Displacement Induced Seismic Force 1

[StrucPEng]

My question is related to ASCE 7 CH. 13 - Seismic Design of Non-Structural Components.

Suppose we have a component such as a stair that spans between two floors. In a seismic event we will have the basic component forces in the x & y direction due to the weight of the component being accelerated per section 13.3. That is straight forward. Where my question arises is the force due to displacement induced by differential movement between floors. If the upper floor moves say 2", for argument sake, relative to the lower floor, that movement will induce internal forces on the stair and reactions at its ends (This all assumes pin-pin end supports, no slots).

The main questions would be as follows:
1. Is there any literature on this type of displacement induced force?
2. When designing for EQ would you treat these forces (acceleration vs. displacement) separately or combine them (X force + X displacement) in the load combinations. And if so or not, is there any code references or papers that would back that up or dispute that approach?
3. Are there reasons to not consider the displacements?

Thanks All!

 

[KootK]

2) I would not combine the forces from the two approaches. I believe that they represent two different approaches to the situation. With a pin-pin setup, I would expect your displacement based loads to dominate utterly which is why, in general, slip connections are the way to go.

3) The only reasons that I can think of are:

a) The presence of joints that allow relative movement to occur.

b) The stair -- and the building -- are designed for the stair to be a bracing element and that entails. This is tough to do of course.

 

[BridgeSmith]

I don't know if this is what you're after, but I'll throw out a couple of thoughts that you probably already know.

If the stiffness and force capacity of the stair in the direction of the displacement has been estimated, it could be included as a resistance in the seismic model. It may or may not be significant enough to be worth the effort to analyze.

If it's not included in the model, it should still be checked at the expected displacement, to ascertain how well or poorly it fares when subjected to that displacement. The performance criteria for the stairway will determine whether the damage it may sustain is acceptable or not. That is out of my realm; I'm a bridge guy, after all.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[KootK]

One argument that I've heard made for ignoring the displacement is this:

My stair is inside of a very stiff concrete shaft. Ergo it will be shielded from relative displacement.

While there's surely some truth to that, I don't buy it as a fully rational argument against considering relative movement. In my mind, it makes little sense to try to say that:

1) My drift between levels is dictated by these spiffy shear walls that I've designed and;

2) Man, these shear walls are pretty stiff so I don't need to consider the displacement occurring within them.

What's good for the goose is good for the gander damn it.

 

[chris3eb]

One argument that I've heard made for ignoring the displacement is this:My stair is inside of a very stiff concrete shaft. Ergo it will be shielded from relative displacement.

I think one thing that can happen is that when people think of a stair away from a concrete core wall, they think about things in terms of allowable building drift, so 1.5-2%. But when people think about a stair within a concrete core wall, they think of things more linear-elastically and end up with a tiny drift. As you mention, the 1.5-2% building drift comes from the shear wall, and of course the actual shear wall drift is a fairly small elastic drift times a fairly large Cd factor (in ASCE 7 terms).

 

[KootK]

Fine points chris3eb. There's actually another merit that I see to being within a rigid-ish core wall system but I've never heard anyone else make the argument to date. Consider:

1) On a taller building with shear walls, much of he large, inter-story drift at the upper stories is a result of shear wall rigid body rotation at that location rather than straight up shear building drift. That, even if it translates into straight up shear drift for the floor decks outside of the cores.

2) A stair within a core can mostly likely be expected to also undergo a rigid body rotation much as the enclosing shaft does. This would impose some vertical/rotational displacement demand on the stair connections but I'd think that to be pretty minor.

3) In effect, this would mean that the true lateral drift to be considered would be limited to little more that just the shear deformation of the wall system at the level under consideration. And that will be a pretty small number in most cases.

It seems to me that success in this space depends, in large measure, on the cooperation of the EOR and the quality of information they are providing. If you're dealing with a by others / their problem EOR, things get pretty ugly in a hurry.

 

[StrucPEng]

I would agree that the displacement loads tend to govern in most cases (especially with pin-pin condition). I am also in the camp that the stairs in the core would need to still accommodate inter-story drifts, maybe being able to make the point that they are somewhat reduced from the max story drift values but still they are there.

I am more thinking for stairs that are not part of the egress system proper so outside of stair cores.

I am back and forth on the idea of combining the effects with:
1. The stair does not experience accelerations for any other reason than it is attached to the structure that is experiencing movement. (Think a magic floating stair not attached to the building during an EQ, no movement without contact. In this frame I would say that the one is a result of the other and really only the worst one would be the governing case (not combined).

OR

2. The displacement happens moving the stair at the top causing internal forces, and the stair is accelerated by virtue of being attached to the lower floor and experiences an acceleration and thus some additional force separate but related. In this case the two acting simultaneously (mind you in the same direction only) would make sense and should be combined.

 

[KootK]

If feel that only one of these things can be true at any one moment in time:

1) The primary structure is restraining the stairs from flying off into space laterally (the acceleration load case) or;

2) The stairs are restraining the the primary structure from moving laterally (the imposed displacement load case).

In this case the two acting simultaneously (mind you in the same direction only) would make sense and should be combined.

In my mind, that is equivalent to saying that the stairs are concurrently the deliverers of the seismic load as well as the receivers of seismic load. And I see that as a logically irrational proposition. Please try not to be offended by that statement. I issue it because:

3) I feel that it's the truth and;

4) I suspect that it may be just what you need to hear.

 

[BridgeSmith]

In my mind, that is equivalent to saying that the stairs are concurrently the deliverers of the seismic load as well as the receivers of seismic load. And I see that as a logically irrational proposition.

Obviously, you're correct that the 2 cannot be simultaneously be true, and they may never both be true for the same structure. However, I believe which one is true for a particular structure will depend on the effective stiffness of the stairs relative to the effective stiffness of the overall structure. That relationship may not be obvious, and may not be similar for different directions of movement. If the relative stiffness values are unknown, it would seem prudent to consider both possibilities.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[StrucPEng]

No offense taken, this is exactly the discussion I was hoping to have to help clarify some thinking.

I see your point about delivering and receiving load and I think while that is a good justification, I still find myself thinking that both situations can happen at the same time.

My thinking is currently like this:

Assume there is no differential movement between floors, in that case the building will move and the stair accelerate and develop a seismic force. This is true regardless of the level of differential movement. Now to that same situation we introduce the differential movement where the upper floor moves say 1" further than the lower floor. We still have the acceleration loads plus we have the loads due to the stair trying to keep the two floors from moving apart more than 0".

For the sake of argument, please indulge this bit of fantasy but assume the above scenario but the differential movement is caused by wind that so happens to strike the building at the same time as the earthquake. In that case I would also think that we would consider the EQ forces due to acceleration plus the loads due to the differential movement.

I know that that scenario is obviously farfetched but the concept I think still holds.

Maybe I am running around in circles here but I welcome some further straightening out.

 

[KootK]

Maybe you're right about the possible concurrence of inertial and displacement based demands. That said:

1) The inertial force on the stairs is likely to be on he order of hundreds of pounds.

2) The force generated by by restraint of displacement is likely to be on the order of thousands, or even tens of thousands of pounds.

In this context, it's probably of little significance to whether or not one includes the inertial loads.

 

[brizstruct]

I would suggest that it might be worth reviewing the failure of stair structures in buildings in Christchurch NZ.
Based on these findings, we allow the stair at the lower landing to slide and not become a stiff and potentially premature failure in the building
The mass needs to be considered
The stiffness needs to be resolved

Cheers

 

[StrucPEng]

I agree the displacement generated force will in general be quite a bit larger than the inertial forces especially if you have a more flexible building system.

I think overall this ha really helped clarify my thinking on this so thank you all for that!

 

[KootK]

1) Welcome.

2) Thank you. I see more clearly now that acceleration and displacement based loads probably are concurrent. Or, at the least, it hurts my brain too much to think through all of the dynamic aspects required to convince myself that they're not. For sport, I was trying to wrap my head around this:

a) When relative displacement is at its peak, relative velocity is... zero?

b) But, when relative velocity is zero, is acceleration not at it's peak?

Yup, my head's starting to hurt all over again...

 

[Prestressed Guy]

One other thing to consider. You do not need to have a sliding connection to dissipate story drift. It can also be done by yielding which often is a much easier way to go.
Make sure that some element in the connection is bendy enough for the needed displacement and that the rest of the stiffs in the connection are strong enough to force bendy to bend.

 

[KootK]

@Haydenwse: thanks for that advice. Any chance you'd want to share descriptions of some of the details that you've used to accomplish that?

 

[Prestressed Guy]

I work exclusively in precast/prestressed concrete so my connections are in concrete. One of the typical ways that i release displacement induced loads is with a long legged angle (L6x6x1/4) with DBA's only near the toe of one leg. The connected part is to the other legs The connection then will resist out-of-plane loads but will release tension parallel to the DBA's. The leg with the DBA's will bend and allow the displacement with minimal load.