Direct Anslysis?

[SteelPE]

This is probably a simple question for some so if it is I apologize.

When designing a steel structure using the DAM. What forces do you design the base plates and foundation for? Do you design them for a regular pdelta analysis neglecting the DAM results? Or do you use the results from the DAM?

 

[Lion06]

I design the baseplate and the footing for the DAM forces. I size the footing ( check soil brg) for the non-DAM service level loads (using a second order analysis. Interestingly enough, as you would expect, this makes the situation more likely that you can have a stable footing at service(for moment and/or uplift) that is unstable at strength level loads.

 

[BAretired]

SteelPE,

I don't think the question of second order effects on framed structures can be considered simple or obvious. I am not familiar with the DAM, but in reading about it briefly, I understand that it uses a notional lateral load of 0.002[Σ]P at each storey to represent erection and manufacturing tolerances. This is presumably based on an erection tolerance of 1/500 times storey height. For a 10' storey height, this would be a tolerance of only 0.24" per storey.

The Canadian standard uses a notional lateral load of 0.005[Σ]P which was recommended by Clarke and Bridge based on research performed at the University of Sydney, Australia. This appears to be considerably more conservative than the DAM and I am not sure why there is such a large discrepancy between our two codes.

Whatever assumption you make, I agree with StructuralEIT that the baseplate and foundation must be designed for the notional load combined with the second order effects of gravity loads operating over the resulting eccentricity, i.e. the P[Δ] effect.

BA

 

[SteelPE]

BAretired

I am not familiar with the Canadian Standard. From my uses with the DAM I do know that part of the analysis requires you to modify the axial and flexural stiffness of the frames. Does the Canadian Code require you to do the same thing?

 

[Lion06]

BA-
that does seem like a big difference in notional loads. Does the Canadian Standard require a stiffness reduction factor, similar to the DAM?

 

[BAretired]

The Canadian Standard does not require a stiffness reducton factor, but if a first-order analysis is done, an amplification factor, U₂ is applied to the factored moments and forces. If a second order analysis is done, no such amplification factor is required.

BA

 

[Lion06]

That's probably the reason for the difference in the notional load magnitude. AISC requires EA and EI to be reduced by 20%.

 

[JoshPlumSE]

The stiffness reduction effects of the DA method are intended (I believe) to account for the inelastic buckling of compression members during your elastic analysis. You need these stiffness reductions to appropriate design forces and moments out of your P-Delta analsyis.

Now, the DA method specifically allows this stiffness reduction to be ignored for things like drift or deflection design. This is because these are deflection based values, not strength based values.

Considering both of these things, the demand moment and axial force of your column bases should be based on a DA method including the stiffness reductions.

However, if you are looking at rotation or deflection limits for your column bases, then you could ignore the stiffness reductions.

 

[Lion06]

Josh,
If I remember correctly, the stiffness reduction is to account for softening of the steel at strength level loading with regard to second order effects. The reason I say that is that even though you use the stiffness reduction for the analysis, you only use that to get the forces - you don't use a reduced EI or EA on the design side when calc'ing the capacity.

 

[JoshPlumSE]

StructuralEIT -

"Softening of the steel".... Not sure what you mean by that.

You make a good point in that these stiffness reductions are used in your analysis and do not apply to capacity calculations at all. Though that is somewhat off-topic....

My basic point remains the same. You use the full DA method to come up with the force and moment demand at the base of the column. But, you can neglect the DA stiffeness adjustments if you are more concerned about deflections or rotations at the column base.

 

[Lion06]

By "softening of the structure" I mean that at strength level loading the members account for a reduction in stiffness as a result of strains that result in Esec (or is it Etan?), not the full E. That is the "softening of the structure" that I'm referring to.

I agree that serviceability considerations (drift, etc.) should not include the reduced stiffness factors.

 

[valleyboy]

This is interesting as it has parallels with current UK design practise for multi storey steel frames.

We design for a notional horizontal force of 0.5% at each storey. Analysis of the bare frame is carried out, and 'alpha cr' value calculated for the whole frame. This is a measure of susceptbility of the frame to second order effects. Second order effects are either neglected, or first order effects amplified, or a full second order analysis carried out depending on the value of 'alpha cr'.

The code (BS 5950 or EC3) specifically states that notional horizontal force effects are exculded from foundation loads as they are not 'real' loads.

VB

 

[WillisV]

For aisc the actual direct shear from notional loads may be negatected but the amplified moments from the analysis should be taken thru the foundation design. Generally the extra shear from the notional loads is so small it doesn't really matter, but you can apply the same notional loads in the opposite direction at the base of the column to eliminate the fake shears if you wish.

 

[Lion06]

Why are the notional loads fake? I understand it assumes all columns lean by the maximum amount permissible in the same direction (extremely unlikely to happen), but if that happens the load is real, no?

 

[WillisV]

The notional loads are applied to push the columns into the leaning position. If you directly model the leaning of the columns (as is allowed) you still get this action without any applied notional loads. The increased moments and associated shears DUE to the vertical gravity load acting on the leaning columns aren't fake, but the actual notional shear loads used to push them into a leaning position are.

 

[Lion06]

If you have a column that leans by H/500, there will be a base shear of 0.002P and this is a real load. This is what the notional load is meant to capture, is it not? While the notional loadagnitude and out-of-plumb base shears are identical, they're overall impact is not identical. From a second order analysis perspective, the notional load will not result in a drift equal to the assumed out-of-plumb dimension. This won't matter for a first order analysis, but it will in a second order analysis.

I recognize we're dealing with tiny loads (relatively speaking), but whether we're talking about an out-of-plumb structure or a notional load that is equal to the out-of-plumb dimension or actually modelling the out-of-plumbness the base shear is really there.

 

[WillisV]

From Engineering Journal, 1Q, 2009 "A Model Specification for Stability Design by Direct Analysis" by Nair (also in draft spec for 2010 Spec):

User Note: The notional loads can lead to additional
(generally small) fictitious base shears in
the structure. The correct horizontal reactions at
the foundation may be obtained by applying an
additional horizontal force at the base of the structure,
equal and opposite in direction to the sum
of all notional loads, distributed among vertical
load-carrying elements in the same proportion as
the gravity load supported by those elements.

 

[JoshPlumSE]

StructEIT -

If you model an H/500 out-of-plumbness to your structure and you run the analysis for gravity loads, there will NOT be a net shear at the base of your structure. There will be a net moment, but not a net shear. Make sense?

The Notional Loads are fictional loads that are intended to approximate the destabilizing moment that results from the out-of-plumbness of the structure. But, they are not real loads.

 

[Lion06]

I see that for the structure as a whole (gravity and lateral elements combined), but here's my point - looking at an extreme example just to make the point, if you have a building with two brace frames in each direction (4 lateral columns) and 496 gravity columns that are leaning on these 2 braced frames. Let's say it's a single story building, the total load is P, and every column has an identical trib such that the gravity load in each column is identical. So the lateral reaction at the base of each gravity column due the out-of-plumb of H/500 is 0.002*(1/500)*P = 0.00004P. This same force is now leaning laterally on these 2 braced frames. So there is a real lateral force at the top of each frame of (496/2)*0.00004P = 0.00099P.

I understand that the total base shear (when you look at gravity AND lateral elements) is 0, but who ever looks at base shear for gravity columns. They all have some based on the displaced shape, but I've never considered that in design unless the column was intentionally sloped......... and even then it's base shear doesn't figure into the actual lateral analysis.

 

[slickdeals]

SEIT:
What's your new handle?