Modulus of Elasticity of a Plastic Laminated Panel

[Jarred]

I am trying to find a formula to show the modulus of elasticity (MOE) of a panel of three layers of different materials when I know the MOE value of the three individual materials. This is for a Plastic Laminated Panel where, the top and bottom layers are plastic laminate (i.e. Formica) .028" thickness which has a MOE value of 1,600,000 psi (normalized to the square inch) and the center layer is 3/4" thick MDF panel that shows and MOE value of 290,100 psi.

 

[Chestermiller]

Is this a homework problem?

 

[Jarred]

No, it is not, I haven't been in school in almost 20 years. More of a curiosity. I see questions regarding metals on here, and was wondering about wood and laminate materials. I work with these materials and see on specification sheets approximate MOE value, so I just want to know how they are calculating it. The values I listed are for the value from the manufacturers. But I always get the approximate value from the guys who laminate the panels. More or less I just want to know how they calculate it. Also, I deal with shelf loads where the MOE value is needed to calculate maximum shelf span, so being able to double check the values I am given would be nice.

 

[Chestermiller]

It depends. What are the other dimensions of the conceptual test sample they are envisioning measuring the modulus of elasticity? 3/4" is a pretty thick sample. Are they envisioning the width to be much more than the thickness, and the length to be much more than the width, or don't they say?

Chet

 

[Jarred]

3/4" of an inch is a standard shelf thickness. The MOE value needed is based on multiple materials glued together.

The individual panels are typically 4'0" x 8'0" in size when they are combined and then cut to the size of individual parts as required.

Top Layer is a Phenolic laminate sheet .03125" in thickness which has a MOE value listed by the manufacturer of 1,300,000 psi (This layer is 4.17% of panel thickness)

Middle Layer is a Medium Density Fiberboard panel .6875" in thickness which has a MOE value listed by the manufacturer of 450,000 psi (This layer is 91.66% of panel thickness)

Bottom Layer is a Phenolic laminate sheet .03125" in thickness which has a MOE value listed by the manufacturer of 1,300,000 psi (This layer is 4.17% of panel thickness)

The Woodwork Institute claims that the approximate MOE value of the three items combined is 710,000 psi (they may not be using the same manufacturer numbers that I have as each manufacturer has different MOE values on their version of the same product, so I am trying to figure out how to combine these MOE Values to verify that I am meeting the requirements that are being called for when calculating the shelving loads.

Shelf dimensions vary from each other. Typical shelves are 3/4" thick x 12" wide x 36" long in a wall hung cabinet and 24" wide in a base cabinet. Shelves can also be 1" thick when the length goes over a certain dimension.

From my understanding the MOE value of these materials is normalized by the square inch, making the thickness of the individual material irrelevant in regards to the MOE of the individual material. An example being that phenolic materials from one manufacturer are all listed as having a MOE value of 1,300,000 psi whether the material is .03125" thick or 1" thick.

 

[Nidum]

Effective value of MoE for composite materials is often determined by practical tests . The deflection of a standard size test panel under given conditions of support and loading is measured and the effective MoE is then determined .

There are also theoretical methods . Easiest is to again determine deflection for given loading but this time by detail calculation or computer methods .

 

[Jarred]

Ok, the effective MoE value of each material is known.
What is the theoretical method to estimate what the MoE value could be?

 

[Nidum]

Do you just want a working formula or do you want to go through the calculation method in detail ?

 

[Jarred]

Both. A working formula that I can use and in detail so I understand how it works.

 

[Chestermiller]

Suppose you had a single layer. Would you know what its modulus of elasticity represents?

 

[Jarred]

For my purposes, I believe it represents the stiffness of the material I am using. I use the MoE when figuring out which material I need to use for cabinet shelves to maintain a shelf load of 50 lbs/sf. This is the Formula I use to figure this out:

 

[Chestermiller]

OK. So you are using the Young's modulus E in a beam bending formula, and you are looking for an equivalent value of E to use in the formula for a symmetric laminated composite beam. I could derive this for you, but we are not supposed to do that in Physics Forums. At the same time, your background doesn't seem to be sufficiently extensive for me to help you derive it on your own. For bending of your composite, the equivalent E is going to be different than for tensile loading. The only thing I can suggest is that you get a book on composites, or Google "bending of composite beams."