Challenges related with lightweight structures

Compared to classical monolithic buildings made from concrete or bricks, lightweight, framed structures are very complex. A concrete wall or floor can often be considered as a homogeneous plate. Timber-frame structu-res, however, comprise detailed connections involving different materials.

The construction comprises a framework with a sheeting typically made from thin sheets. The cavities are often filled with sound absorptive ma-terial. The cross-sectional area of the timber studs or beams as well as their spacing varies depending on the required structural strength of the building element. Floor joists are deeper and potentially need a narrower spacing than walls studs. In addition the material properties of wood are based on the direction of the fibres and annular rings that can vary de-pending on the sawing pattern. To reduce impact sound, floor coverings such as floating screeds are common and can be regarded as state-of-the-art. Additional mass, like gravel in the floor cavities for example, or

1.3 Problem and approach

Figure 1.3: Sketch of typical timber-frame double wall.

various kinds of suspended ceilings are also used to improve sound insu-lation. A collection of common constructions and their associated sound insulation is given in [DIN 4109-33:2016-07].

Figure 1.3 shows an example of a timber-frame wall construction with a single framework. The sheeting can have one or multiple layers that are typically screwed or nailed to the framework. Common sheet ma-terials are plasterboard or wood composites like chipboard or Oriented Strand Board (OSB). Gypsum boards are butt jointed and grouted, whe-reas wood composites are normally tongue and grooved. The choice of material, its thickness and the number of layers can vary depending on requirements on load bearing, fire protection or sound insulation. Hence there is a high degree of detail inherent in the construction of timber-frame walls and floors. This leads to many different junction details between building elements.

Although there are industrial standards on the dimensions of building material or common stud and screw spacings for example, the variety of possible structural variations is large. Due to the complexity of timber buildings the mechanical behaviour is also influenced by craftsmanship and this causes additional uncertainties.

Compared to homogeneous heavyweight building elements, the com-plexity of timber-frame structures provides more sound transmission paths within a single element and at junctions between walls and floors. In

com-bination with high internal damping of the wood, wood-composite and gypsum based materials, this leads to high material damping which is a major characteristic of such structures [e. g. Schoenwald 2008]. Con-cerning mechanical excitation, the vibrational energy is significantly at-tenuated with increasing distance within a timber-frame wall [e. g. Nig-htingale and Bosmans 1999]. However, common engineering prediction models in building acoustics are typically based on the laboratory measu-rement of direct sound insulation of the walls and floors [e. g. ISO 12354-1:2017]. In addition to direct sound transmission, flanking transmission is modelled by introducing coupling terms across the junctions between the elements. This approach typically requires building elements to have a uniform vibro-acoustic behaviour and energy distribution across its spa-tial dimensions. This is provided by weakly damped monolithic building elements of concrete and masonry [e. g. Schoenwald 2008]. However due to the high damping of timber-frame structures, these approaches may not always be applicable.

In terms of direct sound transmission, lightweight double leaf con-structions show characteristics that differ to those of heavyweight homo-geneous structures. Although there is structural coupling between the leaves through the framework, sound transmission across timber-frame constructions is characterized by a mass-spring-mass behaviour where the air in the cavity acts as a spring. At and below this frequency the per-formance of double wall constructions is weak compared to monolithic structures with a similar total thickness. Above the mass-spring-mass resonance frequency the sound insulation of double wall constructions increases rapidly until the frequency where the bending wavelength of the structure and the wavelength of airborne sound waves match. At this coincidence frequency, sound radiation is very efficient. For timber frame-constructions the coincidence frequency is significantly higher than with monolithic structures because of the thin sheet material. Below the coincidence frequency, both resonant and non-resonant components are involved in the sound transmission. For timber-frame structures the

coi-1.3 Problem and approach ncidence frequency is well within the buildings acoustics frequency range;

hence both components are involved.

In building acoustics single number ratings are determined in the fre-quency range from 100 Hz to 3.15 kHz, but this range is sometimes ex-tended down to 50 Hz and up to 5 kHz. For heavyweight impact sound insulation, maximum sound pressure levels Li,F,max are measured from 63 Hz. Typically the mass-spring-mass resonance frequency of common timber-frame constructions is below 100 Hz. Hence the poor sound in-sulation of lightweight buildings is not covered by these values although spectral adaptation terms were introduced to expand the range down to 50 Hz. As the audible frequency range typically starts at 20 Hz occupants can be annoyed by low frequency sound transmission in lightweight con-structions [Rabold 2010; Ljunggren et al. 2014]. Additionally machinery tends to inject most vibrational energy at low frequencies. As lightweight structures are not as inert as heavyweight constructions they are prone to structural excitation by machinery. To estimate the vibration trans-mission the mechanical characteristics of the source and the receiver are required at the contact points. However the prediction of parameters for inhomogeneous timber-frame constructions is very complex as the vibration field varies significantly across the surface.

To cope with these challenges related to the the complexity of light-weight structures two main approaches are applied in this thesis: (a) Statistical methods that use averaging procedures, such as SEA. SEA provides the possibility to investigate the transmission paths individu-ally which can be used to identify dominant or weak paths, and (b) an empirical approach, based on measured data to globally describe the transmission from the power input of a source to the spatial average sound pressure level in a distant room including all paths. Deterministic approaches like Finite Element Methods (FEMs) are not considered in this thesis because of the problems related with the determination of the actual material properties, complex unknown boundary conditions and relatively high computation times.