Calculating Beam Deflection and Failure Load for Plywood Beam Design

In summary, this student's professor asked them to design a beam out of luam plywood and they didn't know how to calculate the deflection. They emailed their professor and haven't heard back yet. They looked up the stress at which the material fails and found that the maximum bending stress is .667 times the load. They calculated the load to generate this maximum bending stress and put it into their equation for the deflection.
  • #1
sol_angel187
5
0
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
p= load
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!
 
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  • #2
anyone?

I emailed my professor this yesterday and he still hasn't emailed me back yet . . .
 
  • #3
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
thanx for your help- i think i got it!
 

1. What is the formula for calculating the failure of a beam?

The formula for calculating the failure of a beam is typically known as the Euler-Bernoulli beam theory, which is expressed as F = (π²EI)/L². F represents the maximum load or force that a beam can withstand, E is the modulus of elasticity, I is the area moment of inertia, and L is the length of the beam.

2. How do material properties affect beam failure?

Material properties such as modulus of elasticity, yield strength, and ductility can greatly affect the failure of a beam. A higher modulus of elasticity means that the material is stiffer and can withstand higher loads before failure. Yield strength is the point at which a material will permanently deform, and a lower yield strength means that the material is more likely to fail under stress. Ductility is the ability of a material to deform without breaking, and a lower ductility can lead to sudden failure of a beam.

3. Can a beam fail even if it is within the calculated limits?

Yes, a beam can still fail even if it is within the calculated limits. This is because the formula for calculating beam failure is based on ideal conditions and does not take into account factors such as imperfections in the material, external forces, or structural flaws. It is important to also consider safety factors and conduct thorough testing to ensure the structural integrity of a beam.

4. How can beam failure be prevented?

To prevent beam failure, it is important to use high-quality materials with appropriate properties for the intended use. Proper design and construction techniques should also be followed to ensure the structural integrity of the beam. Regular inspections and maintenance can help identify potential issues and prevent failure before it occurs.

5. What are some common signs of beam failure?

Some common signs of beam failure include cracks or deformities in the beam, excessive deflection or sagging, strange noises or vibrations, and visible signs of stress such as discoloration or warping. If any of these signs are observed, it is important to address the issue immediately to prevent further damage or potential failure.

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