Elastic hangers for suspended ceilings – are they really needed? Bengt Johansson 1 Efterklang (Part of AFRY) Frösundaleden 2, 169 70 Solna, Sweden

ABSTRACT Suspended ceilings made of several layers of gypsum boards are a common way to increase the sound insulation of slabs in buildings. The ceiling is typically hanging 100-500 mm below a slab. There are many manufacturers of the hangers and most of them supply elastic hangers, made of rubber or metal springs. The elastic hangers are very costly and there are very little scientific data of the effect of these elastic hangers, especially at low frequencies and especially for concrete slabs, which are the most common slab type. The sound insulation of normal buildings is increasing with frequency and the low frequency region is the most interesting region. The author has for more than 30 years been part of many cinema projects where elastic hangers have not been used. Still, the sound insulation at low frequencies is excellent. What are the most important parameters? Could it be that elastic hangers are even reducing sound insulation due to resonances at low frequencies? In this paper we will discuss measurement data both from laboratory and real buildings with focus on air-borne sound insulation at low frequencies. We will also discuss calculations methods.

1. INTRODUCTION

Suspended ceilings made of several layers of gypsum boards are a common way to increase the sound insulation of slabs in buildings. The ceiling is typically hanging 100-500 mm below a slab. There are many manufacturers of the hangers and most of them supply elastic hangers, made of rubber or metal springs. Unfortunately, there are very little measurement data of the sound insulation of suspended gypsum board ceilings from concrete slabs, especially if the ceiling is suspended without any elastic springs.

The aim of this paper is to investigate the available prediction methods and compare with measurement data. Since the most common slab type is made of concrete, the focus will be on gypsum board ceilings suspended from concrete slabs.

The low frequency region is often the most problematic region, since the sound insulation is low by nature is this region. Due to this the focus will also be on the low frequency region.

2. PREDICTION METHODS

2.1. Theoretical methods In the book “Sound Insulation in Buildings” [1] by Rindel one method is described for calculating the air borne sound insulation of double constructions with bridges. The bridges can be line- or point-bridges with or without elastic elements.

1 bengt.johansson@efterklang.org

The total sound reduction can be devided into the sound transmission through the cavity and the sound transmission via the sound bridge.

Figure 1: The total sound reduction can be devided into the sound transmission through the cavity

and the sound transmission via the sound bridge.

𝑅= 10𝑙𝑜𝑔[ 𝑃 1 𝑃 2𝑙 + 𝑃 2𝑏

] = −10𝑙𝑜𝑔[10 −𝑅 𝑙 10 ⁄ + 10 −𝑅 𝑏 10 ⁄ ]

(1)

𝑅 (1+2) = 20 log(𝐾 1 + 𝐾 2 ) (𝑓< 𝑓 0 )

𝑅 2 + 𝑅 2 + 20𝑙𝑜𝑔[2

𝑓

𝑓 𝑑 ] (𝑓 0 < 𝑓≤𝑓 𝑑 )

(2)

𝑅≈

𝑅 2 + 𝑅 2 + 6(𝑓> 𝑓 𝑑 )

𝐾 1 = 10 𝑅 1 20 ⁄ 𝐾 2 = 10 𝑅 2 20 ⁄ 𝑅 𝑖 is the sound reduction of panel i.

(3)

The mass-air-mass resonance f 0 can be calculated from:

2𝜋 √𝜌 𝑑 𝑐 𝑑 2

𝑓 0 = 1

𝑑 ( 1

+ 1

(4)

)

𝑚 1

𝑚 2

𝑚 𝑖 is the surface weight of panel i [kg/m 2 ], d is the panel distance [m], 𝜌 𝑑 is the density of the gas in the cavity [kg/m 3 ], 𝑐 𝑑 is the speed of sound of the gas in the cavity [m/s]. If we have air in the cavity 𝑐 𝑑 = 𝑐 (342 m/s) and 𝜌 𝑑 is 1,2 kg/m 3 .

The knee frequency for standing waves in the cavity:

𝑓 𝑑 = 𝑐 𝑑

(5)

2𝜋𝑑

We rewrite the sound reduction through the bridge as:

𝑅 𝑏 = 𝑅 (1+2) + ∆𝑅 𝑚

(6)

2

∆𝑅 𝑚 = 10𝑙𝑜𝑔 [ 𝑆𝜋 3 𝑓 𝑐𝑝

]

(7)

8𝑐 2 𝑁 𝑝 𝛾 𝑝  𝑝

𝑅 (1+2) is the sound reduction of panel 1 and 2 close together.

𝑓 𝑐𝑝 = (𝑚 1 𝑓 𝑐2 + 𝑚 2 𝑓 𝑐1 )

𝑚 1 + 𝑚 2

𝑓 𝑐𝑖 is the coincidence frequency of panel i.  𝑝 is the resonant radiation factor  𝑝 = 1 +

𝜋𝜎 2 𝑓 𝑐2

4𝜂 2 𝑓

N p is the number of connections

−1

2

𝑓

𝛾 𝑝 is the coupling factor 𝛾 𝑝 = [1 + (

𝑓 𝑘𝑝 )

]

𝑓 𝑐𝑝 8𝑐 2 𝑚 𝑚

𝑓 𝑘𝑝 = 𝑘 𝑑𝑝

𝜎 2 is the radiation efficiency of panel 2. 𝜂 2 is the loss factor of panel 2. 𝑘 𝑑𝑝 is the stiffness of the connection [N/m] We want the sound reduction through the bridge to be high.  R m is large if N p is small, i.e. number of connections is small  R m is large if 𝑓 𝑐𝑝 is large: 𝑓 𝑐𝑝 =

( 𝑚 1 𝑓 𝑐2 +𝑚 2 𝑓 𝑐1 )

𝑚 1 +𝑚 2

This means 𝑓 𝑐1 and/or 𝑓 𝑐2 should be high and m i should be low

−1

2

𝑓 𝑐𝑝 8𝑐 2 𝑚 𝑚 is small, i.e.

𝑓

 R m is large if the coupling factor 𝛾 𝑝 = [1 + (

is small where 𝑓 𝑘𝑝 = 𝑘 𝑑𝑝

𝑓 𝑘𝑝 )

]

stiffness 𝑘 𝑑𝑝 is low. At frequencies below 𝑓 𝑘𝑝 the sound bridges behave as stiff connections.  R m is large if the resonant radiation factor  𝑝 = 1 +

𝜋𝜎 2 𝑓 𝑐2

4𝜂 2 𝑓 is small.

The radiation factor 𝜎 2 should be low (f << f c ) and internal loss factor 𝜂 2 high. Please notice that 𝛾 𝑝 is 1 for a stiff point connector which means ∆𝑅 𝑚 is (almost) independent on frequency. Calculation example:

• 200 mm concrete slab. 468 kg/m 2 • 200 mm cavity with 200 mm mineral wool. • 2x13 mm gypsum board suspended in point connections. 18 kg/m 2

Figure 2: Example slab with suspended gypsum board ceiling. In diagram 1 we can see the calculation results according to ref [1] for a 2x13 mm gypsum board ceiling suspended 200 mm below a 200 mm concrete slab. The distance between point connections are 600 mm. The stiffness of the elastic coupling is chosen to give 14 Hz mass-spring resonance. If we look at the individual paths, airborne through the cavity and structure borne through the connections we can see that the transmission through the stiff connections is higher than the air borne path through the cavity for the whole frequency range. On the other hand, the transmission through elastic point connections is lower that air borne transmission if the stiffness is sufficiently low.

Diagram 1: Calculation results according to ref [1] for a 2x13 mm gypsum board ceiling suspended

200 mm below a 200 mm concrete slab. 600 mm distance between point connections. Sound

reduction through elastic point connections is higher than the air borne sound reduction.

In diagram 2 the calculation results are presented for hangers with different stiffness. The stiffness is chosen to represent the basic resonance for the mass-spring system of the actual ceiling.

Diagram 2: Calculation results according to ref [1] for a 2x13 mm gypsum board ceiling suspended 200 mm below a 200 mm concrete slab. 600 mm distance between point connections with different

stiffness. Total sound reduction including both air borne and structure borne paths. The sound

reduction with elastic point coupling can be almost as good as without connection.

2.1. Software There are few commercial software that can be used to predict the sound insulation of a slab with suspended gypsum board ceiling.

2.1.1 Insul Insul [2] is the most common prediction tool, sold in over 4 000 licenses worldwide. It is developed by Marshall Day Acoustics in New Zealand. Insul can predict sound insulation of single, double or triple constructions with many types of studs and bridges. In diagram 3 prediction results with different types of point connections are shown. For low frequencies there are almost no effect of elastic hangers compared to stiff.

Diagram 3: Prediction results from Insul for a 2x13 mm gypsum board ceiling suspended 200 mm

below a 200 mm concrete slab. 600 mm distance between point connections. Almost no effect of

elastic hangers at frequencies below 100 Hz compared to stiff hangers.

2.1.1 ENC ENC [3] is software containing calculation methods from the book “Engineering Noise Control” by Bies & Hansen. Module 5 deals with sound insulation calculations with theories from Davy and Sharp. In diagram 4 prediction results with Sharp theory with different stiff point connections are shown.

Diagram 4: Prediction results from ENC for a 2x13 mm gypsum board ceiling suspended 200 mm below a 200 mm concrete slab. 600 mm distance between point connections. Elastic coupling is not

possible for Sharp theory.

In diagram 5 prediction results with Davy theory with different stiff point connections are shown.

The effect of elastic point connections are only visible for high frequencies.

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Diagram 5: Prediction results from ENC for a 2x13 mm gypsum board ceiling suspended 200 mm

below a 200 mm concrete slab. 600 mm distance between point connections. Different types of elastic couplings are possible for the Davy theory, but a strange gap in the results is present between

160 Hz and 630 Hz. The elastic coupling only affects the high frequency region and not below 125

Hz.

2.1.1 NorFLAG NorFLAG [4] is software that is based on the Transfer Matrix Method, TMM. It is developed by Tor Vigran in Norway. The TMM technique is often used for prediction of sound absorption but can also be used for sound insulation prediction. Norflag has the possibility to add rigid or flexible connections, of both point type and line type. In diagram 6 prediction results are shown for point connections with different elasticity.

Diagram 6: Prediction results from NorFlag for a 2x13 mm gypsum board ceiling suspended 200

mm below a 200 mm concrete slab. 600 mm distance between point connections. User defined

spring constant of the elastic couplings are possible.

3 MEASUREMENTS There are surprisingly few available measurement results of gypsum board ceilings suspended from concrete slabs. This includes both field measurements and laboratory measurements. The reason for this is not clear.

3.1 Measurement methods When measuring vertical sound insulation in a laboratory, the test slab is often positioned inside an opening in the laboratory slab. In order to limit the structural coupling, there is an elastic connection to the rest of the slab.

The measurement methods are standardized in ISO 140-3 or ASTM E90. One of the suppliers below have used an alternative method with a tapping machine. It is not clear how well this method works.

3.2 Problems with measurements All laboratories have a certain limit for the maximum sound insulation possible to measure in the lab, without having flanking sound affecting the measurement result.

Since the sound insulation of a concrete slab with suspended gypsum board ceiling is very high, it is important that the limit of the lab is not affecting the measurement result. This limit is often indicated in the measurement result.

This problem is an even bigger with field measurements, where the flanking transmission can be severe, especially with poured concrete walls. The flanking issue can often be less problematic with gypsum board walls (Dry walls).

3.3 Measurement results

3.3.1 Measurement of AMC hangers [5]

• Laboratory: Labein Tecnalia in Spain • Original slab: Ceramic hollow block with concrete according to Figure 3. • Surface mass 356 kg/m 2 • Measurement method: EN ISO 140-3

Concrete layer ‘Ceramic hollow block — Plaster 250m Rock wool (4 cm; 160 kg/m*) 61.5cm M6 Rod —~# 1,5 cf Rock wool (5 cm; 20 kg/m*) Metallic profile _ jt Een Plasterboard (15 mm; 11 kg/m?)

Figure 3: The tested slab with suspended gypsum board ceiling. Tested ceilings: 3x15 mm gypsum board suspended 255 mm from slab. Rockwool, 40 mm 160 kg/m 3 + 50 mm 20 kg/m 3 .

• M6 rod (stiff) • Elastic hangers “Akustik 4’ (45 shore A) • Elastic hangers “Akustik 3 + Sylomer 30 Type B’

The predictions are made for a massive concrete slab with the same surface weight of 356 kg/m 2 .

Diagram 7: Prediction results from NorFlag and Insul of original concrete slab compared to

measurement result

Diagram 8: Prediction results of concrete slab with 3x15 mm gypsum boards ceiling suspended 255

mm below a concrete slab in stiff point couplings, compared to measurement result.

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Diagram 9: Prediction results of concrete slab with 3x15 mm gypsum boards ceiling suspended 255

mm below a concrete slab in elastic point couplings, compared to measurement result.

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Diagram 10: Prediction results of insertion loss,  R, of the ceiling with 3x15 mm gypsum boards

ceiling suspended 255 mm below a concrete slab in elastic point couplings, compared to

measurement result. None of the prediction methods work well.

Diagram 11: Prediction results of insertion loss,  R, of the ceiling with 3x15 mm gypsum boards ceiling suspended 255 mm below a concrete slab in stiff point couplings, compared to measurement

result. Measured 30 dB insertion loss for stiff point connections at 1 kHz is impressive.

Comments: There were no measurement results below 100 Hz. According to diagram 8 to 11 the measurement result is much better than all prediction methods for frequencies above 200 Hz. Insertion loss of 30 dB at 1 kHz is impressive for stiff point connections, see Diagram 11. The insertion loss is less for frequencies above 1 kHz and 0 at 5 kHz, which may be due to measurement problems but is not commented in the measurement report.

3.3.2 Measurement of Vibratec VT-SFC hangers [6]

• Laboratory: Akustikverkstan, Sweden • Original slab: 160 mm concrete • Surface mass 374 kg/m 2 • Measurement method: Tapping machine

Diagram 12: Prediction results of insertion loss,  R, of concrete slab with 2x13 mm gypsum boards

ceiling suspended 250 mm below a concrete slab in elastic point couplings, compared to measurement result. Measurement result show good effect above 200 Hz, in alignment with Rindel

predictions. Below 200 Hz little effect and much less effect than Rindel prediction. Comments The measurement result show very good effect at frequencies above 200 Hz, but very little effect below 200 Hz. The reason for this result is unclear but may be due to the chosen measurement method with tapping machine. The measured insertion loss (  R) corresponds well with predictions from Insul and Rindel above 200 Hz. No measurement data is reported for frequencies above 1 kHz.

3.3.3 Measurement of Kinetic Noise ICC Isolation hangers [7]

• Laboratory: NRC, Canada • Original slab: 150 mm concrete • Surface mass 356 kg/m 2 • Measurement method: ASTM E90. Excitation with 4 speakers. 9 microphone positions

Diagram 13: Prediction results of 150 mm concrete slab, compared to measurement result.

Measurement shows very good agreement with Insul prediction.

Diagram 14: Prediction results of concrete slab with 2x15 mm gypsum boards ceiling suspended

330 mm below a concrete slab in elastic point couplings, compared to measurement result.

Measurement shows very good agreement with Rindel prediction.

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Diagram 15: Prediction results of the insertion loss (  R) of the ceiling with 2x15 mm gypsum

boards suspended 330 mm below a concrete slab in elastic point couplings, compared to

measurement result. Measurement shows very good agreement with Rindel prediction.

Comments: The measurement result show good agreement with the Rindel method. There are few point connections separated 1200 mm, which give low structure borne transmission through the connections. This allows the prediction for the structure borne path to be less accurate without affecting the total result.

3.3.4 Measurements of stiff vs elastic hangers There are very few measurements of gypsum board ceilings suspended in elastic hangers from concrete slabs. There are even fewer measurements for stiff hangers. This means there are very few measurement results available to prove if the elastic hangers actually are efficient.

To prove this we need the same configuration with and without the elastic element. We need the identical slab, ceiling and cavity.

Only one measurement has been found and the slab is unfortunately not a massive concrete slab.

• Laboratory: Labein Tecnalia in Spain • Original slab: Ceramic hollow block with concrete. See Figure 4. • Surface mass 356 kg/m 2 • Measurement method: EN ISO 140-3

Figure 4: The tested slab with suspended gypsum board ceiling. Tested ceilings: 3x15 mm gypsum board suspended 255 mm from slab. Rockwool, 40 mm 160 kg/m 3 + 50 mm 20 kg/m 3 .

Concrete layer ‘Ceramic hollow block — Plaster 250m Rock wool (4 cm; 160 kg/m*) 61.5cm M6 Rod —~# 1,5 cf Rock wool (5 cm; 20 kg/m*) Metallic profile _ jt Een Plasterboard (15 mm; 11 kg/m?)

• M6 rod (stiff) • Elastic hangers “Akustik 4’ (45 shore A) • Elastic hangers “Akustik 3 + Sylomer 30 Type B’

Diagram 16: Measurement result of the insertion loss (  R) of the ceiling with 2x15 mm gypsum

boards suspended 255 mm below a concrete slab in point couplings. Elastic hangers seem to be about 2-6 dB better than stiff hangers above 160 Hz. Very little effect of elastic hangers at is seen

frequencies below 160 Hz.

Diagram 17: Measurement result of the insertion loss (  R) of the AMC elastic hangers compared to

stiff point connections. The rubber hanger shows negative effect at 125 Hz, meaning amplification

of low frequency noise.

Comments: There seem to be between 2 and 6 dB to gain from the AMC elastic hangers compared to stiff hangers. From diagram 17 it is seen that the rubber hanger gives -2 dB insertion loss at 125 Hz, meaning amplification compared to stiff m6 rod. The Sylomer hangers gives 2 dB  R at 100 Hz and 125 Hz. Unfortunately, no measurement data is available at frequencies below 100 Hz.

3 CONCLUSIONS Calculations according to ref [1] show elastic hangers should increase sound insulation in the whole frequency range 50 Hz - 5000 Hz, if the stiffness is selected well.

Predictions with Insul show that elastic hangers do not increase sound insulation below 100 Hz. At higher frequencies elastic hangers increase the sound insulation depending on the elasticity.

Predictions with ENC show elastic hangers increase sound insulation at high frequencies only. Predictions with NorFLAG show very lite benefit from elastic hangers at frequencies below 100 Hz and no benefit at 50 Hz. There are very limited measurement data that can show increased sound insulation for elastic hangers compared to stiff hangers. Only two measurements of AMC hangers were found. One of the elastic hangers shows 2-6 dB increased sound insulation at frequency 100 Hz – 1 kHz. The other one show decreased sound insulation at 125 Hz compared to a stiff hanger. Unfortunately, no measurement data for these hangers was available at frequencies below 100 Hz. Measurement data of suspended gypsum board ceilings show that even with stiff hangers the ceiling can improve sound insulation with up to 30 dB, which is much higher than calculations and predictions show. Adding elastic hangers only improves sound insulation with 2-6 dB compared to stiff hangers. Considering the cost of elastic hangers compared to stiff hangers the price per dB is very high. The author is aware of the limited number of measurements the conclusions are based on. The suppliers of elastic hangers are suggested to perform measurements also with stiff hangers and also for the original slab without the ceiling.

4 REFERENCES 1. Rindel, J H. Sound Insulation in Buildings , Chapter 9 (2018).

2. INSUL version 9.023, Software for sound insulation predictions, Marshall Day Acoustics,

www.insul.co.nz 3. ENC version 5.5, Software based on the book Engineering Noise Control, by Bies, Hansen.

www.causalsystems.com 4. NorFlag, software for calculation of sound absorption and sound transmission with Transfer

Matrix Method. https://web2.norsonic.com/product_single/norflag/ 5. Measurement result AMC, LABEIN report 91.2184.0-IN-CT-10/28, B0082-IN-CM-26-M53-I, -

M56-I, -M59-I 6. Measurement result Vibratec VT-SFC, Akustikverkstan report 18-718-R3 7. Measurement result Kinetic Noise ICC, NRC Canada, report B-3448.12, B-3463.1