Modulus effect on material thickness 1

[cyrix7x86]

I need some help to determine what the stiffness increase is with increase of material thickness.

Sheet of material would be a perfect example. A sheet of material with a given width and length......and changing the then increasing the thickness.......how does the modulus increase? Is there a simple formula or link to this?

I know it might seem like a simple question to some on here..........but I would sure appreciate the help.


Thanks

 

[paddingtongreen]

The section modulus is proportional to the thickness squared. Is that the modulus you want?

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[rb1957]

if bending modulus is what you're after ... then a plate is an easy example, an I-beam is similarly pretty easy.

but is section modulus (Z or S) the measure of stiffness that you want ?

 

[SWComposites]

The material elastic modulus does not change with thickness (at least not for most metals; composites is another story).

The structural axial stiffness is proportional to the cross-sectional area (thickness with constant width)

The structural bending stiffness is proportional to the square of the thickness

 

[hokie66]

When someone just uses the word "modulus", to me it means the modulus of elasticity, E. E doesn't change for most metallic materials, e.g. steel, aluminum. E does change for other materials, and particularly for composites which are not isotropic. Some materials don't have a well defined modulus.

But I don't know if that is what the OP meant, as he asked about stiffness increase with thickness, and as others have said, there are several types of stiffness.

 

[cyrix7x86]

Thanks for all the comments......please be patient with me as I am trying to learn about all this.

I would like the modulus of elasticity.

Simple example.

Sheet of aluminum 6 inches X 6 inches. How much will it give if it were a diving board type setup. stress being applied to the loose end. Lets say a thickness of 1mm, 2mm, 3mm.......etc. Is there a simple formula for this?


THanks

 

[hokie66]

Yes, there are formulas, which you can find in many reference books. The modulus of elasticity does not change.

 

[cyrix7x86]

It seems like something changes, because it doesnt move as much.......so what is changing.

 

[JAE]

The moment of inertia.

Stiffness of an object (in flexure) is based upon the EI of the member (modulus times moment of inertia)

What is your question specifically for? Are you studying this or have an application you can describe?

 

[cyrix7x86]

its for an application.

I have a sheet made of a given material. Actually many different types of materials.

What im trying to figure out is.......how will the sheet hold up to bending in different thickness for different materials.

Example.......will a 2mm thick aluminum sheet hold up better than a 1mm thick titanium. Or many other combinations of thickness and material stiffness. This will help me to choose a proper material for my final project.

Hope that makes some sense...........is there a simple formula to use to see how the sheet stiffness increases with added thickness?


Thanks

 

[paddingtongreen]

"how will the sheet hold up to bending in different thickness for different materials."

Do you mean strength or stiffness? It will bend, first in the elastic range with lower stresses and in the plastic range with higher loads. In the elastic range, the material will spring back when the load is removed, in the plastic range it will stay bent.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[cyrix7x86]

ok, imagine this........

A diving board setup clamped on one side holding a 2ft X 2ft sheet of material.

The sheet is 1mm from a surface on the opposing side. In other words, it takes 1mm of movement to hit the floor.

I need to find a material with the best stiffness to weight ratio that will hold up best from bending. The sheet will not bend enough to cause deformation or stresses. Its a matter of stiffness. Now the stiffness to weight ratio is pretty easy to figure out from the material properties........however, the thickness effects how the stiffness holds up.

Aluminum VS titanium is about the same when it comes to stiffness to weight ratio.

However, you would gain volume with aluminum......in other words 1mm sheet of titanium is about 1.67mm thick aluminum sheet given the same weight. In this case.......what do you gain in stiffness due to the structure volume change (increase) with aluminum?

This is what I want to understand.....but there should be some simple formula that can be applied to multiple materials as I will be using mulitple materials for the project. And I need to choose the best material regarding stiffness to weight ratio with the volume changes figured into the ratio.

Hope that makes sense.

thanks

 

[JAE]

Ok - I have to ask. Is this a school project?

 

[SWComposites]

cyrix - have you never had a course that covered beam bending? do you understand the concept of moment of inertia? do you understand simple beam bending equations?

 

[ToadJones]

Grab mechanics of materials book and look at the nice tables in the back for plane areas.

If you need the material properties themselves (modulus of elasticity "E") , this book will have those too.

Take these tables & formulas and determine the section properties of your diving boards (namely the moment of inertia "I")

Apply a unit load to the tip of the diving board.

Use the formula for deflection of a cantilever beam with a point load at the free end (your unit load).

Plug and chug to determine the deflection at the free end.

The material (and corresponding thickness) that deflects the least is the more stiff of the two (which will be EI as stated before) .

http://www.advancepipeliner.com/Resources/Others/Beams/Beam_Deflection_Formulae.pdf

 

[ToadJones]

...If you are designing airplanes, please have some one check your results

 

[BAretired]

The formulas are all simple and are available in elementary strength of materials textbooks.

Describe your exact problem and perhaps someone can help you.

BA

 

[cyrix7x86]

thanks

 

[rb1957]

i think you're confused with terminology ...

"I would like the modulus of elasticity.

Simple example.

Sheet of aluminum 6 inches X 6 inches. How much will it give if it were a diving board type setup. stress being applied to the loose end. Lets say a thickness of 1mm, 2mm, 3mm.......etc. Is there a simple formula for this?"

this is not affected by E, modulus of elasticity; in this case it's affected by section modulus, see above.

then you continue with numerous posts about stiffness ...
about how a diving board deflects, how different materials have different deflection.

ok, comparing Ti and Al and combinations is affected by E. research "rule of mixtures". determine the equation for deflection of a diving board as a function of geometry and material; hint, a diving board is a cantilever with a point load.

but i think you give yourself away, asking a Very basic question, then "help me to choose a proper material for my final project" suggests non-professional

 

[rb1957]

continuing confusing terminology ...
"Aluminum VS titanium is about the same when it comes to stiffness to weight ratio.

However, you would gain volume with aluminum......in other words 1mm sheet of titanium is about 1.67mm thick aluminum sheet given the same weight. In this case.......what do you gain in stiffness due to the structure volume change (increase) with aluminum?"

do yyou realise you start by saying stiffness to weight is the same (between Al and Ti), and end with it isn't ?

the first "stiffness" is actually elastic modulus ... specific elastic modulus (E/w) is pretty constant for Al, Ti and Steel.

the second "stiffness" is structural stiffness, EZ for bending, and like you say for the same weight the Ti board would be thinner than the Al one and so less stiff.