# Failure of a beam formula?

1. Dec 6, 2004

### sol_angel187

Hey, this is my first post on this forum- I hope that someone can help me because I'm going crazy! I'm an architecture student taking a required engineering class, and it's pretty challenging for me. So anyway, here's my problem.

We were assigned to design a beam made of luam plywood out of a sheet 24" x 8" x 1/4". I decided to cut the plywood into (4) 2" pieces and use wood glue to glue them together so it's dimensions are 1"x2"x24". The assignment is to to say how far the beam will deflect, and what load will cause the beam to fail. We will test it in class on a machine. It will be simply supported on each end and a load will be placed in the center.

So, the formula I think I need to use for deflection is

D=P(L^3)/48EI

d= deflection
l= length
e= modulus of elasticity
I= moment of inertia

I=b(d^3)/12

b=base
d=depth

so I= (1)(2^3)/12=.667
I found the modulus of elasticity for luam plywood on the internet (after an hour of looking) and it is 1,500,000
L= 24

so I know I, E, and L, but I still have two unknowns, P and D. The problem is I don't know another fomula to figure out what P is. I'm going slightly crazy because I can't find it in the book, and I've been looking online for a long time. I'd really appreciate it if someone could point me in the right direction! thanx!

2. Dec 6, 2004

### sol_angel187

anyone?

I emailed my professor this yesterday and he still hasn't emailed me back yet . . .

3. Dec 7, 2004

### rdt2

First, you have to know the stress 's' at which the material fails, which you have to simply look up. That's the maximum bending stress that the beam can take so put it into the famous formula M/I = E/R = s/y where 'y' is the distance from the neutral axis. Set this to be half the depth of the beam, i.e where the stress will be greatest. That'll tell you the maximum moment it can take. Calculate the value of the load P to generate such a moment and then put this into your equation for the deflection.

4. Dec 7, 2004

### sol_angel187

thanx for your help- i think i got it!