How to Predict a Bouncy Floor

Background

The model International Residential Code (IRC) permits a design live load of 30 psf for “sleeping rooms.” The model codes specify 40 psf for all other rooms. Of the annoying floor vibration complaints we have received, the most common scenario stems from the use of:

• 30 psf live load,
• L/360 live-load deflection limit, and
• joists at 12-inches on-center (OC).

The combination of a 30 psf floor design load and code minimum L/360 live load deflection limit permits a long joist span for a closer OC spacing (e.g., 2x10 up to a 21-foot span). While floors designed to minimal code-permitted criteria may provide the least cost alternative for the joist framing materials, some designs have created less than desirable floors and contributed to performance complaints.

Bouncy residential floors[1] are easily prevented by knowledge of the potential issue and follow-up with the homebuilder in the planning stages of new home construction. After construction and the home is furnished, a repair can be difficult, costly, or practically impossible. For example, in the case of a 2^nd floor issue, repairs to the joists can’t be made without removal of the drywall. Moreover, after a repair is attempted, there’s no guarantee the result will resolve the issue.

Floor Vibration Research

In the 1990s, research led by Professor Dan Dolan at Virginia Tech on full-scale solid-sawn joists, I-joists, and metal-plate-connected (MPC) floor trusses addressed the issue of wood floor vibration control. The laboratory testing program and field validation were limited to wood joist floors spaced at 24-inches OC with structural wood sheathing, thus the typical design dead load was 10 psf for solid-sawn and I-joists tests and 15 psf for 4x2 floor trusses.

Professor Dolan and his graduate students tested 13 full-scale (16 ft. x 16 ft.) floors with 23/32" rated T&G plywood floor sheathing, glued and nailed. The joists were supported on the ends by concrete blocks simulating a rigid support condition (not flexible as from a header or girder). In addition to the laboratory tests, he tested a total of 73 in-situ floors in unoccupied and occupied homes.

In a nutshell, using standard methods for testing floor vibration, he found that, for the laboratory floors and unoccupied homes, human subjects did not detect annoying vibrations for floors with a vibration frequency of 15 Hz or higher. However, for joists in occupied homes with furniture, human subjects did not detect annoying vibrations for floors with a vibration frequency of 14 Hz or higher.

Example Calculation of Joist Frequency

The fundamental frequency of joists can be calculated by the equation [see PDF or View in Full Issue]:

where: ƒ is the fundamental frequency of the joist in Hz,
E is the modulus of elasticity in psi,   
I is the moment of inertia in inches⁴,
W is the actual total supported permanent (dead) load in lbs, and
L is the joist span in inches.

This formula applies to the joist installations that bear on a sill plate or framed walls-- not on a flexible support such as a header or girder.

To demonstrate the calculation method, consider an example assuming 2x10 No. 2 SPF floor joists spaced 12-inches OC with an (2015 IRC) allowable maximum span per code of 19’-0”. Further assume an actual carpet-type floor dead load of 7 psf for “W,” because the vibration formula requires the actual dead load, not the commonly used design dead load of 10 psf found in the IRC.

“E” for different grades and species and “I” for different joist sizes can be found in the 2015 NDS Supplement, published by the American Wood Council. For the 2x10 No. 2 SPF example,

E = 1,400,000 psi
I = bd³/12 = 1.5* 9.25³/12 = 98.93 in⁴
L = 19’x12 in/ft = 228”
W = (19-ft.x1-ft.) 7 psf = 133 lbs

“W” is the total dead load of a strip of the floor, 1-ft. wide and 19-ft. long.

Returning to the formula for fundamental frequency of a joist and substituting the data for the 2x10 No. 2 SPF, the result is [see PDF or View in Full Issue]:

Thus, the calculated frequency is near the middle of the most sensitive range of vibration for humans (7-10 Hz)[2]. The example calculation demonstrates how a “code conforming” floor can be problematic with respect to annoying vibration.

In addition to the calculated 9.1 Hz frequency that is likely to generate complaints of annoying floor vibration, the use of 30 psf IRC live load for a “sleeping room” is not recommended for two reasons:

1. Some floor areas may be subject to heavy loads such as a large water bed. Water beds can be supported by as few as two joists depending upon the specific waterbed framing. Only 8 inches of water weighs 41.6 psf, 12 inches weighs 62.4 psf.
2. In modern construction and homes, “sleeping rooms” are used as offices, exercise rooms, play rooms, and so on, thus the concept of a single purpose sleeping room is outdated.

Improved Floor Design Calculation

For a 2x12 joist, the “I” value (moment of inertia) is 178. in⁴, much larger than the “I” for a 2x10 (98.93 in⁴). Also, as a matter of good design practice, a 40 psf live load is assumed (instead of 30 psf) for determining an alternate design that meets the 2015 IRC.

Based on the 2015 IRC, Table R502.3.1(2) for joists at 16-inches OC, a 2x12 No.1 Southern Pine (SP) will span 19’-1”, exceeding the 19’-0” requirement for the example. The “E” for 2x12 No.1 SP is 1,600,000 psi. The “W” (actual dead load) in the vibration equation must be re-calculated as follows:

W = (19-ft.x1.33-ft.) 7 psf = 177. lbs .

Using the design data for the 2x12 No.1 SP at 16-inches OC (verses 12-inches OC), the calculated fundamental frequency is [see PDF or View in Full Issue]:

While the 2x12 No.1 SP joist at 16-inches OC raised the frequency above the most sensitive range of vibration for humans (7-10 Hz), it’s still marginal based on the 14Hz threshold for occupied homes reported by the Dolan studies. With the clear span being fixed, other design options that have a larger “EI” should be considered to arrive at a robust design that takes into consideration serviceability issues and occupant comfort.

4x2 Floor Truss Option

The floor truss option accommodates the use of strongbacks that provide a number of benefits—uninterrupted installation of HVAC ducting, plumbing, electrical, and other services, “load sharing” between trusses when they experience elevated loads in-service (such as a refrigerator or kitchen island), and added protection from the occurrence of annoying vibrations. A properly installed 2x6 strongback(s) increases the effective stiffness of the truss that is impacted by a foot-fall, which causes it to vibrate at a higher frequency. In other words, the “EI” in the vibration frequency formula is effectively larger due to the vertical support provided by the 2x6 strongback(s), thus the actual frequency in-service should be higher resulting in a better floor system with respect to the vibration issue.

The strongback, running perpendicular to the trusses (Figure 1), should be a minimum of 2x6 in size and nailed to a vertical web, typically the chase opening at the center of the span or multiple locations as specified by the truss design drawings. In addition, the strongback should be placed at the bottom of the vertical web as shown in Figure 1 which prevents lateral movement of the bottom chord (a side-to-side vibration) due to normal human activity (walking).

Regarding the connection of the strongback to the truss webs using nails, it is very important that the strongback to truss-web connections be gap free, as gaps will substantially reduce the effectiveness of the nail connections. As a practical matter, it’s difficult for carpenters to eliminate all gaps when nailing the strongback to vertical webs. Moreover, even when the nailing eliminates small gaps at the time of installation, it is likely that some nails will “back out” in-service. For these reasons, I recommend using structural screws such as FastenMaster 2”-7/8” FlatLOK or Simpson ¼”x3” SDS screws as a good option for producing a stiff connection between the strongback and truss webs.

Additional Information for a Joist-Girder System

Not covered in this article, an additional design consideration is the case where one end of the joists bears on a flexible support, such as a floor girder. The formula for calculating the fundamental frequency of the joist-girder system is more complicated, requiring the use of an additional formula for the floor system. Visit http://csengineermag.com/article/is-a-spring-in-your-step-causing-problems/ for details.

Summary

A floor joist design based solely on conformance to IRC provisions does not ensure the constructed floor will be free of annoying vibrations as felt by some occupants. A method for calculating the fundamental frequency of wood floor joists has been demonstrated and the results can be used to predict which floor designs may be prone to an in-service vibration issue and related customer complaints.

The time to be concerned about the possibility of annoying floor vibrations is before a new home is planned and purchased. After construction and the home is furnished, a repair attempt to mitigate the vibration issue can be difficult, costly, or practically impossible.

Frank Woeste, P.E., is Professor Emeritus, Virginia Tech University and a wood construction consultant. He can be contacted by e-mail: fwoeste@vt.edu

Dan Dolan, P.E., is Professor & Director of Codes and Standards, Department of Civil and Environmental Engineering, Washington State University, Pullman, WA. He can be contacted by e-mail: jddolan@wsu.edu