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Annoying vibration is probably the most common performance complaint for light-frame wood floors. The International Code Council’s 2006 International Residential Code (IRC) and its 2006 International Building Code (IBC) do not address this issue, yet the engineer-of-record for a project may face the issue at the design stage, or the consulting structural engineer may be engaged to determine the cause of an annoying vibration problem in a dwelling designed and built under the prescriptive provisions of the IRC. While wood floor vibration is not typically a structural safety issue, it deserves attention by the design professional at the design stage because such a problem can be costly or practically impossible to fix.
The purpose of this article is to provide analysis tools and rules of thumb for the design professional to minimize annoying vibration problems in light-frame commercial wood floors, and to provide guidance in diagnosing problems in residential applications. We used the word "minimize" in the objective statement to emphasize the fact that human occupants will respond differently to in-service floor vibrations—some may feel nothing while others may be very uncomfortable. It may be prudent for the design professional to discuss this subject with the owner at the project planning stages. The design approach described in this article offers a good mechanism to communicate to the owner the following three aspects of floor design:
* Annoying vibrations are possible when floors are designed to the building code minimum;
* The threshold of what’s annoying is subjective; and
* Various steps can be taken to prevent the likelihood of annoying vibrations, probably with minimal added costs.
Research at Virginia Tech on full-scale solid-sawn joists, I-joist, and metal-plate-connected (MPC) floor trusses in the 1990s addressed the issue of wood floor vibration control. The laboratory testing program and field validation of a simple design rule were limited to wood joist floors with structural wood panel sheathing, thus the typical design dead load was either 10 pounds per square foot (psf) for solid-sawn and I-joists test cases or 15 psf for 4x2 floor trusses. Results presented in this article may not apply to wood-floor applications with 1 or 2 inches of concrete because of the change in stiffness, mass, and composite action involved. Wood floors with substantial mass need to be analyzed differently for vibration due to impulses from ordinary foot traffic, and thus the equations and rules of thumb presented in this article do not directly apply to wood-floor constructions with a concrete topping or other elements that raise the design dead load to more than 15 psf. Analysis of floors with relatively high mass should use different equations such as those used for steel and concrete floors as described in the Manual of Steel Construction.
Basics of wood-joist vibration analysis
Analysis of light-frame wood floors starts with estimating the natural period of the floor system. This is done by considering a strip of floor that includes a single joist and the tributary sheathing material, assuming a simply supported beam.
Joist fundamental frequency—The fundamental frequency of joists can be calculated using the equation developed by Thomas M. Murray in the article "Building floor vibrations," which appeared Engineering Journal in 1991:
f = 1.57 √386EI (Equation 1)
WL3
In Equation 1, ƒ is the fundamental frequency of the joist in Hertz (Hz), E is the modulus of elasticity in psi, I is the moment of inertia in inches4, W is the total supported permanent (dead) load in pounds, and L is the joist span in inches.
It should be noted that W is the actual dead load, which can be substantially less than the design dead load for light-frame wood construction.
Research results—We tested 13 full-scale floors (16 feet wide by 16 feet long) at Virginia Tech, constructed with joists (solid-sawn, I-joists, and floor trusses) at 16 inches on-center. In all cases, the joists were sheathed with 23/32-inch rated tongue-and-groove (T&G) floor sheathing. On each end, the joists were attached to a 2x6 sill plate that was connected to a short concrete block wall. Each floor was "excited" by dropping a weight, and the dynamic response variables were recoded by electronic means. A human subject was located in the center of the floor on a chair, and the subject recorded when vibration was detected. An additional 73 in-situ floors were evaluated using heel drop tests with second-party evaluation of annoyance. These floors were tested as empty rooms, as well as furnished rooms, to validate the design criteria.
General vibration design principles—Occupants are very sensitive to vibrations in the range of 7-10 Hz. In theory, joist designs (or floor system designs) that vibrate well above 7-10 Hz should be judged by the occupants as acceptable simply because they can’t feel the higher frequencies. As a general rule, wider joist spacing (24 inches on-center versus 12 inches on-center) will produce a higher frequency because deeper members, having a greater bending stiffness (EI), will be required to meet building code deflection requirements.
Live load and deflection limit—The 2006 IRC permits a design live load of 30 psf for "sleeping rooms." As will be demonstrated later, the 30 psf limit for sleeping rooms can be an unintended source of vibration problems in one- and two-family dwellings. The IRC specifies 40 psf for all other rooms. 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 space is outdated. Depending upon the occupancy, the 2006 IBC specifies various uniform live loads, and in some cases, concentrated loads for sizing the joists. Typical design live loads range from 40 to 100 psf. The higher design live loads are beneficial to preventing annoying floor vibrations because the resulting designs will typically have a greater bending stiffness (EI), and therefore, higher fundamental frequency from Equation 1.
Example frequency calculation of rigid joist supports—Of the calls we receive on floor vibration, 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. Assuming rigid (but simple beam) end supports, such as bearing on a block or concrete stem wall, Equation 1 can be used to predict the natural frequency of the joist. From the 2003 IRC, Table R502.3.1(1), a 2x10 No. 2 Spruce-Pine-Fir (SPF) floor joist will span 19 feet. For light-frame construction, design span is defined by convention to be the clear span, from face-of-support to face-of-support. [However, in general, span is defined by the American Forest and Paper Association’s (AF&PA) 2005 Supplement to the ANSI/AF&PA National Design Specification for Wood Construction (2005 NDS), Section 3.2.1 as distance from face-to-face of supports, plus half the required bearing length at each end.] For this example, assume the actual dead weight of the floor to be 7 psf for the joists, floor sheathing, and carpet. Referring to the 2005 NDS, E is obtained from page 35 and I is tabulated on page 14. The required input data for a 2x10 No. 2 SPF at 12 inches on-center includes the following:
E=1,400,000 psi
I = bd3/12 = 98.93 in4
L = 19 feet x 12 inches/foot = 228 inches
W = [19 feet x (12 inches/12 inches/foot)] x 7 psf = 133 pounds
Substituting this data into Equation 1 yields:
f = 1.57 √386*1,400,00*98.93 = 9.1Hz
133*2283
Thus, the calculated frequency is near the middle of the most sensitive range of vibration for humans, which is 7-10 Hz. The example calculation demonstrates how a "code conforming" floor can be problematic with respect to annoying vibration. Therefore, at least for lower live loads, closely spaced joists at allowable maximum span may produce objectionable floors.
System effects on joist vibration—When a joist bears on another beam (girder) with a separate stiffness and natural frequency, the two interact to produce a theoretical combined frequency. The fundamental frequency of the joists is affected by the vibration of their supports, and therefore, the frequency of the joists and any girder used to support the joists must be combined using the following equation:
f system = √f 2 joist * f 2 girder (Equation 2)
f 2 joist + f 2 girder
As discussed earlier, full-scale laboratory tests of joist floors having "rigid" bearing supports led to the conclusion and recommendation that joists with the same bearing conditions should have a fundamental frequency of at least 15 Hz at the design stage to minimize the possibility of "annoying vibrations." Assuming, however, the same joists are supported by a flexible girder having the same natural frequency of 15 Hz, the combined theoretical frequency is much less than 15 Hz. For example, when fjoist=fgirder=15Hz, the system equation yields the following:
f system = √152 * 152 =10.6 Hz<15Hz
152 + 152
The instructive aspect of this formula is valuable! A system may produce "annoying vibrations" even while each of the components could have a natural frequency not detectable by most occupants (again using the most sensitive range of 7-10 Hz).
Equation 2 also provides insight into possible causes of annoying vibration not linked to the actual joist design properties or girder design properties. For example, a solid-sawn joist may have "twist," and as a result, the joist bearing on top of the girder might only be on one edge of the narrow face of the joist. This condition could add additional "spring action" to the joist-to-girder connection. Another example is a joist face-mounted to the girder with the joist not securely seated in a joist hanger or the hanger itself is not installed per the manufacturer’s recommendation. To summarize, any construction deficiency that compromises the apparent design stiffness (EI) of the joist when connected to the floor girder may negatively impact fjoist and thus cause the system to vibrate in the sensitive range. Because of the complexity of actual constructions and the variability of materials, the root cause or causes of a vibration problem can be misdiagnosed, and thus the repairs deemed necessary may not cure the problem. Knowing the potential difficultly of solving annoying vibration problems in a completed structure, the project design professional should have ample motivation to address the vibration issue at the design stage.
We attempted to apply Equation 2 to typical joist-girder construction and found that it was not practical to achieve a predicted system frequency of 15 for residential applications, and thus designer judgment is needed in every case and application. For residential applications, we have recommended the use of L/600 when coupled with good construction practices for solid-sawn, I-joist, and floor trusses. Experience with designs that perform well in a residential application (such as the response from a single foot fall) may not carry over to the general, non-residential case because of differences in the dynamic loads involved. In general, the project design professional for all projects must rely on their own design experience, product and research information, and manufacturer’s recommendations while taking into account the performance expectations of the client.
Good practices for residential applications
We realize that Structural Engineer is devoted to engineered construction and that residential floors are often not designed by a structural engineer. However, since structural engineers are often called upon to evaluate and possibly design repairs to annoying vibration problems in residential applications, we offer some good practices for the residential case in "General rules of thumb" below.
Specific rules of thumb for solid-sawn, wood truss, and I-joist floors
Solid-sawn joists—In 1964, the Federal Housing Administration published Minimum Property Standards for One and Two Living Units, which recognized that solid-sawn joist spans over 15 feet in length may be inadequate to prevent annoying floor vibration. The agency proposed a rule limiting live-load joist deflection on a graduated scale from L/360 at 15 feet to L/480 at 20 feet, and a total deflection of no more than 0.5-inches for spans over 20 feet. These recommendations are conservative and show that the floor vibration problem is not a new one, dating back at least four decades.
We propose a simple rule of thumb for the design of solid-sawn joists up to 20 feet in length (a practical maximum span): Use 40 psf live load and a live-load deflection of L/480 for joist spans up to 20 feet.
This rule is very easy to remember, and it can be easily applied to span tables based on an L/360 deflection limit. As it turns out, a maximum joist span under an L/360 live-load limit can be conservatively reduced to a maximum joist span under an L/480 live-load limit by multiplying the maximum L/360 span by 0.91.
4x2 MPC floor trusses—An important step in preventing annoying vibrations in floor truss systems is the application of a strongback. Strongbacks control annoying vibrations by stiffening the impacted floor truss, which causes it to vibrate at a higher frequency. As discussed earlier, a higher frequency is desirable because the occupants will not likely feel vibrations. The strongback, running perpendicular to the trusses, should be a minimum of 2x6 in size, installed at the center of the span, and securely nailed to a vertical web—usually at the chase opening (if the floor truss configuration provides only diagonal webs, a vertical 2x4 scab can be nailed to the top and bottom chord and used in lieu of the vertical web).
We recommend that the strongback be nailed to each truss web with 3-10d Common nails (0.148 inch-diameter by 3 inches long) or 4-10d Box nails (0.128 inch-diameter by 3 inches long). It is important that the strongback and the truss web connections be gap-free, as gaps would reduce the effectiveness of the nail connections. Simpson Strong-Tie (0.25-inch diameter by 3 inches long) SDS screws are a good alternate to nails for producing stiff connections between the strongback and vertical truss webs. For spans longer than 20 feet, the strongback should still be installed near the center of the span, but we recommend installing an additional 2x6 strongback or one 2x8 in place of the two 2x6s. (Note—the effectiveness of a strongback is related to its stiffness. The moment of inertia (I) of one 2x8 is greater than the I of two 2x6 members, therefore if space permits, a 2x8 is the more desirable option.)
Wood I-joists—Preventing annoying I-joist vibration is generally more complicated than for other joist types. Our best advice is to consult the I-joist manufacturer on the subject of vibration control. One I-joist manufacturer, Trus Joist (now part of Weyerhaeuser’s iLevel business), conducted extensive testing of floor performance and developed the proprietary TJ-Pro Rating system. Using its TJ-Beam software, a user can select a TJ-Pro Rating between 20 and 70, with higher values offering greater levels of protection against potential floor vibration problems as judged by an occupant. For example, the designer can select a floor design that would satisfy 98 percent of the population. This system allows the owners, through their design team, to select the level of floor performance that meets their expectations.
Summary
Design to prevent annoying vibrations is not covered by the building codes, yet it can be a very important issue for the owner and building occupants. We have summarized our research findings at Virginia Tech University on lightweight floors (design dead load up to 15 psf) and listed some rules of thumb for minimizing complaints of annoying vibration in residential applications. Communication with the owner on the vibration issue is important at the project planning stage when it is possible to incorporate levels of protection against annoying vibrations into the floor system design.
Frank Woeste, Ph.D., P.E., is professor emeritus at Virginia Tech University, in Blacksburg, Va. Daniel Dolan, Ph.D., P.E., is a professor of civil engineering in the Wood Materials and Engineering Laboratory at Washington State University in Pullman, Wash. Please e-mail comments to Frank Woeste at fwoeste@vt.edu.
General rules of thumb
Easy ways to avoid vibration problems in residential applications
Use a live load of at least 40 psf—The IRC permits a 30 psf live load for "sleeping rooms," but when this lower load is used in design, the joists will generally be more flexible and more likely to produce annoying vibrations.
Increase the joist depth by one size—If the code requires a 2x8 joist at 16 inches on-center, then use a 2x10 joist of the same grade, species, and spacing, or a 14-inch-deep floor truss when a 12-inch-deep truss would meet code requirements. This rule should provide good results when used in conjunction with a 40 psf live load. (Using a smaller allowable deflection limit such as L/600 also results in similar changes to the floor framing.)
Glue and screw the floor sheathing—Sheathing should always be glued, and screws work better than nails for long-term bounce control. Reducing the on-center spacing—from 16 inches to 12 inches, for example—is probably the least efficient way to improve floor performance. Occupants feel "bounce" as the result of a foot impacting an individual joist, and even at 12 inches on-center, the joists are not close enough for the shock of a foot to be carried by two joists.
