Box beam moment equation for different elasticity modulus. HELP!

[Integrator62]

Equation of Flexure stress due to bending moment is Stress= (Moment x y / I) is for materials having the modulus of elasticity same for both Tension and Compression. And consideration is Strain is Linear. And its applicable for all types of cross section with a very minor error.

But for different modulus of elasticity things get rough! Neutral axis doesnt go through Geometric First moment of area. To keep the strain Linear and forces in equilibrium it changes its position.

So equations are also much more different.

I have equation for Rectangular cross section. But it is applicable only for rectangular cross section.

Is there equation derived for Box beam cross section? I find it too difficult to try it by myself! Please help!

Again I have to go through a long self made Transformation process to apply the Differential equation of elastic curve of this type of Rectangular cross section beam. Is there any process done before? Please help!

 

[RobertHale]

I would use the modular ratio to transform the section into an equivalent section with a uniform Modulus of Elasticity. You will be able to determine the centroid of the section then the elastic stresses will follow. Any basic strength of materials book should have the procedure outlined. I can't see why this wouldn't work provided you are looking at linear elastic materials.

 

[paddingtongreen]

Select one piece of material, and multiply the thicknesses of each of the other pieces by the ratio of their modulus of elasticity over that of the selected piece. Then calculate using the ratio'd thicknesses.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[Integrator62]

I did this procedure (equivalent area) to apply the Differential equation of elastic curve.

But before that I have to find out Neutral axis position. Because it determines the region for tension and compression. If position is determined
1) using the equivalent area I can find out stress.
2) I can derive direct equation for stress.
It is done in this pdf [

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740010415.pdf

]

For rectangular cross sectioned beam, its very simple.

For box beam it should be complicated. And it gets too tough for me.

Thanks