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?

 

[desertfox]

Hi cve60069

Look at this site for the transforming of sections:-

http://www.roymech.co.uk/Useful_Tables/Beams/Beam_theory.html#composite

desertfox

 

[paddingtongreen]

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.

 

[dhengr]

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 “

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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.

 

[cve60069]

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?

 

[dhengr]

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 “

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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. But, good engineering judgement might lead to a successful testing program.

 

[cve60069]

Thanks dhengr