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Transformed Section Problem

Transformed Section Problem

Transformed Section Problem

(OP)
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?

RE: Transformed Section Problem

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.

RE: Transformed Section Problem

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.

RE: Transformed Section Problem

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

BA

RE: Transformed Section Problem

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

RE: Transformed Section Problem

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

RE: Transformed Section Problem

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?

RE: Transformed Section Problem

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

RE: Transformed Section Problem

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
 

RE: Transformed Section Problem

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

RE: Transformed Section Problem

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/
 

RE: Transformed Section Problem

(OP)
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

RE: Transformed Section Problem

(OP)
Yakpol

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

RE: Transformed Section Problem

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 ??

RE: Transformed Section Problem

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.

RE: Transformed Section Problem

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

RE: Transformed Section Problem

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 ?

RE: Transformed Section Problem

hokie66, Ron and others are correct, you do not have strain compatibility. You have alternating concrete beams and glass beams spanning in the same direction. With the steel providing the tensile element, there will be large shear forces between the steel and the glass block. Even if you get good bond between the concrete and the glass, the concrete will crack in the tension zone.

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

RE: Transformed Section Problem

Cve:
Why not look at precasting and post tensioning those 36"+/- square panels.  Lay down 76.2x7.6 bars, continuous in one direction and about 170 long fillers in the other, with the fillers beveled on their ends.  Weld these together on their tension face, flip them over and weld some ears on them to locate and hold the glass blocks for casting; maybe apply some small shear studs, or a light deformed bar with a "WWW" shape akin to the webs on a bar joist, welded to the flat bars.  Then you should be able to achieve a more uniform bending in both directions.  Harp the center two tendons in each direction slightly, but mostly you just want to keep the whole panel in compression under loading.

RE: Transformed Section Problem

(OP)
All

From what I am reading, is it being implied that, because of the strain compatibility problems caused by the tension part of the web with the concrete (due to the high horizontal shear forces, the bond will be insufficient); I will need to either improve the bond with shear-studs, or (if I am reading you right dhengr) do away with the web and to tie the concrete to the steel-plates using shear-reinforcement.

I have modified the one-way spanning rib (see attached).  would this arrangement allow me to use the concrete and the steel as a composite?

RE: Transformed Section Problem

Cve:
I've seen and walked on floor systems like you are proposing, and never gave them real much thought other than to think they were novel.  One of my concerns would be the three different materials, in fairly small volumes, each with different thermal expansion and contraction characteristics, and each with different stress/strain characteristics under loading.  We have a fairly good understanding of how conc. and steel act together, but are much less familiar with bonded conc. or mortar and glass, other than in compression.  Glass acts quite predictably in pure tension and compression, but very poorly in bending or w.r.t. concentrated stresses or strains perpendicular to its plane.  The corners of each glass block where the small conc. joists cross (very complex stresses and strains), or the edges of each glass block where a conc. joist might crack in tension (concentrated stresses and strains, caused by bond) could be problem areas and are very tough to get a handle on from the stress analysis (Theory of Elasticity) standpoint.  Then run your tests to confirm your design and its performance.

Reread my earlier post, and some of the other posts for potential pitfalls, and precast and pre or post tension the panel so that it still act in compression when under load.  You've changed the shape of your panel form a 3' square which would act as a two-way mini joist system; to a long panel which will tend to span predominantly in the short direction.  Weld the 76.2x7.6 bars together on their tension face to form something of a support and casting bed for the conc. and glass blocks.  Flip this grillwork over and tack weld the glass block holders in place.  These might consist of lt. ga. stl. strip forming a 7"+ square box about 2" high into which the glass block is placed.  Press a small dia. foam backer rod all around btwn. the stl. strip box top edge and the sides of the glass block and cast the conc.  You show the "WWW" deformed bar about as I had intended, exact shape to be determined, but I would run these in both directions probably.  These can make the conc. and 76.2 bars act compositely.  Then pre or post tension, and harp, horiz. wires in both directions to maintain compression in the conc. mini joists under the final loading condition.  The various component member sizes and shapes are your design problem, and your stress analysis should be tempered with much good engineering judgement and experience.  Only someone without much experience and judgement will assume that their CAD or FEA numbers are accurate to more than 12 significant figures, if you get my drift.   smile But, good engineering judgement might lead to a successful testing program.
 

RE: Transformed Section Problem

(OP)
Thanks dhengr
 

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