Examining the Relationship Between Vibration, Frequency and Steel Joists
Our three experts met to discuss the intersection of vibration, damping and natural frequency as they relate to steel joists.
- Tom Murray, Ph.D., Professor Emeritus at Virginia Polytechnic Institute and State University
- Brad Davis, Ph.D., SE, Associate Professor at University of Kentucky, Owner of Davis Structural Engineering
- John Whiteman, SE, Business Development Manager at Vulcraft
When do we feel vibration? What vibration levels can we tolerate?
By definition, we feel vibrations when the level of vibration exceeds the threshold of perception, which depends in large part on what we are doing and what is going on around us. When we are sitting still in a quiet environment, we can feel very low vibration levels on the order of 0.2% of gravity (%g) to 0.3%g. Also, humans are more sensitive to low frequency, long duration and vibrations that occur often.
It’s generally accepted that humans in quiet areas don’t tolerate vibrations due to walking where the acceleration is greater than 0.5%g to 0.55%g. Our Technical Digest No. 5 contains recommended tolerance limits for various situations.
It is noteworthy that establishing precise human tolerance limits can be difficult because testing requires using real people in a structure. This can be expensive and time-consuming and must satisfy the requirements that come with using human subjects in experiments. Whiteman notes that people have different tolerances to vibration.
It should be emphasized that human-induced vibration is a serviceability issue and not a safety concern. “Reducing vibration is more of a serviceability issue for end users in their comfort than it is a strength consideration,” Whiteman says.
Damping and vibration
Imagine you’re in an airport terminal. You arrive early and take a seat among a couple other patrons. You can feel the floor shake as other people walk and cause short resonant responses. As your departure time approaches, more passengers enter the terminal. The more people fill the space, the less you feel the vibration because the vibration level decreases as damping increases. Also, vibrations have shorter durations when damping is higher. “Humans are very good dampers,” Dr. Murray says. “That’s a very definite effect of added live load.”
This anecdote isn’t just true for airport terminals. Schools and churches are also good examples of this diminishing vibrational effect. Dr. Murray uses this example to outline the relationship between vibration and damping.
Most of the damping in a floor system is due to the nonstructural components such as drywall partitions, furniture and ceilings. Thus, the shift to larger, open floor plans has a major effect on damping. “Buildings in the 1970s with lots of interior separation have been retrofitted by taking out these partitions. All of a sudden, there’s a vibration problem,” says Dr. Murray. “The owner would say, ‘Well, it’s been this way for 20 years, what happened?’ And I’d explain they’ve taken away lots of damping.”
Steel joists don’t play a very active role in increasing damping. However, compared to other types of framing, they have high stiffness relative to their low mass. Therefore, joist-supported floors have higher natural frequencies, which makes it difficult for structures to resonate due to human activity.
Natural frequency and vibration
When a floor vibrates enough to cause complaints, the issue is almost always resonance. When an integer multiple of the walking frequency equals a natural frequency of the floor, resonance results. This effect is less severe when natural frequencies are higher, so natural frequency is one of the most influential parameters in vibration analyses.
Also, the floor will vibrate primarily at its natural frequency. If the frequency is higher, occupants will be less sensitive to the vibrations and thus more likely to find the floor acceptable. This is illustrated in our Technical Digest No. 5, Chapter 1.
Natural frequencies increase with increasing stiffness and decrease with increasing mass. Thus, designers must estimate these parameters.
The joist, Joist Girder and W-shape girder stiffnesses are computed by considering the member to be partially or fully composite with the concrete slab. The details of the calculations depend on the type of joist-to-girder connection.
The designer must estimate the mass of any superimposed dead loads such as ceilings and other components supported by the floor. Also, live loads such as people and furniture should be included in the mass estimate. Best estimates — not high-end values used for strength and deflection checks — are used. “In strength and deflection checks, we have a safe side on which we can err. We can overestimate the load and be on the safe side,” starts Dr. Davis. “For vibrations, there is no safe side, so you need to have a pretty accurate estimate of the actual mass.”
Our Technical Digest No. 5 has guidelines for computing the stiffnesses and choosing the right masses to use when evaluating vibration due to human activities.
Steel joists and vibration
Everything involved in the design of a joist floor system has the potential to affect vibration. The size of joists, Joist Girders or hot-rolled W-shape girders; slab thickness; and joist connection type are all aspects that affect vibration.
When you vary the slab thickness, for example, you change the mass. And when mass changes, the natural frequency changes. Another example is the change from traditional joist seats to newer flush-framed connections that allow the Joist Girder or W-shaped girder to be fully composite for vibrations, which increases the natural frequency.
If you vary spacing of joists, you increase or decrease the stiffness. This affects the natural frequency of the floor. “It’s a trial-and-error process to optimize the stiffness and spacing,” says Whiteman. “So, you’re getting proper performance of the system, resulting in vibration below the acceptable limits.”
Studying human and structural responses to vibration
Throughout the years, Dr. Murray and Dr. Davis have collected information comparing the subjective reaction of individuals to over 100 floors. In most cases, participant complaints aligned with predictions covered in Technical Digest No. 5. Over 96% of procedures correctly predicted whether or not there would be complaints.
FloorVibe, an acclaimed software package developed by Dr. Murray, is a very practical tool for evaluating floor vibration on building design projects, including joist-supported floors with rhythmic group loading or vibration-sensitive equipment. Dr. Davis describes the software as “the go-to resource for evaluating floor vibrations.” He says, “There are various other software packages out there, but FloorVibe is the way to go. It’s complete. Dr. Murray developed it, and his quality control is legendary. It covers a lot of different systems and covers a wider range of situations than other programs, including the newest joist floor systems and joist-to-girder connections.”
You can learn more about FloorVibe here.
Floor Bay Analysis Tool
We’re excited to announce an update to our Floor Bay Analysis Tool. Version 3.0 includes vibration analysis for walking excitations. The update — which is based on AISC Design Guide 11 and SJI Technical Digest No. 5 — allows users to modify bay sizes, evaluate excitation patterns and receive recommendations for better performance.
Vibration of Steel Joist – Concrete Floors
Our 58-page Technical Digest No. 5 communicates the response of steel joist-supported concrete slab framing systems exposed to human activity. This publication was written by Dr. Tom Murray and Dr. Brad Davis and reviewed by SJI Research and Engineering Practice Committees.
Vibration Analysis of Steel Joist Concrete Floor Systems
Watch our webinar on concrete floor system vibration analysis, featuring guest speaker Dr. Tom Murray. Content covers information from Technical Digest No. 5. Procedures presented are backed by 20 years of research and verified through an extensive database of tested steel joist-supported concrete floors.