Slenderness (magnified moments)

[hyper]

I need to know if every analysis needs the presence of cracking in slenderness (sway and non-sway) I mean reduce inertia beams (0.35Ig) and columns (0.7Ig) specially in structural analysis, do I have to not consider fhi(k)=0.7 in the Pcr formula.

and also; if I am running a PD analysis in SAP2000 for instance, I was trying to know if the moments exceed 5% from PD to a first-order analysis, do I have to reduce the inertia in the PD analysis only, both or none.

Thanks
Regards
P.S. for concrete specially and using ACI318-99 (10.11.1)

 

[Polecat]

Anytime factored loads are being used in an FEA program to anaylze concrete structures, you need to reduce the EI product since the members will be in a cracked state.

The easiest way to do this is to modify the modulus and leave the moment of inertia alone. Since the stiffness is a function of EI, reducing one of them will suffice. For example, in high strength concrete the uncracked modulus can reach 5000 or 6000 ksi, whereas the cracked modulus is in the 2000-2500 ksi range.

Try running the frame uncracked (full modulus) and then check the moments at some critical points. If the moment exceeds the cracking moment resistance (where the concrete tension is at the modulus of rupture), then go back and start reducing the E values for those members to account for the cracked condition. Your P-Delta will then increase due to the increased deflection.

In FEA analyzes, as long as the program converges, you don't have to worry about moment magnifiers since that is inherently accounted for in the process.

http://www.spiraleng.com

 

Polecat, how do you say that reducing one of either E or I would suffice?Won't it be better that a moment curvature section analysis done so that the value of the product EI equated to moment/curvature?May be the effect of axial load to may be needed to be incorporated to have a thrust moment curvature section analysis and then get EI.Please suggest.

 

[Polecat]

Visitor 111:

Yes, a moment curvature section analysis most certainly would be more accurate if you have enough time in your life to do so each time you are confronted with this kind of problem. Adjusting the EI product is a compromise ---- as all work with a non-homogeneous material such as concrete would be.

The problem is that as concrete approaches ultimate flexure , both E and I are diminishing rapidly at every iteration until the ultimate strain of 0.003-0.004 is reached. Since each range of concrete strengths will behave differently, there is no way of knowing what the real E or I is.

So, some compromise with your assumptions is always necessary. No matter how fast or accurate computers are, if the material you are working with cannot physically behave as you would like it to, you must modify your assumptions accordingly.

I have no doubt, however, that the next several generations of processors that emerge will be such that moment- curvatures can be fully included at every section and incorporated in such a way as to give us an accurate EI product at each iteration.

Meanwhile, we should not forget that the likes of the Golden Gate Bridge and the Empire State building were designed with moment distribution, log tables and slide rules. And they, barring the acts of some mindless suicide bomber on a mindless mission, will be standing for years to come.

http://www.spiraleng.com

 

[Ibeam]

Well said Polecat.

Ingenuity tempered with common sense. Sometimes I forget that, and I'll end up analyzing something to death, only to find myself way behind.

 

[Polecat]

Thanks for your comment, Ibeam.

Don't be too hasty, though, to stop "analyzing your problems to death." Better that than the alternative.

The most valuable advice I've ever gotten was from a rough-and-tumble, came-up-thru-the-ranks type professor who taught us reinforced concrete design.

He told us that anytime we finished a design, just set aside your calc's (we had no computers then) and sit back and look at it. If anything at all seemed out of kilter, it probably was, and you'd better revisit the problem. If it looks good, then it probably is good.

He would emphasize the point by drawing a spindly little column on the chalkboard with a huge weight on the top and bowed somewhat in the middle. Then, with a high pitched, nasal voice he would stand back, point at it, and say, "You know, that just don't look right to me, boy!"

Whatever it takes to deliver the message --- I for one, never forgot it. As a result, I have caught countless errors over the years just by looking at the results.

We are always reminded that, "Doctors bury their mistakes and lawyers just appeal to a higher court. Only the engineer builds monuments to them!"

http://www.spiraleng.com