Stiffness Modifiers: Is this the correct procedure?

[BasementCarpark]

I just review an Etabs model from others and he adjust the stiffness modifiers for all members (wall, columns, slabs, beams) as per ACI suggestion. As per his computations, he used this model to design the vertical elements (concrete walls and columns) and retrieve the reaction to design the footings. My questions are as follows,
1. Is Adjusting the stiffness modifiers for all members and then design vertical elements accordingly safe? In my opinion, the earthquake will be reduced as the structure stiffness has been reduced and thus it will underestimate the actions on the vertical elements. Also, reducing the vertical element stiffness will underestimate the moments of them under gravity loads although beams/slabs stiffness have been reduced too but not as great as vertical moments. right?
2. In my view, the purpose of reducing the stiffness is to evaluate the story drift under lateral load. (pleas correct me if I am wrong) But as this model is just a 5 story building with core walls, I doubt the necessity to reduce the stiffness, the lateral drift won't change much any way considering it's not high rise. Also, there is no dynamic analysis (just wind and static earthquake), nor P-delta. Does this sound reasonable?
3. The retrieve the reaction from this model whose beams and slabs bending stiffness have been reduced too, will this safe for footing design considering there are two transferred flat slabs and reducing the stiffness will affect the gravity load distribution, which might be underestimation for the reaction of some columns and are more closed to transferred columns/walls above?
4. When and how do you adjust the stiffness modifiers? as far as my understanding is concerned, I will remain the modifiers to be 1 and then check the axial force of walls/columns to see if any columns/walls stress will cause crack and then amend those members if so instead of reducing the stiffness of all members.


Thank you.

 

[ggcdn]

Couple of thoughts:

a) If the building has multiple basement levels, you could be severely underestimating the footing design loads if you are just reading the reaction loads from the model.

b) I think there is nothing wrong with using effective stiffnesses to determine member forces for seismic analysis. You are right that this is probably not accurate for determining gravity loads, especially if you are dealing with transfers and modifying stiffnesses differently for various elements. I would confirm with an old fashioned load takedown.

 

[BasementCarpark]

No, there is no basements.

In my opinion, if you run response spectrum, reducing the stiffness will make the structure softer and thus gets less seismic loads.

 

[ggcdn]

Are you designing your structure to remain uncracked, or are you using an R factor?

 

[BasementCarpark]

Hi Sonofatkins, the structure is not designed by me. I am just reviewing the model. They used Etabs to design the columns and walls (reinforcement etc) and footings (getting reactions). The stiffness of all walls are reduced to 0.35I and columns 0.7I. I understand they tried to model the cracked section using this simplified linear method but in my view, modelling the cracked section is more to do with the lateral deflection after walls/columns crack and then p-delta effect on the members. But I doubt whether or not we use them for strength design because like I said, the earthquake action will be underestimate since the structure stiffness has been reduced. Also, for a low-rise building, is it really necessary to modify the stiffness (the lateral deflection won't be a big issue for low rise building). That's what I couldn't figure out.

 

[Retrograde]

I would use the reduced stiffness for values for strength design. The columns and walls will crack during an earthquake; so it is appropriate to take this into account.

 

[Lomarandil]

If cracking is unacceptable (liquid retaining structure, severe client requirements), then it may be appropriate to design a building to remain uncracked in a seismic event, and in that case I would use the uncracked sections/stiffnesses to ensure behavior matches that expectation.

However, this is extremely uncommon. Typically the cracked assumption is reasonable and efficient. While your building will momentarily experience larger responses due to being "uncracked", these actions will create the assumed cracking and revert to the design assumptions. (For ordinary, properly designed and detailed structures).

(Plus, in most cases, gravity loads lead to some degree of cracking in flexural sections)

----
just call me Lo.

 

[BasementCarpark]

Hi Retrograde & Lomarandil, I agree that at design stage you can design vertical elements to allow them crack. But reducing the structure stiffness will reduce the earthquake input. The structure should get more earthquake before crack occurs. Simply put, I agree with the following design steps: uncracked structure -> get earthquake -> design as cracked elements based on the earthquake getting from uncracked structure. But if you manually reduce the stiffness it will affect the second step (analysis).

 

[Retrograde]

Simply put, I agree with the following design steps: uncracked structure -> get earthquake -> design as cracked elements based on the earthquake getting from uncracked structure.

Simply put, I do not agree with your design approach and I do not think it the intention of the Codes. I agree with Lomarandil that the cracked assumption is reasonable and efficient.

 

[SPR Baker]

Cracked Section reflect the shrinkage, shortening of members... then stiffness loses and will be weaker than the original

 

[KootK]

While I disagree with OP's final conclusion that the analysis that he's reviewing is flawed, I do in fact agree with the lion's share of his reasoning:

1) The stock, ACI stiffness modifiers are intended to represent lower bound member stiffnesses.

2) Using lower bound member stiffnesses will lengthen periods and underestimate seismic demand.

3) If I were inventing RSA myself, from scratch, and not scaling the base shear the way that ASCE7 prescribes, I would also worry about the lack of conservatism associated with using lower bound member stiffnesses.

It is my understanding that the ASCE7 scaling procedures are, at least in part, intended to address exactly OP's concern. Once scaled, however, I do believe that an RSA analysis using the usual cracked section stiffnesses is valid.

In my opinion RSA is more about identifying demand "hot spots" within a complex structure than it is about providing a realistic estimate of base shear.

 

[Agent666]

The way I think about the situation being described by the OP regarding why lowering the seismic loads occurs and use of reductions is as follows.

Take a structure thats uncracked, subject it to some seismic load, it will briefly carry some level of load based on the stiffer uncracked sections. But at some point it cracks (at a relatively low flexural load compared to ultimate capacity in many cases for practical cross sections). Stiffness then incrementally changes, rinse and repeat for a few cycles and elements with moment exceeding the cracking moment of members have for the most part cracked throughout the structure. Leading you to the situation whereby the response has softened and with correspondingly lower base shear. The reality of the situation is that yes its stiffer when uncracked, but the structure can't really take the base shear based on gross section properties without cracking.

In design we shortcut to the end result and simply take the stiffness reduction. Sometimes the reduction is just applied everywhere to all members, but in reality it should be applied where cracking is expected at the ultimate limit state. Keep in mind as well that the code reductions are sort of an average over the entire member length for example in a beam.

The reductions should be used for strength design and also analysis of drifts.

 

[Settingsun]

I would think (but don't know) that a member that doesn't attract enough load to crack may not be a great contributor to the stiffness/frequency. If that's the case, underestimating its stiffness wouldn't be the end of the world.

What about plastic rotation? That would reduce the overall stiffness (secant stiffness) below cracked elastic stiffness, but is that already accounted for by the codes when they relate EQ load to elastic frequency?

 

[Agent666]

Steveh49, for a force based procedure usually you'd analyse the structure under a load that accounts for the level of the ductility expected (I.e lower level of load).

Then you'd multiply deflections from this analysis by the ductility to account for the final total inelastic drift (zero stiffness after you form your ductile mechanism), you might also need to look at accumulation of inelastic drift at a particular level (drift profiles).

You'd then work back to the total rotation and curvature at hinges, taking off the yield curvatire to give you the inelastic component of the potential plastic hinge curvature. This can then be compared to code curvature limits and hence level of local ductile detailing required can be determined.

Each codes going to have its own way of approaching the same fundamental thing outlined above.

 

[KootK]

I feel that it's also worth noting that:

1) the whole point of RSA is to capture the effect of higher mode responses when those responses would be meaningful and;

2) higher mode responses are much more likely to be elastic or near elastic than are first mode responses. This is reflected in recent ASCE provisions for seismic diaphragm design that only apply (R) values to the first mode effects.