by itself, and the 5000# load by itself. The total deflection at the free end is obtained by superposition.

3. Jul 9, 2011

### wildleaf

there are two equations for one load for 4000 and two equations for 5000, Do use all 4 of them.. The two equations have a limit, the first equation is from the left end to the Force/load and second is from the Force/load to the right end. Here is the link: Look at case 2:
http://www.advancepipeliner.com/Resources/Others/Beams/Beam_Deflection_Formulae.pdf

So i will have to use all 4 equations, 2 of each force, and add them?

4. Jul 9, 2011

### SteamKing

Staff Emeritus
If you look at Beam Type 2 and the equations for deflection y, note that each equation is applicable for a certain portion of the beam:

Eq. 1 - x is between the load P and the fixed end of the beam 0 < x < a
Eq. 2 - x is between the load P and the free end of the beam a < x < L

However, your problem asks you to calculate the tip deflection, so use the eq. in the right hand column (Max. deflection) of the table for dmax.

5. Jul 9, 2011

### wildleaf

Thanks bro :)
Wasted about 4 hours trying to calculate the two load, lol.

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