The equivalent translational compliance of steel or wood studs and resilient channel bars

Abstract

A number of recent papers have determined the compliance of steel studs for use in models for predicting the sound insulation of cavity stud walls. However, in these papers, the compliance of resilient channel bars on one or both sides of wood studs or on one side of steel studs has not been determined across the whole of the frequency range. The present paper determines the compliance of the combination of resilient channel bars, mounted on wooden or steel studs and modeled as point or as line connections. Steel studs have usually been modeled as line connections. In this paper, they are also modeled as point connections where the points are the screws attaching the wall leaves to the steel studs and individual results rather than average results are analyzed. The compliance that makes Davy's sound insulation predictions agree with experimental sound insulation data was calculated by inverting Davy's equations for sound insulation. Linear regressions of the logarithm of the compliance, against the logarithms of frequency, reduced surface density, cavity depth and number of point connections or stud spacing, were conducted in a low frequency range and in a high frequency range.

Improvement in Airborne Sound Insulation of Cross-Laminated Timber (Clt) Walls

“…The Rw-frequency curve of the W2 specimen revealed a declining trend at 3150 Hz due to a coincidence effect at high-frequency bands caused by the incident acoustic wave being in the same phase when superimposed. As the bending wave propagates upwards, the vibration becomes more intense with distance, resulting in a sound isolation trough at high-frequency (Hirakawa and Davy, 2015;Mao et al, 2014;Reynolds, 1984). Lin et al (2021) found the same resonance and coincidence dips of the CLT wall system in Rw-frequency curves as this study, indicating that wood is generally considered as disadvantage compared with other building element regarding airborne sound insulation.…”

Empirical corrections for predicting the sound insulation of double leaf cavity stud building elements with stiffer studs

“…The equivalent translational compliance of a steel stud frame and the method that fastens the wall leaves to the steel stud frame is the compliance of translational line springs spaced at the stud spacing distance for the line connection model, or the compliance of translational point springs for the point connection model, which transfer the same amount of vibrational power between the two wall leaves as the steel stud frame and the method that fastens the wall leaves to the steel stud The empirical equations for the equivalent translational compliance CM are A is a constant, f is the frequency, f0 is 1 Hz, mr is the reduced surface density, mr0 is 1 kg/m 2 , b is the distance between the line connections (stud spacing), b0 is 1 m, n is the number of point connections per unit area calculated from the stud spacing and the screw spacing, n0 is 1 1/m 2 , g is the gauge of the sheet steel used to manufacture the steel studs, g0 is 1, S is the area of the wall and S0 is 1 m 2 . The constant A has units of 1/Pa for line connections and m/N for point by Davy et al (2018) with that derived by Hirakawa and Davy (2015). There is rough agreement between these compliances derived by different authors.…”

“…The point compliance of nominal 25 gauge steel studs, with gypsum plaster board leaves with a reduced surface density of 4.9 kg/m 2 , with 5.4 point connections per square metre and a specimen area of 7.4 m 2 derived by Davy et al (2018) with that derived by Hirakawa and Davy (2015).…”

“…Formulae for the equivalent translational compliance or stiffness of steel studs have only been provided for 25 gauge steel studs (Poblet-Puig et al, 2009;Vigran, 2010a;Davy et al, 2012;Hirakawa and Davy, 2015), except for a conference paper (Davy et al, 2018). Narang (1993) and Davy et al (2017) have provided experimental evidence for the use of the isothermal speed of sound in a wall cavity which is filled with sound absorbing material.…”

A review of the different approaches to predict the sound transmission loss of building partitions

“…As explained in detail by Davy, 61 this happens because it is possible for total internal reflection to occur for vibration incident at a non-normal angle to a line connection. More recently, Hirakawa and Davy 64 have obtained empirical formulae for the translational compliance of resilient channel bars and of thicker gauge steel studs. Vigran 65 developed a modified decoupled approach within the transfer matrix method (TMM), which allows to take into account the structure-borne sound transmission due to point and line connections.…”