# Failure of beam formula

1. Dec 6, 2004

### sol_angel187

I posted this again here because I just realized there was an engineering forum here too. I hope 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

### Gokul43201

Staff Emeritus
P is the applied load. Plugging in different values of P tells you what the corresponding deformations will be.

From D, you can get the approximate strain, depending on what kind of approximation you use. Fing the load at which the strain approaches the breaking strain for your particular type of wood. That's the maximum load. To get the maximum allowable load, you must incorporate a suitable safety factor. For architecture, FS = 3 or 4 is not uncommon.

3. Dec 7, 2004

### michaeldouglassewell

Try the Forest Products Laboratory at www.fpl.fs.fed.us[/url] or the Engineered wood Association at [url]www.apawood.org[/URL]

If you can quantify the modulus of rupture (maximum stress at the extreme fiber), and the section modulus, you can solve the FLEXURE FORMULA for the maximum moment. From this you can calculate the applied load that will fail the beam by using the formula for a concentrated load at the center of a simple beam.

There will probably be quite a bit of difference in the actual modulus of rupture from one beam to another.

-Mike

Last edited by a moderator: Apr 21, 2017
4. Dec 7, 2004

### sol_angel187

thanx so much for the help- I think I got it. The number I found for fiber stress was 1400 and I used that along with the section modulus I found to get a p of 155 lbs. I substituted this and found d to be .045 inches. I don't know though, because that seems to be a very small amount of deflection and really not that much force.

5. Dec 7, 2004

### michaeldouglassewell

1400 LBS/IN^2 Sounds too low to be the modulus of rupture. It sounds more like ALLOWABLE STRESS.

Is the beam going to suffer a catastrophic structural failure, or fail by an unacceptable amount of deflection? e.g. L/360