Floor Vibrations in Buildings: From Modern Designs to Adaptive Reuse

Liz Pimper

Hello and welcome to today's WJE Webinar Floor Vibrations in Buildings: From Modern Designs to Adaptive Reuse. My name is Liz Pimper and I'll be your moderator During the next hour, engineers Mohamed ElBatanouny, Chris Freisinger and Rich Lindenberg will provide a practical overview of floor vibration issues and buildings focusing on how to evaluate and improve performance to meet a variety of occupancy and equipment needs. This presentation is copyrighted by Wiss Janney Elstner Associates. And now I will turn it over to Chris to get us started. Chris.

Chris Freisinger

Thanks, Liz, and thanks everybody for joining us today. I'm Chris Freisinger, structural engineer in our Chicago office. Joining me today is Mohamed from our Janney Technical Center and Rich from our DC office. Collectively, we have decades of experience with understanding and solving floor vibrations in buildings, especially as related to modern design and adaptive reuse in older buildings. We'll be using our project experiences to give an overview of the relevant industry guidelines, basics of floor vibrations, assessment techniques in the field and evaluation methods. We'll be able to share case studies with you to give you tips on how to tackle these fun and challenging problems with a variety of mitigation techniques.

Vibrations are part of our daily life and if you ask AI, you'll get a detailed answer describing the repetitive motion of particles moving around an equilibrium position. And in our daily life, we have examples of vibrations all around us, including mobile phone alerts running on a treadmill, car engines, washing machines. And if we think a little bit more about running on a treadmill, we can probably guess that a man running on a treadmill will produce more vibrations than a child running on a treadmill. We can describe the vibration in terms of frequency, which is the number of repetitive motions within a period of time, like beats per minute when running amplitude, which is the maximum displacement that a vibrating object moves from its equilibrium position, which could be based on the weight of the person running and duration.

So thinking a little bit more about vibrations in our building life and expanding that to buildings. External vibrations from buildings can be from construction ongoing, next door blasting in the area or train or vehicular traffic nearby. And then internal vibrations could be from interior equipment such as cooling towers or pumps or human induced vibrations from fitness centers or walking. Today's focus will be on human induced vibrations within buildings. The most common vibration concerns in buildings are due to people walking around and they typically show up in one of three ways. Human perception is the most common and occurs when building occupants feel the vibration and their work is disrupted. As buildings are increasing amenities to attract tenants, fitness centers are on the rise, and often these fitness centers are installed on floors that were intended to be an office space. So the vibrations from the treadmills or weight machines can travel into the framing and be felt by tenants and adjacent portions of the building.

Often solutions include special raised floor systems to help limit the vibrations and special hangers for ceiling fixtures below. Human perception can also occur due to just someone walking around next to you on the floor. If flexible monitors are not locked into position as the floor vibrates, the vibrations can easily translate to the monitors. Sometimes just swapping out the monitor arms can reduce the human perception to an acceptable level. As modern buildings are designed with more open spaces and less columns, the floor systems become more flexible, and this may be allowing vibrations to travel farther in a building and could be more perceptible. Also, within these large areas, there are a lot of typical setups with cubicles and the adjacent walls are off in glass and stop at the ceiling line. The vibrations of the floor can cause sway of the partitions. The second way that these vibration concerns show up in building is for sensitive equipment and medical labs.

Often the equipment in these areas have very high tolerances for floor vibrations to allow the equipment to stay calibrated. The floor framing needs to be stiff enough to limit the vibrations to acceptable levels. In adaptive reuse projects, this is often not the case and the framing ends up being too flexible and needs to be stiffened. And the last way that we see vibrations in buildings is with artwork. Sue the T-Rex at the Field Museum in Chicago is an excellent case study on artwork. As part of a renovation project, Sue was moved from one location to another within the field museum, and the museum was interested in understanding the difference in vibrations from the original location to the new location and how to limit vibrations that could affect the fossil.

With all these concerns, there are often common questions that arise that we'll tackle today. One of the first few questions everybody wants answered is, why do I have these vibrations? Why now or why does our floor meet? Or sorry, does our floor meet the appropriate vibration performance criteria? The answer to these questions probably depends on how the building is being used or what is being subject to the vibrations. Other questions include, how hard is it to figure out if I have a vibration problem? If people can feel the vibrations, is there a risk of structural damage and what does it typically cost to fix a vibration problem For solving, we have a lot of tools in our tool belt ranging from field testing to analytical modeling to understanding the building behavior. This understanding will help us review possible remediation opportunities to fit the needs of a specific project. But before we learn about that, let's hear from Rich about the fundamentals of vibrations.

Rich Lindenberg

Thank you, Chris. Before diving into building performance and floor measurements, let's take a step back and talk about vibration from a more familiar context our daily life. On the left side here, you see a classic example of free vibration. Think of a ball on a spring, you pull it down, let it go. It bounces up and down. That's what engineers call free vibration. There's no one acting on it after that initial action. It just keeps oscillating for a while because of the energy you gave it. On the right. We see something that should be familiar with everyone, a child on a swing. From an engineering context, we think this is a great example of force vibration. Someone maybe a parent, is giving them repeated pushes. That external force keeps the motion going and depending on how you time it, you actually make them go higher. And we like to think of that in a vibration. Classic vibration terms is what we call resonance, being perfectly in sync with pushing them right as they're ready to come back to you and be pushed again. So these two basic ideas, free vibration and forced vibration are the foundation of how we understand building floors and how they respond to movement. So now let's connect this to the built world.

I'll be showing an animated set of slides here to understand that behavior. The animation as we start out, we'll be showing a beam, which is the model of our floor, a blue line with a red dot, and that.is a measurement device. And as it motions, we have a time history plot that I'm circling around. And then on the right side we have a frequency plot. The frequency tells us how many times an oscillation is happening in a second, so that would be measured or the unit for that would be hertz and we can change various parameters. So there are three things that really shape how a floor vibrates mass, stiffness and damping. And we'll walk through each of those behaviors and each of those will have an animation to kind of show that context and behavior.

So the first step will be mass. This is how much a floor weighs along with the stuff it supports. Heavier floors move relatively more slowly, adding mass and reduce the sensitivity to higher frequencies, but also can lead to natural frequency. Moving closer to how we walk. So here you can see I'm adjusting the mass of the floor, less mass, tighter, faster vibrations, more mass, slower. The frequency also as we increase the mass slows down the oscillations and we see that with the red dot less mass than moving to more mass. So we're changing the frequency. We're also changing how long those vibrations last holding other things fixed.

Next is stiffness. Stiffness is how the floor resists bending. The stiffer the floor, the less it moves, the quicker it responds. As we increase the span length or reduce the structure depth, the stiffness would then decrease. That is what making longer spans often more problematic. So you can see here as I adjust the stiffness, higher vibration is very rapid, the frequency is increased, and then we move the stiffness to be less stiffness. The vibration are longer, slower and more vulnerable to people walking. Lastly, we have damping. Damping is how quickly the vibrations die out, just like a shock absorber on a car with more damping, bouncing, fades faster. So there's high damping. Now transitioning to low damping, you can see with a low damping, we have vibrations that last a really long time. They don't attenuate very little at all. The other really important note in an analytical sense is that the damping doesn't change the frequency. So just by changing damping, the frequency plot has never shifted left or right as those changes are being made, damping is really desirable for structural retrofits.

Okay, so moving on to force vibrations, we're going to do a similar plot. We have a beam. Again, what we've added or what we're adding is a forcing function. And that forcing function, as I say, is analogous to footsteps on a floor. And so we'll show that philosophy, and this is a simplistic approach, but we'll have basically six footsteps all in the center right on top of that red dot, and then we'll stop responding or stop walking and we'll see that free vibration response. So opening up that animation and the things, again, calling attention to, we have the beam, the red dot, we have the time history plot. So how that red dot's in motion and the frequencies. The important thing here is there's two frequencies. I'm hovering on 2.3 hertz. That's the floor's natural frequency. And the second frequency that I'm shifting to is 1.66 hertz.

That's the walking frequency which aligns with the 100 beats per minute. So as I change how we walk the speed of walk, you can see a really large amplification at one moment and we'll see that happen again and that's going to be resonance. So as we step through these images, so now just as I did before, we're going to change the mass low high does the same things, but what's really notable as we pass through and that frequency causes the floor's natural frequency to align with the walker's frequency, those vibrations get really large and that's the condition of resonance that we're often concerned about. This can be everybody walks at their own speed. And so this is one of the largest reasons why at times vibrations can seem random because different people might tune into the floor's natural frequency.

Next we have stiffness and one way we fix stiffness or we have a really large vibration problem. Here we can increase stiffness. And what we're doing by when we change these parameters, particularly in this force vibration problem is we're shifting the frequencies of the forcing away from the natural frequency of the floor. And so obviously when they're aligned, we have very large vibrations and they can build up and when they're apart, vibration problems are not as problematic and many times. So stiffness is one of the things that we will often use as a repair methodology to address four vibrations. And then lastly, we'll look at damping again, damping remember doesn't change the frequency. So as we vary damping, what we see is the forcing function not changing here, but the natural frequency of the floor, we'll be affected by that damping. And so we change the mass and again, if we align the mass to a natural frequency of the floor, we see the resident buildup, the damping can directly attack that I, okay, so hopefully that gives you an idea of the mechanisms, how vibrations occur in floors. So what are the rules? What are the guidance that we use to evaluate vibrations?

So is there a problem when it comes through floor vibrations? It's complicated. Vibrations are not analogous to question strength, which is something that we've got figured out. We've codified it in building codes. We know how strong beams need to be and floors so they don't collapse. But vibrations which affect how a floor feels when you walk on it or it performs when you place sensitive equipment on it, that's where things get a little bit more complicated and it's what we call serviceability issues. The floor might be strong enough not to fall, but it might still vibrate That causes disturbance to workers or causes equipment not to perform acceptably. We have guidance for this along with industry recommendations, but it's not cut and dry in all cases.

So when we say there's a problem, what we really mean, there's a lack of clarity and consistency when it comes to vibration standards. So really kind of a survey of all these guidance that exist in the industry, particularly when it comes to human footfall traffic, most notably for steel structures. We do have basic guidance from the American Institute of Steel Construction, AISC 360 just tells engineers at a codified level that they need to be considering vibrations for various activities. The Steel Design Guide series 11 by AISC is a seminal guidance. It's world renowned for its benchmarks on vibration performance under human activity for both offices as well as sensitive equipment considerations down an overarching umbrella standard ISO ten one thirty seven is an international standard that provides guidelines on overarching performance as well as evaluation in the industry. We also have various other construction types, producing documents, many cases founded on Design Guide 11 guidance, but specific to the various industry. This is CRSI, Concrete Reinforcing Steel Institute.

Separately, American Society of Heating Refrigeration and Air Conditioning Engineers gives recommendations on mechanical vibrations. So obviously times we put chillers and performance of buildings due to those type of considerations, we would look to this guide. Even the wood industry now is providing guidance on performance of vibrations. Now lastly, let's take a closer look about where vibrations are acceptable. We have here a chart comparing different guidelines for vibration performance across the spectrum of concerns from sense of equipment to building damage. So they come from the guides that I just was talking about. On the X axis we have the frequency, which is how fast the floor is vibrating, measured in hertz. On the Y axis we have the amplitude in this case velocity, how strong those vibrations feel.

So as a reminder, frequency matters a lot when it comes to consideration of vibration issues. So each line below represents a threshold. If you're building vibration is above the line, it could be a noticeable problematic for that use below the line, acceptable. At the bottom, we've got somebody working on a lab bench. This represents very sensitive environment laboratories. Clean rooms, the criteria are very strict. Even small vibrations can be disruptive to delicate equipment. More importantly, these vibrations are imperceptible to humans. We can't use our own context to judge them. Next up would be the ones we can judge personally. In the middle we have the person standing. This is the typical office or residential environment. Vibrations here are perceptible. They're less critical to be controlled. So the space feels solid or more critical to control for that space feels performative. You're comfortable working or comfortable resting at your home.

And then lastly at the top we can show the crumbling building. This is a more extreme case to remind us that all structures have thresholds. Vibrations can cause damage, but they are considerably larger in magnitude than typical vibrations that would be impactful to us. So we'd be very disturbed as humans if we have vibrations at levels that would cause damage and this might be driving piles next to a building. We have concerns. So now we understand on the basics of vibrations, we have some insights into the various guidelines. Mohamed is now going to address how we measure, understand if we're okay and how do we remediate.

Mohamed ElBatanouny

Thank you Rich. So now we'll talk about the vibration assessment approach. So following understandings, initial vibration concern from the client, which Chris covered earlier in this presentation that can be is a human perception problem, a sensitive equipment problem or artwork problem. We then usually do a vibration investigation and the first step in that investigation is to do a field investigation or a field study. And that involves collecting field measurements because these are usually a lot more accurate than just doing an analytical check on what the vibrations level would be because the structure is in service and it's existing and we can go out there, put some sensors on it and actually measure the vibration performance of the floor. The second step is to evaluate the measurements that we collected. And there is many different standards as rich covered that require different analysis techniques. And the purpose of this will be to process the vibration data that we collected to be able to compare it to the industry standards that are appropriate for the use that we had.

And then the third step is to doing the analytical investigation. And that usually include us building a finite element model of the structure using the measurements that we collected to calibrate the model and then trying out different vibration mitigation strategies that we'll be covering later in this presentation. And then finally, the field verification. As rich described, this is not a strength problem, this is a serviceability problem, it's not well codified. So we usually try to do a final step, which is optional, but it's highly recommended to actually go out after a repair was implemented on the structure and verify that the measurements we are collecting agree with what we protected and that the structure or the floor is now in compliance with the applicable industry standards.

So what do we do for the field measurements? We usually do either forced or free vibration measurements. We have different ways to end with these vibrations that we'll go through, but we use accelerometers to mainly collect the vibration data. These accelerometers are then connected to that acquisition systems. And then we have proprietary software that record and process the data in real time and allow us to also do post-processing of the vibration data to understand the vibration characteristics of the floor and the two types of testing that we do. The first one is the free response testing. Again, this is when you, like Rich was describing, you pull something and then you release it and let it vibrate on its own. In that case, what we do here is what we call a heel drop test and we usually have a heel drop plate to actually measure the input force that we're inputting in the floor.

But simply put a heel drop is when you raise your heels of the floor and drop them down. And when you do that you basically put an impact force in the floor that causes it to vibrate. And we have a short video here that demonstrates that process. Rich is performing a heel drop and if you look at the monitors in the video, you can see them vibrating in response to the force as the rich inputs on the floor. And then we use accelerometers that we have to collect the data, vibration data from the floor and then we process that data to understand what is the frequency response. And in this case here there are three main natural frequencies that we are concerned about the 5.4 7.6 and at about 10 hertz for that particular floor. The second type of testing that we do is a forced vibration testing.

And this is basically a simulated walking scenarios. So we also call this like a stress test because we walk at the specified frequencies to cause that floor to go in resonance or close to resonance similar to what Rich was describing. And that will give us the worst case vibration amplitude that we can expect for that floor. So what we do in that case is we put an array of sensors similar to what I'm showing here in yellow in the first plot. Then we do some simulated walking scenarios similar to the video where rich is walking on a floor. Then we take the data that we collected from all the different sensors and we can use this to get the vibration amplitudes at the different locations in the floor and we can also use it to plot how the floor is actually responding to the force that we are putting into it.

Once we collect the data, then we do the analytical modeling. And the reason we do finite element models and not hand calculations is our structures are usually regular in geometries, there is regularities in load passes and there is slap openings and other things that basic complicate the problem. That's why we do the modeling and our purpose is if we do the model, we can get the vibration response of the model similar to what I'm showing here. We can compare that vibration response from the model to what we collected in the field. We can do a calibration to calibrate our model with the field results similar to what we're showing for the model calibration plot here. And once we get a good agreement then we can try the mitigation strategies on the model before we actually go to the field and put it on. The one thing I would like to note here for that plot is the shaded gray area is frequencies above nine hertz and below nine hertz frequencies.

If the floor has a frequency below nine hertz, we call it a flexible floor because basically that means that a person walking at a regular walking pace can actually excite the floor response and cause vibration issues. So in the example we're showing here, we have two frequencies that are below the nine hertz and that could be problematic for that floor. And then we look at the different retrofit solutions. So starting with replacing the floor, that will definitely solve the vibration problem, but it is usually our last option because that is very costly and it also takes a lot of time. Another option which is the easiest option in that list is increasing or decreasing the mass. This is a very low cost option, but it also could be not very effective for a lot of the cases that we have to deal with. Adding damping is another option, whether it's a passive or an active tune mass damper, this option is very effective if we have a targeted approach or a targeted frequency that we're trying to address.

And also if the area is small, we can try the damping, but it has localized impact. So if the area is very large then you might need more than one damper to actually solve the problem. The next option is stiffening the floor, and that can be done by adding columns or adding beam stiffening. And this approach is very effective. If we need a big shift in our stiffness or if the area is very large, then we can stiffen the floor. However, that option is difficult. You really can't mock this up because you actually need to stiffen the floor before you verify that you're getting the results that you want. It's costly and in some cases there is constructability issues. So for example, if you have a floor and there's a tenant that is in the floor below and you want to stiffen that floor, you'll basically fill that tenant that they have to move while you are doing the work. And then lastly, you can change the use or rearrange the space. And while this is an easy solution on paper, in most cases it's not always practical. So now I will take it to CREs to take us to our first case of study.

Chris Freisinger

Thanks Mohamed. Tenants, in a modern 55 story steel frame building were reporting excessive vibrations on one of the three floors that they leased. It was in an area of open cubicles. The structural framing in this area consisted of a concrete top metal deck spanning 15 feet between beams and the floor beams were spanning almost 45 feet. So first we did our own field investigation and we performed a walkthrough observing the furniture, the partition walls, mechanical, all the factors that could affect the damping. And then as Mohamed had outlined, we completed the field vibration testing at several locations on several floors involving the heel drop plate tests and the walking tests. We also make sure to pull back the carpet tile to connect the sensors directly to the slab to avoid any noise in the system.

Then we can compare our field measurements to the recommended limits. In the AISC Design Guide 11, we've highlighted the limits for offices with orange and plotted our field measurements. In red, you can see that we are just at or above the limit. So without tenant reports of vibrations, we might even just say there's a potential for vibration concerns, but it's not very strong. However, we know there are vibration concerns as at tenants are complaining and their work is being disrupted. So then we can move into modeling. As Mohamed mentioned, the goal of the analysis is to create a model of the structure that we can use to calibrate to our field data and then ultimately model different mitigation options. The image on the left is the frequency response for the floor system. The black is the field data and the blue line is the calibrated model. So we're matching the field data pretty good. The image on the right shows the deflected shape of the first vibration mode and we're getting pretty good match at everything below nine hertz, which is the area that we're concerned about.

So now we can start trying mitigation options First we start by adding a post and you can see within the area of the green box, this is the area of the frequency plots that we're most concerned about. So the post takes care of that first mode, but posts are really disruptive to the space. And so while it's effective, we wanted to keep looking for some solutions. We also tried stiffening the existing beams and again in the green box you can see the frequencies are shifted higher, but it's not really taking care of the amplitude of the vibrations. We considered adding steel members below. This was a little bit more effective but it's really hard to mock up so we can't trial the option before installing it. Then we settled on a tune mass damper. So in this model we set the tune mass damper to the frequency of 5.4 hertz and you can see that it really takes care of that first mode.

So what is a tuned mass damper? A tuned mass damper can add dampening to the floor to help dissipate the vibrations quickly. Back to Rich's swing analogy. It's like pushing a swing at the wrong time. The swing is just unable to gain energy. So in our models we can put in a simple mass in a spring with a set of stiffness and then we can build this tuned mass damper with extreme adjustability including stacked weights, locations, spring stiffnesses and dampers. We can take the tuned mass damper to the field, tune it on the top of the slab, make sure that we think it's working appropriately before we install it on the underside of the framing for our project, we ended up installing two tuned mass dampers tuned to the first two frequencies of the floor and this worked out great. The tenants aren't complaining anymore. We ended up modeling the floor for a couple weeks to make sure that we were getting consistent damping of the floor throughout different workers using the space and the clients were happy. So I'll send it over to Rich for a few more case studies.

Rich Lindenberg

Thanks Chris. So moving into one of the more demanding use cases for floor vibration, medical and research spaces, especially where sensitive equipment is installed, what you see here is an example is a medical imaging device commonly used in hospitals. These systems are extremely sensitive to even small vibrations and they need to stay precisely aligned for their performance. Particularly where many cases worried about blurred images, the manufacturer provides four vibration limits. An example is shown here on the right of a chart. This is the biggest concern in these environments isn't the building swaying or things like that, but rather footfall traffic operations near the unit as well as mechanical systems to address. This is a fairly simple setup to do testing. Basically a laptop and a simple mobile accelerometer array allows us to make those sets of measurements. And what you see here is the upper left-hand corner is the space before its renovations, and the right is the small system set up with measurements in the plot below we are measuring in three axis and we have that manufacturer specification from the prior slide shown that the limit threshold line plotted on there and the red, blue and black curves show are under.

So in this case we passed. It's a simple example approach demonstrates taking measurements early in the process can provide confidence and very expensive equipment and renovations can proceed with confidence and it's not difficult to get those answers.

In this next case study we were brought in during conversation of a retail building that was adaptably reused to a medical facility that included laboratories and operating rooms. The original building was not designed for vibration sensitive functions. So the client raised an important question during construction which arose in part because people were feeling vibrations when the design team visited the site and they said, well are felt vibrations, okay? And so we were brought in to assist with that set of questions and if there was an issue, can we basically assist them with vibration criteria for the sensitive equipment and how to address any concerns if it doesn't comply. So this is a common circumstance that can arise in adaptive reuse projects. So we conducted the testing two ways. As Mohamed described, we performed a heel drop, which is the plot here on the left. We were able to get the frequencies out of the floor and magnitudes and then we perform walking tests which simulated real world activity on the floor space. You can see in the walking test on plot on the right, particularly in the vertical direction, the tall mountain of response, which well exceeds the red line, which is the compliance requirement for operating rooms specified by AISC Design Guide 11. This meant that in the current state, the floor system didn't meet the requirements for operating use.

So when we went through a similar approach as described by Chris, the picture on the left shows an image of the space prior to the renovations. The client was hopeful they could be limited any modifications they had to do to their design. We performed analytical modeling and included options to try to utilize the wall framing, which is known in the industry to anecdotally contribute to improved damping performance but difficult to predict. So in this particular case, after our analytical modeling, which didn't seem to show enough improvement, the client did ask for a mockup and we did another round of testing. Unfortunately as predicted, it didn't perform well enough. And so through all our modeling work we basically recommended we had to do more than just stiffening, but in this case localize floor replacements. So the analysis work provided the confidence to limit the scope of where we needed to do floor replacements and help with the correct sizing of members.

So it's important to understand it's not a small decision involved a significant cost, but we were able to coordinate that during a rapid ongoing construction process to avoid significant delays. As with a retrofit, we went back and retested in this time as shown in the lower plot, the space now meets the requirements for operating rooms. So this case highlights the importance of evaluating vibration performance, especially in adaptive reuse where the original structure wasn't built for the use such as medical reuse. With the right approach, testing, modeling, and targeted intervention, you can deliver a compliant space without compromising functionality. Mohamed.

Mohamed ElBatanouny

Thank you Rich. So now for our last case study, which is for the field museum and the Sue Gallery. So for you who don't know, Sue is a T-Rex specimen of a dinosaur. It is the most complete in the world. Up to 90% of the dinosaur is actual fossil. So it's a very important specimen. It was purchased by the Field Museum in 1997 and then it was on display from the year 2000. In 2018, the film museum decided to move Sioux from its location in the Stanley Field Hall to its own gallery in the second floor. And while preparing that area of the new gallery, they noticed that human traffic was causing a resonance-like shaking of the fossils, the fossils of the dinosaur are moving. Of course they couldn't change the location. So the only option that the museum has was to mitigate in place.

So there were main two reasons or things that the museum was looking for. The first one was the human perception. Again, this was going to be a new gallery that will have a lot of visitors to see sue on display and you wanted to make sure that human annoyance or human perception is not going to be an issue in that space. The second and actually the more primarily reason of eliminating or reducing the vibration of the floor was damaged to the object because again, this is the most complete object, very important object, and the museum wanted to protect it. So for human perception, like Rich described and Chris as well alluded to A ISC design guide. 11 is a very good document to use to address human perception, but for the object or the T-Rex dinosaur in that case there's no limits. This was never really done before.

So what we did for that case is we basically went to the old Sue location where it spent about 18 years in the Stanley Field Hall, collected some vibration measurements and then we repeated the measurements at the new location of the new gallery. And then we did the comparison. And as you can see here at the old locations hold, the frequency was about 13 hertz. The new location, it's only six. The damping in the old location was 8%. New location is four. And as rich described earlier, if you have less stiffness and less damping, you may have a higher response which we had here. And the response was about seven times higher, at the new location compared to the old location. So what we did was basically creating a finite element model of the floor and doing a dynamic analysis. And we again calibrated the model similar to what we described before, calibrating the output of the finite element model to the actual field measurements as you can see here on the chart to the right.

And then we tried different retrofit options. I'm going to only show the options that we selected, which in this case was adding three columns and that basically shifted the magnitude of the vibrations down and also shifted the stiffness or the natural frequency of the floor to be higher than what it was. And then we designed the repair, which again included installing three columns. There were located locally under where Sue was going to be placed, which is near the middle of that gallery. And these columns extended all the way down to the ground floor and two of them needed a new foundation in order to ensure that the columns will be carrying the load from the beginning. What we did is we did a hydraulic preloading of the columns and we also did preloading of the new footings to make sure that the retrofit is engaged from the time it is installed.

And then we did verification testing. So that verification testing was done the night of the opening of the gallery. So our fix had to work and you could see here the results of the new location compared to the old location where we were able to increase the natural frequency from six hertz to 12 hertz. So almost double. We also increase the damping from 4% to 6%. We reduced the amplitude of the vibrations to be similar to what we measured at Stanley Field Hall, which was the original location too. And we also confirmed that there will be no human annoyance or human perception issues because we are below the recommended limit by AISC Design Guide 11. So here is a picture of the completed gallery of Sue. We also published the paper on this work that is available in the resources on the webinar page. Now I'll give it to Rich to take us through the summary and key takeaways.

Rich Lindenberg

Thank you Mohamed. So at the beginning of the webinar we provided a number of common questions. We'll come back to that. So why do I have a vibration problem? Because a lot of times we have a question. Flexible floors is a very common situation in many cases we get human perception and as we've talked about different people, how people walk as they go through an adaptive reuse. Owners don't appreciate the structure fundamentally has changed in many cases. Now we're seeing in addition to the existing flexible floor, high density cube spaces. So we have more people moving and more people perceiving those vibrations. Does my floor meet the vibration criteria?

Yeah. So depends on the use. If you have people complaining, it's a good sign. Performance isn't acceptable for human perception. Office workers for sense of equipment like imaging machines or microscope measurement based evaluation is essential. You can't really rely on your feel for the data in most cases there. How hard is it to figure out if you have a vibration problem? It's actually not hard. With modern sensors and tools, we showed an example, we can conduct onsite quick testing, compare the results to published criteria, manufacturer limits, and you can get an objective answer fast. If people feel vibrations, is there a risk of structural damage? This does come up and so for the most part, no, not necessarily. Perceptible vibrations is rarely a safety concern unless we're seeing motion levels on the order of seismic activity. Generally this is about comfort or equipment performance, not a sign that the building is unsafe.

What does it cost to typically fix a problem? This really depends on the source and severity. For localized discomfort, we have had a lot of success with tuned mass dampers. Those are relatively low cost solutions. Typically a project is on the order of 20 to $50,000 depending on how many and where for more severe issues, especially as we highlighted, an entire slab needed to be stiffened or dropped, replaced as we showed in the case study, that cost can be significantly higher. The good news is using a combined approach of measurement and modeling, we can simulate and evaluate multiple retrofit options before anything is built. So sometimes we can even test those cases onsite for the example of the TMD before really committing to that retrofit solution. I think the point here is the measured data-driven process helps clients make better informed cost effective decisions. So our key takeaways, final slide four vibrations are a serviceability issue, not a structural one.

That means they affect comfort, usability and performance. They're not covered by the building code. And instead we rely on guidelines such as the AISC Design Guide 11, ISO standards or manufacturer specifications for sensitive equipment. Second, the best way to understand if you have a problem and how big that problem is is to collect data. That's where floor measurements come in with modern sensors and tools we showed we can evaluate vibration performance quickly and objectively. And finally, there's no one size fits all fix. There are many possible solutions, but success depends on matching the right tool to the right problem. This could be a localized damper, a slab replacement in some cases, or a simple confirmation that no action is actually required as we've shown today, finding the right solution starts with the right approach, measurement, evaluation, modeling and testing when needed. With that, we are happy to open the floor to any questions, Liz?

Liz Pimper

Alright, thanks Rich and Mohamed and Chris for the great presentation. Alright, let's take our first question in existing wood framed elevated floors, what's the most effective way to reduce vibrations for gym use? Add a tuned mass damper, stiffness or dampening or add mass stiffness or dampening. And then this person says that they're in a seismic zone, so adding mass is problematic.

Rich Lindenberg

Oh, I'm sorry, I was reading a question. Could you repeat that list?

Liz Pimper

Sure. So in an existing wood framed elevated floors, what's the most effective way to reduce vibrations for gym use? Add mass, stiffness or damping and then they note that they're in a seismic zone, so adding mass is problematic.

Rich Lindenberg

In general, we don't recommend adding mass for most of the solutions period. Adding stiffness is typically where it is at wood frame structures are also a little bit more tricky. One, most people don't pay a lot of money to retrofit them, but some of the retrofit solutions sometimes are because of concerns of the individual joists and the floor system behavior allows the individual joist to respond. So we get some more complicated sets of issues out of wood, but in most cases the solution's going to be some focus on stiffness based solution.

Liz Pimper

Okay, our next question, how do you determine what are the boundary conditions of the slab?

Chris Freisinger

Yeah, I can help out with that one. So when we're modeling the slab analytically, we can make some determinations at the beginning on how much of the building framing we think will be affected by the vibrations and then we can adjust the area that we're modeling or the boundary conditions of the slab when we're calibrating against the field data. So we're not modeling what's their real life, we're modeling to get the behavior out of the system in the model to match what we're getting in the field.

Liz Pimper

Alright, our next question, can you stiffen only a portion of a floor safely?

Mohamed ElBatanouny

Yeah, I can take that one and yes you can. And we showed this in the case example for Sue where we just installed the columns, right? Then there's the three beams that will support us. You can definitely do that. You can also do it for if you have beams and you're just stiffening the beams, you can just step in the beams that are directly in the areas that you're trying to reduce the vibration and that would likely solve the problem.

Liz Pimper

Okay. Our next question, I think you addressed this briefly, rich, in your conclusions, how much did the tuned mass dampers cost? Very expensive, especially if only for a tenant, not for the full building or are you just talking about a very mini tuned mass damper, not something major like the New York Citicorp Tower from the seventies,

Rich Lindenberg

Chris had a tuned mass damper. In most cases, the tuned mass dampers we're using are much smaller. And like I said, I'm seeing on a lot of typical projects we've seen about 20 to $50,000 and that can be for more than one tuned mass damper, they're very easy to install, they're very easy to test and so they are often a preferred option for many clients that don't want to make structural changes to the space.

Chris Freisinger

And I would add that for our project, the cost of the tuned mass dampers ended up being similar to the cost of adding additional steel. However, we had more confidence with the tuned mass dampers because we were able to trial them before putting in the steel. So there's a chance you'll spend a lot of money installing additional steel and you may not get the results that you're looking for.

Liz Pimper

Okay. Mohamed, this is a question for you. For the fossil relocation, why was localized floor isolation not used?

Mohamed ElBatanouny

So this was one of the options that we investigated for that case. However, due to the low natural frequency of the floor, we were concerned with rocking of the specimen. We equated it to putting the fossil on a water bed in a way so it might rock and that was not acceptable to the museum and wasn't our main recommendation, but we did look into it.

Liz Pimper

Okay. Rich, this is a question for you. For the retrofit of the commercial building for medical use, does the technique of adding steel stud walls work by bracing one floor slab to the other floor slab above or below? How is the slab replacement solution done with thicker slabs or more steel framing or something else?

Rich Lindenberg

So with regard to steel studs, no, generally we don't want to try to lock the floors together. That poses structural problems and really the behavior that we're after is actually with the drywall all attached and it's physically damping. So damping here is just really micro friction of building systems moving together. So that's where when we see walls add to a space, that's where their improvement comes. And we do see that anecdotally out of many structures. With regard to the second question, what was that Liz, about the thickening of the floor,

Liz Pimper

How was the slab replacement solution done with a thicker slab, more steel framing or other?

Rich Lindenberg

I think Mohamed can also comment both thicken the floor as well as the steel so that because of sensitive equipment we typically need something much more than what you might find in a normal commercial retail space.

Liz Pimper

Okay. Our next question, how applicable is the AISC guidelines for equipment impulse related vibrations as opposed to human walking?

Rich Lindenberg

That's where the AISC design guide is focused on human related footfall traffic. And so that would be where one we would look at ASHRAE is intended for mechanical systems and two, in many cases there are guidance from the mechanical providers. So those would be the two cases. Then lastly, we can do analytical work to work towards that, which is we demonstrated an approach today that shows we can apply an impulse and evaluate the performance.

Liz Pimper

Okay. What are cost-effective options to address vibration from RTUs on a metal deck roof?

Mohamed ElBatanouny

That would depend I think on how high the vibrations are and how big the areas that you are trying to fix the vibrations on.

Rich Lindenberg

But normally the industry standard uses vibration absorbers and it comes standard with most equipment. That's what you see that springs under RTU systems and that would be again, what ASHRAE would work to address and that's what guidance the industry utilizes most often.

Liz Pimper

Okay. Next question. What type of accelerometer was used uni by or triaxial?

Mohamed ElBatanouny

So in most cases we at least have one triaxial accelerometer to record data and then we rely on uniaxial for the rest of the floor. For most of the walking scenarios, the vertical direction is a direction of interest, so any axis will work, but we use a triaxial to just confirm that the other two horizontal directions are not problematic. One thing I'd add is for the type of sensitive equipment we have to use, you're really trying to limit vibrations that are very, very small.

Liz Pimper

Alright. In the example you showed using T MDs, why did you choose TMD as opposed to increasing stiffness?

Chris Freisinger

Yeah, so on our project we decided to use the tuned mass damper because we could actually test it on the floor before having a contractor come in and install stiffening on the floor below. So the floor where we were having reported vibrations, there was a different tenant below. So any access we needed to the underside of the slab that we were working on had to go through a tenant below. So we wanted to really try to focus on a solution that we could test in the field before disrupting the tenant below and removing and replacing their ceiling.

Liz Pimper

Okay. A related question, how do you hide unquote the tune mass damper on a tenant floor?

Chris Freisinger

I mean if it was up to me it would not be hidden, right? It would just be shown in all its glory and everybody would get to see it. However, I can imagine that some tenants don't want to see it. So the ones that we use are relatively slim and we're able to either hang them from one of the beams in the space between the underside of the beam and the drop ceiling or the second location. We did have to install a few spreader beams to put the tuned mass damper up between the two steel beams. So they're smaller. You definitely need to do your homework on making sure there's no utilities in the way or let's say live sprinkler lines. That'll be hard to move.

Liz Pimper

Okay, next question. Let's see. Are there any cases where reducing vibrations caused undesired structural side effects?

Mohamed ElBatanouny

So not for what we've shown here, because you basically design, so first you need to have a very good experience with fixing existing structures. You can do things that cause undesired effects. But in our cases that we showed here, this was taken into consideration that when you are dealing with existing structure, you need to put the repair in a specific way so it doesn't have an undesired effect, but to actually have the effect that is desired. So for the Sioux example, we did need the preloading to make sure that we are actually engaging the new columns that support the structure to take some of the dead load. So when the human induced vibrations, which are very small in amplitude are caused by human walking as it can be mitigated effectively. So dealing with existing structures is a little challenging, but with good designs you can do it without undesired effects.

Liz Pimper

Okay. We've got time for one more question and this is a good follow up to the previous question. Under what conditions, if any, can vibrations become a structural problem? One,

Mohamed ElBatanouny

So Rich showed us in one of his slides, but for vibrations to become a structural problem, they need to be very perceptible up to annoying to be honest in most cases for a structure problem. The one thing I would note is historic buildings typically have much smaller vibration limits than modern design buildings. So that will depend on the type of the building, but you'll need to be very annoyed by the vibrations to actually cause structural damage.

Rich Lindenberg

I mean follow up just, I always hear people, the radio show, the kind of talk shows people can knock over a building if they know exactly. Most humans cannot damage a building. We all see the Tacoma Narrows famous, but rare for someone with a hammer or you just jumping, causing a problem. But we do see issues with mechanical systems that can cause problems to structures.

Liz Pimper

Okay, well thank you Rich and thanks Chris and Mohamed for the great presentation. That is all the time that we have for questions today. Thank you for joining us. We hope it's been educational. So again, thank you so much for your time and we hope you have a great rest of the day.