Transformed Section Problem 1

[cve60069]

I need to calculate the stresses in a composite slab made from glass, concrete and steel and I transformed the glass and concrete into the equivalent area of steel using modular ratios.

Using excel, I calculated the position of the neutral axis and then applied the parallel axis theorem to obtain the transformed inertia.

To check my answer, I drew the transformed section in AutoCAD and checked the properties using the Mass Properties Enquiry Tool. The position of the Neutral Axis was ok and so was the transformed Area but I cannot confirm the Transformed Inertia. Using Excel I obtain 5.492E7mm4 and the AutoCAD check gave 3.432E6mm4.

I attach three PDFs showing my results.

Would anyone be able to point out my error, please?

 

[PMR06]

Only one pdf is attached.

I use MASSPROPS in AutoCAD all the time and have checked it many times. If the area calcs are equal in Excel and AutoCAD I bet AutoCAD is correct and that your spreadsheet has an error (no offense).

I would double check your parallel axis calc. Make sure it uses the correct transformed area and distance to transformed centroid.

 

[rb1957]

a quibble ... are these "mass" moments of interia (as per text) or "area" moments of inertia (as per your units) ?

post your s/sheet and we'll have a look.

there are plenty of canned s/s online for calculating section properties.

 

[BAretired]

Why would you include glass? It is usually considered a non-structural material.

BA

 

[MiketheEngineer]

You might test out your spreadsheet on a very simple section so that you can verify accuracy.

Agree w/ BA on glass - why bother - its properties are rather nasty

 

[Brad805]

I am curious, what the heck are you doing with this section? As BA suggests, the glass is typically a dead weight only. A little too much deflection and I think you know what happens to it.

Brad

 

[cve60069]

Sorry

I thought I has uploaded all the information

I attach the drawing

 

[cve60069]

And I attach the spreadsheet result.

The glass occupies a lot of the volume so I must include it.

Thanks for all your attention. I will produce a "simpler" case and check it in AutoCAD.
Regards

 

[PMR06]

Did you calculate the neutral axis based upon the untransformed section? The transformed section will not have the same neutral axis location as the untransformed. In fact, transform the section into one material then again for each material. Each transformed section will have the same neutral axis.

Now that I see what you have set up, I agree with others. I would not rely upon the glass for any stiffness contribution. I might not rely upon the concrete either. You will need to justify shear transfer from one material to the next. Steel to concrete could be done with some kind of shear connectors?

 

[BAretired]

cve60069. I am not familiar with the glass block product you are using. How do you ensure that blocks are continuous, i.e. that they can take tensile stress at the edges normal to the beam? Can the glass blocks develop bond with the concrete?

Are you planning to reinforce the concrete with bars as well as the Tee section? How do you bond the steel Tee to the concrete?

BA

 

[yakpol]

cve,
It seems that formulas for transformed moment inertia of concrete and glass you are using are incorrect.

Formula in the spreadsheet for concrete contribution to moment inertia:
Ic + ncAc(N.A.-Xc)^2
shall be:
ncIc + ncAc(N.A.-Xc)^2

Ic has not been reduced... Check.

Yakpol

 

[hokie66]

Just design the steel to take the entire load. That is the normal approach, and any other way is too difficult to justify.

 

[IDS]

What axis are the Ic and Ig values on the drawing taken about? If they are supposed to be about the centroid of the material then the values given are much too high.

As for the question of whether the glass and steel should be included anyway, it depends what the results are going to be used for. If you want to know the stress in the glass then you'd want to use the upper bound stiffness of the member in an analysis.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[cve60069]

All

Thank you for all of the advice. I made several errors. I had the wrong cell-address in the spreadsheet to calculate the ModRatio for the glass and I had calculated the inertias about the base and not through the N.A.s. I simplified the shape of the structure and at 3am this morning: the right result! I attach my calculations.

The reason for doing this analysis is I am having to design an experiment. I am going to construct a composite slab made from steel supporting glass blocks encased in concrete and then it is going to be tested.

It is very satisfying to obtain a result but I suppose this is the easy bit.

Regards

 

[cve60069]

Yakpol

Thank you for pointing me in the right direction with the transformed inertias

 

[rb1957]

i got to go back to PMR06's post ... the neutral axis of the transformed section should be the same as the untransformed section ... if calc'ing properties about the yy axis, you transfom the y dim'n, if xx, then x. this way the neutral axis and section properties are correct for both axes.

the more knowledgable gys are posting about the value of including the glass as effective. you could recalc your properties assuming the glass is ineffective, E = 1? 0?, so it'd act as a spacer. How is the load getting into the glass ? is the glass floating inside the steel frame ??

 

[Ron]

Strain compatibility....you have none. That's why you need to design as hokie66 noted...let the steel take it all..otherwise you'll crack both the glass and the concrete.

Further, if you are planning to bond glass block to concrete, it won't happen with just the concrete alone. So if that is truly a "concrete" and not a compatible glass block mortar, you'll have a bond issue. If it is a glass block mortar, your material properties for the concrete are overstated.

 

[PMR06]

rb1957, the untransformed NA is NEVER the same as transformed, as cve60069's last pdf shows.

 

[rb1957]

mea culpa (again) ... the NA of the untransofrmed section doesn't mean anything.

question ... are all the elements of this section going to strain as one ? i'm guessing that there's adhesive between the Al channels and the glass and between the galss and the St tee ... doesn't this provide a strain discontinuity ?

 

[cve60069]

All

Thank you for your interest. I attach a pdf of the slab that I am designing and hopefully it will answer some of your questions.

Thanks again.

cve