on the

With the increased availability of timber materials, such as cross-laminated timber, the number of buildings using timber as a structural material has been rapidly increasing. As these buildings are new to the market, limited data and research on their long-term structural modal performance are available. This is particularly important in timber buildings since the material properties of wood are highly affected by environmental factors, especially the moisture content. Over time, the evolution of the dynamic properties is essential for damage indication in structural health monitoring systems since natural changes can mask the influence of damage. This work presents three years of observations from a structural monitoring system collecting data ever since completing a four-story timber-concrete hybrid building in Sweden. Ambient vibrations of the building were measured using geophones, resulting in 3,100 datasets. The temperature and relative humidity were measured both externally using a weather station and internally using sensors embedded in several walls and a slab in the building. The observed natural frequencies of the building vary with ± 0.2 Hz around the mean value over time. Linear regression analysis shows a significant correlation between the moisture content of a cross-laminated timber slab and the natural frequencies (coefficient of determination R 2 up to 0.84). A predictive model for the natural frequencies is presented, taking seasonal variations and a dry-out of the structure into account. Variations from the expected values are ± 0.1 Hz at most. The model clearly narrows the error margins for damage indication in a structural health monitoring system.


Introduction
The use of timber as a structural material in modern buildings is growing due to increased availability [1], beneficial CO 2 factors [2], and new directions for regulations forcing the building industry to be more sustainable [3], among other factors.Cross-laminated timber (CLT) is a relatively new timber product that has been available only since the early 2000 s [4].The industrialized construction of such buildings with CLT is thus in its early stages, and the long-term consequences are not yet known.Various building types have been introduced, with CLT as the main part of the load-bearing structure.One type is timber-concrete hybrid buildings, where concrete elements are used in addition to the timber elements, e.g., for shear walls and elevator shafts.
Environmental factors, such as relative humidity (RH) and temperature, affect timber and concrete.In timber, there is a close relationship between RH, temperature, and the moisture content (MC) of the material [5].MC has a significant effect on almost all timber properties, such as density, strength, and elastic characteristics.Both RH and temperature show variations over time due to daily changes in weather and seasonal changes throughout the year.MC also varies over time since timber aims to be in equilibrium with its surroundings.For concrete, a material with a structure of open pores is also influenced, where changes in RH and temperature affect its properties, most significantly during the hardening process.In the long term, the environmental effects will cause a volumetric change.This mainly affects phenomena such as creep, shrinkage, and cracking, resulting in a changing the elastic characteristics [6].
The consequences of these variations on the performance of a building are usually not considered during design.Altogether, this indicates that it is necessary to study the effects of such environmental factors on the structural behavior of timber-concrete hybrid buildings when using structural health monitoring (SHM) systems [7].
Vibration-based SHM (vSHM) is a method used to detect and localize structural damage based on the dynamic response of structures.Most vibration-based damage detection methods require continuous monitoring of the global dynamic properties of the building, such as natural frequencies, damping ratios, and mode shapes.Deviations of these properties from their baseline values are often used as damage indicators [8].However, there are several examples of how environmental factors such as temperature [9] and humidity [10] affect the dynamic response of a building.Previous studies concluded that a change of 5 % in the natural frequency as an indicator for structural damage is only valid if the environmental changes in natural frequency are already known [11].Therefore, before using vSHM for damage detection, it is necessary to understand the natural changes in the dynamic response of timber buildings under seasonal variations in temperature and RH in order to define appropriate baseline values.
Several long-term studies have been conducted to evaluate the environmental effects on the dynamic properties of buildings in which timber was not used as a structural material.Such studies can be seen in modern steel and concrete buildings from Italy [12], the USA [13], and China [14,15,16], for example.In addition, there are several studies regarding adobe buildings in Peru [17] and Italy [18,19,20] where the latter uses CLT in the roof replacement.
Regarding timber buildings, Riggio and Dilmaghani [21] show in a recent literature review that most of the previous investigations on the dynamic behavior in timber structures have been conducted over a short monitoring period.For example, there are measurements on buildings in the USA [22], Sweden [23], Norway [24], and the United Kingdom [25] that were performed during a single day.In terms of long-term dynamic monitoring of timber buildings, the House of Natural Resources in Switzerland [26] is one example.The structural system consists of a post-tensioned timber frame and concrete-timber composite slabs.However, the relation between the environmental factors and the dynamic response was not studied.
This paper aims to identify and model the effects of seasonal variations in temperature and relative humidity on the dynamic properties of a hybrid timber-concrete building.The data used in this work has been collected over more than three years of continuous monitoring of House Charlie, which is a four-story office building located in Växjö, Sweden.The construction of this timber-concrete hybrid building was completed in 2018.The building has a post-beam system in glulam timber (GLT) and cross-laminated timber (CLT) slabs.Precast concrete walls in the elevator shafts and additional steel bracings in the façade provide horizontal stability.During construction, a SHM system was installed.Combined sensors for temperature and relative humidity (RH) were embedded in the CLT-slabs and light-frame exterior walls at different positions to monitor the building since August 2018.The dynamic response of the building has been continuously monitored using geophones mounted at certain corners of the building.Additionally, the external weather conditions have been tracked by a weather station.
Firstly, the paper presents the building and the measurement system installed during construction.Observations for three years are then presented, including the hygrothermal measurements as well as the vibration mode shapes, natural frequencies, and damping.Secondly, the paper analyzes the collected data and the correlation between the dynamic properties and environmental readings.Finally, a predictive model is presented to define the appropriate baseline values for the natural frequencies.

House Charlie
House Charlie is a four-story office building in Växjö, Sweden, shown in Fig. 1.The climate in this region is characterized by a humid continental climate with four seasons per year [27].The four stories include 5,700 m 2 , consisting mainly of office spaces, conference rooms, and supporting facilities.The building was constructed in 2017 and 2018 at a total cost of about € 11 million and opened in September 2018.

Structural description
The building is 55 m in length, 14.5 m in width, and has a height of 16 m.The structural system consists of a post-beam system in GLT with CLT slabs, described in Table 1.The building has two elevator shafts with shear walls in precast concrete and steel bracings in two facades to provide lateral stability.The complete load-bearing structural system is shown in Fig. 2. In addition to the structural system, there are nonstructural walls in light-frame timber as well as a putty casting on top of the CLT slabs.

Measurement system
During construction, a measurement system was installed to monitor the hygrothermal and structural performance of House Charlie.The system consists of 27 temperature/RH sensors, three potentiometers, 12 uniaxial geophones, a single three-axial accelerometer, and a weather station placed on the roof.The positions of the sensors used in this study are shown in Fig. 3, followed by a brief description of the data acquisition thereafter.
The 12 geophones were installed in pairs to measure ambient vibration response in the buildings' x-and y-direction at six locations.Each pair was placed in a steel box and mounted on the top of a column, right below the beam supporting the slab.On floors 1-3, the geophone boxes were mounted at the northeast corner of the building.On the top floor, the geophone boxes were placed in three corners, as shown in Fig. 3.
To measure MC in the CLT slab, combined temperature and RH sensors were placed within a slab on the first floor.The three sensors were placed at different depths to measure different lamellas of the CLT plate.Measuring from the bottom of the CLT plate, the depths of the three sensors are 225 mm (1), 185 mm (2), and 15 mm (3).Fig. 4 shows the placement of the sensors along with the additional slab finishing in House Charlie, where the putty, acoustic insulation, and rock wool are added due to fire, acoustics, and dynamic demands of the slab.In a plan view perspective of the CLT plate, the distance from the sensors to the edges of the plate is 300 mm.
In the exterior walls on floors 1 and 4, sets of combined temperature and RH sensors were placed in three locations, according to Fig. 3.Each set includes six sensors placed throughout the section of each wall.The innermost sensors were placed right behind the interior gypsum board and are used in the study to assess room climate.The weather station was placed on a stick 3 m above the roof in the southeast corner of House Charlie.
Internally, the system is divided into low-frequency and highfrequency measurements.The low-frequency measurements include data from the weather station as well as the combined temperature and humidity sensors.With a reading interval of 60-minute intervals, this results in approximately 27,000 datasets during the measurement period from August 1st, 2018, to August 31st, 2021.
The high-frequency measurements include all six pairs of geophones with time synchronization.The geophone measurements are triggered two times per day at pre-defined times.Additionally, a wind speed measured at the weather station exceeding 5 m/s triggers logging at separate times, followed by a rest period of 240 min.Each set is 90 min long and sampled at 120 Hz resulting in approximately 3,100 vibration datasets for the period studied.The central unit for control, data collection, and remote access to the system is located on the ground floor.More information about the system, its individual components, the communication between the components, and the system from the outside can be found in [28].

Results of vibration monitoring
The voltage signals measured by the geophones are converted to velocities according to the method given in [29].These velocities are then differentiated to calculate the corresponding acceleration a x and a y .The root mean square (RMS) values of the acceleration measured in both directions at the three locations on the top floor are then calculated and presented as histograms in Fig. 5.The observed acceleration levels are well below the basic human comfort criteria given in the vibration standards for buildings, both for residential and office buildings [30].

Natural frequencies
The data processing of the observations from the geophones was performed in two steps.First, the global vibration modes are identified on a single dataset.Secondly, the entire dataset is evaluated, sorting each frequency to the previously identified mode from the first step.
The global vibration modes of House Charlie were identified using an operational modal analysis (OMA) of a single vibration dataset collected on August 31st, 2019.A high-pass filter with a cutoff frequency of 1 Hz was applied to eliminate unwanted low-frequency components.The filtered signals were downsampled by a factor of six to 20 Hz.The correlation matrix was calculated considering the 12 degrees of freedom as reference signals.The Hankel matrix required for OMA was computed from the correlation matrix.OMA was then carried out in Matlab using the Multi-reference Ibrahim Time Domain (MITD) method [31] implemented in the ABRAVIBE Toolbox for Noise and Vibration Analysis [32].The stable poles were manually picked from the stability diagrams.This initial analysis gave the first three natural frequencies and the corresponding mode shapes presented in Fig. 6.
Compared to the methods in different guidelines, the Canadian (NBCC) and Japanese (AIC) standards give equations estimating the first natural frequency for a building height of 16 m [33].These estimations give f 1,NBCC = 40 h = 2.50Hz for a braced building and f 1,AIJ = 67 h = 4.19Hz for a concrete building in comparison to the observed first frequency at 3.31 Hz for House Charlie.
The second step includes an automatic OMA process that was carried out over the entire data sets collected between August 1st, 2018, and August 31st, 2021, to evaluate the long-term variations in the natural frequencies of the three modes.The signals were filtered, downsampled, and processed by the MITD algorithm to extract the poles in each dataset, identical to the initial modal analysis.The stable poles having a frequency within the range of 3.0 to 4.2 Hz were identified.K-means clustering was applied to split the identified poles into three clusters corresponding to the three vibration modes.The frequency of each mode was calculated as the average frequency of the poles in the corresponding cluster.These results are shown in Fig. 7.
The results presented in Fig. 7 show a clear seasonal pattern for all three frequencies.The lowest frequencies are recorded in the spring (March and April) and the highest in the late summer and early autumn (August and September).But also, a daily variation can be seen where the frequencies of the three first modes are lower during the daytime and higher during the nighttime.There are several gaps during the entire measurement period due to missing timestamps in the data files caused by system downtime and software bugs in data collection.
Fig. 8 shows the statistical analysis of the first three modes, including a histogram of the recurrences of the natural frequencies.Similar histograms are obtained for each of the three frequencies.

Damping ratio
Fig. 9 shows the damping ratio of the three natural frequencies during the first three years.As opposed to the frequencies, no seasonal relationship is seen, and the mean damping ratios are close for all three frequencies.

Results of hygrothermal monitoring
The environmental observations consist of three datasets.The first is the external observations from the weather station on the roof of House Charlie.There are three gaps in this data set with a total duration of 13 weeks due to technical issues with the weather station.Weather station no 64510, operated by the Swedish Meteorological and Hydrological Institute (SMHI), and located approximately 1,170 m from House Charlie, was used to fill the gaps.Between November 2019 and August 2021, the temperature/RH values measured by the two weather stations were in good agreement, with a mean absolute error of 5.0 % for RH and 1.0 • C for temperature.These results suggest that the SMHI weather station can be used to fill the gaps in the data collected by the weather station at House Charlie.
The second dataset is the interior climate in the rooms.The mean value of temperature and RH measured from wall sensors on floors 1 and 4 is used in the following (see Fig. 3 for reference).The third data set consists of the reading of the sensors built into a structural timber CLT slab element on floor 1 (see Fig. 4 for reference).

RH
Fig. 11 presents the RH readings (RH ext , RH int and RH slab ).Unlike the temperature readings, a clear seasonal trend can be seen in all three locations suggesting that the exterior conditions (RH ext ) affect the indoor humidity conditions as well, both RH int and RH slab display seasonal  variations.However, absolute values in RH differ highly between these locations; the highest variation is observed in RH ext and the lowest in RH slab .As for the short-time variations, Fig. 11b shows the RH measurements during the first week of April 2019.Similar to temperature, significant daily variations are observed for RH ext , while only small variations are noticed in RH int and RH slab is nearly constant for such short time spans.
Previous studies have shown that the correlation between the exterior and interior RH is weak, while the correlation between the exterior and interior absolute humidity (AH) is significant [34].For House Charlie, the temperature and RH readings were used to calculate the interior AH (AH int ) and exterior AH (AH ext ) according to a method by Bolton [35].Fig. 12 shows the interior and exterior AH of the building, which exhibits a better correlation than the corresponding RH readings shown in Fig. 11.

CLT slab
Fig. 13 shows the temperature and RH observations through the CLT slab on the first floor in House Charlie.Among the slab temperatures at the three measurement locations through the CLT slab (T 1− 3 slab ), the highest temperature variance occurs in location 3, the closest to the bottom of the slab.However, the mean absolute difference between positions 1 and 3 is only 0.3 • C, implying that the temperature is relatively constant within the slab.
The corresponding RH observations in the CLT slab (RH 1− 3 slab ) show that RH differs between the top and the bottom of the slab.Looking at the seasonal variations in RH at the measurement points, one can notice that the RH is approximately equal through the slab around July to September and diverges again during winters.The MC in the slab is calculated from the measurements of temperature and RH as given in Equation ( 1) [5].The MC in the CLT slab, presented in Fig. 13c, clearly follows the same seasonal behavior as seen in the RH readings.This is due to the relatively constant temperature in the slab, making RH the only variable factor in the calculation of the MC in Equation (1).

Analysis
As presented earlier, the dynamic behavior varies clearly over the measurement period.In the following, the correlation between temperature and humidity with the first three natural frequencies is investigated.Additionally, the seasonal variations in MC and natural frequencies are modeled, allowing for forecasting these parameters outside the observed period.

Natural frequencies and hygrothermal parameters
Fig. 14 shows the environmental parameters for temperature (T ext , T int ), relative humidity (RH ext , RH int ), absolute humidity (AH ext , AH int ) and moisture content within the CLT slab (MC 1− 3 slab ) co-plotted with the first natural frequency.For better readability of the figure, a moving average with a window size of one month was applied to the data.The plot indicates clear seasonal variations in all readings implying that the dynamic behavior of House Charlie, in terms of the first frequency, is directly affected by the environment.These observations are valid for the second and the third frequency as well.
Linear regression was used to investigate the correlations between the environmental variables and the three identified frequencies.Fig. 15 shows the correlation between the natural frequencies and the exterior and interior environmental readings, along with the corresponding coefficients of determination R 2 .Fig. 16 presents the correlations with the calculated MC at the three positions in CLT-slab.
The correlation between the natural frequencies and external RH and temperature in Fig. 15 is low, with R 2 -values of 0.12 at most.The calculated values for AH ext show slightly higher R 2 -values (0.18-0.27).The correlation for the measurements inside the building is even higher, resulting in R 2 -values in the range of 0.27 to 0.42 for the RH int and AH int readings.
However, these values are still low compared to the correlation be-tween the natural frequencies and the MC within the CLT slab shown in Fig. 16.With R 2 -values in the range of 0.36 to 0.84, the highest correlation is observed between the MC at the bottom of the slab (MC 3 slab ) and the three natural frequencies.
The findings in Fig. 16 show a close relationship between the MC at the bottom of the CLT slab (position 3) and the three natural frequencies.For timber, increasing MC gives higher density and lower E-modulus [36], which is expected to lower the natural frequencies.Interestingly, the results indicate the opposite; the natural frequencies of House Charlie increase as the MC increases.These results are consistent with previous studies on long-term monitoring, both for a modern concrete building [15] and for an adobe masonry church [17].
As the concrete shear walls and steel bracings significantly affect the natural frequencies of the structural system of House Charlie, the MC in these materials would be of great interest.However, since no sensors were installed in these elements, it is difficult to draw any conclusions about the influence of these elements compared to the CLT slabs in the natural frequencies of House Charlie.
For concrete, the MC in the elements is expected to follow the surrounding humidity as for timber [35].A higher MC in the concrete increases its E-modulus, which is the opposite of timber behavior [37].However, two studies on single concrete elements conclude that an increased MC leads to a lower natural frequency due to an increased mass [38,39].Considering the concrete material properties alone, an C. Larsson et al. increase in MC would decrease the natural frequencies for structural elements, which is similar to the behavior of timber.
Non-structural walls are also known to affect the natural frequencies of a building [40].For House Charlie, there are light-frame timber walls with sheathing panels in gypsum, both in the façade and internally.Since these walls also are made of timber, they may affect the variation seen in the natural frequencies as well.
Due to the high amount of timber in House Charlie, the discrepancy in the general behavior of wood may be explained by the behavior of timber products on a microscale.Increased MC leads to swelling and increased internal friction and, therefore also, stiffness, which may affect dynamic behavior [41].Another hypothesis is the role of the connectors and their possible performance changes at different MC levels.As a result, increased MC would lead to swelling of the wood and a tighter fit of screws and nails, increasing connection stiffness.However, in a dynamic evaluation of an eight-story CLT building, it was concluded that the influence of the connectors was negligible [24].

Predictions of MC and natural frequencies
As mentioned earlier, it is of importance in vSHM systems to predict the dynamic behavior of the building in order to provide appropriate baseline values of the dynamic parameters according to the current time and season.The high correlation between the MC and the three natural frequencies indicates that MC can be used to predict the variations in natural frequencies over time.In this section, a prediction model for the MC is defined, taking two factors into account.The first factor is the initial dry-out process within the timber, while the second is the seasonal changes as the material aims for equilibrium with the surrounding humidity.Analogously, the prediction model for MC is thereafter used as a basis for deriving a prediction model for the natural frequencies of the building.

MC
Three variables are assumed to predict the MC over time: the balanced MC, the initial dry out, and the seasonal changes.These variables are considered to vary with time, as shown in Fig. 17.The entire formula for the MC prediction model is given in Equation ( 2), where t is the time in days since the start of the observations.
The initial dry out of the slab is assumed to follow an exponential function in terms of the excessive moisture content ΔMC b , and the decay constant k b , providing information on the drying speed.In physical terms, it is assumed that the timber has a higher MC after the construction is finished, as is expected of the equilibrium conditions in an indoor climate.This is caused by factors such as the manufacturing of the timber material and weather conditions on the construction site during construction.
Seasonal variations are expressed as a sinusoidal function with an amplitude ΔMC c and a phase offset t c .The period is fixed to a full year, i. e., 365 days.
The balanced MC a is considered the moisture content in equilibrium, reached after the dry-out is completed, where the annual variations oscillate around.A curve fitting analysis is performed on the MC values measured at the three depths within the slab according to Equation (2).The unknown parameters are calculated for each depth of the CLT slab to fit the observed data within the entire monitoring period between August 1st, 2018, and August 31st, 2021.The results are shown in Fig. 18 and Table 2, along with the coefficients of determination.
The analysis shows that the balanced MC of the slab, MC a , is higher at the top of the slab, MC 1 a = 9.22% compared to MC 3 a = 8.16%.These results suggest that there will be no equilibrium throughout the plate and that the upper part of the CLT slab will remain more moister than the bottom.
The analysis also confirms a higher annual variation at the bottom of the CLT slab, ΔMC 3 c = 1.23%, in comparison to the corresponding value at the top of the slab,ΔMC 1 c = 0.52%.This also means that the seasonal variations ΔMC The highest initial dry out is observed at the top of the slab, with ΔMC 1 b = 3.79%, about 29 % of the total MC at the start of the observation period.The lowest value is obtained at the bottom surface, ΔMC 3 b = 1.82%,only 18 % of the initial MC.This is most likely since the top surface of the slab was exposed during the construction time while the bottom surface was protected.
The initial dry-out is higher than the corresponding annual varia-tions for all three positions, around seven times higher for positions 1 and 2 but only by 50 % higher for position 3.The dry-out occurs faster in the bottom of the CLT slab as the factor k b is the lowest for position 1.

Natural frequencies
The high correlation between the MC within the CLT slab shown in Fig. 16 suggests that the approach used to derive the MC prediction model (Equation 32 can also be used to predict the natural frequencies of the building.The prediction model for the natural frequencies of House Charlie is given in Equation ( 3), where frequencies replace the MC parameters.
The results from the curve fitting analysis of Equation (3) to the measured frequencies are shown in Fig. 19 and Table 3, including the coefficients of determination, which are close to 0.8 for all three frequencies.
The analysis shows that the balanced natural frequencies (f a ) given in Table 3 are close to the mean frequencies shown in Fig. 8.The increase in frequency due to the initial dry out is 2.6 %, 3.4 %, and 4.5 %, respectively, as compared to the balanced natural frequency (f a ).Corresponding seasonal variations, Δf c , are 2.2 %, 1.7 % and 1.7 % for the three natural frequencies as compared to the respectively balanced frequencies (f a ).This highlights that dry-out is a significant variable in addition to the seasonal variation for predicting the natural frequencies.

Use in a vSHM system for House Charlie
For damage detection in a vSHM system, the natural frequencies are obtained at regular intervals, and deviations from a baseline frequency are determined.Fig. 20 shows histograms where the deviation from the mean values as well as from the predicted values are plotted.The deviations are in the range of ± 0.1 Hz for all three natural frequencies using the predicted frequency as the baseline.That is a significant improvement compared to using the mean frequency as the baseline, where the corresponding deviations are about ± 0.2 Hz.These results emphasize the conclusions from previous studies that if deviations in frequencies are to be used as a damage indicator in a vSHM system, it is vital to understand the ambient conditions affecting the frequencies of the structure [11].However, this proposed model does not consider the daily variation in the natural frequencies.

Conclusion
The dynamic behavior of House Charlie, a timber-concrete hybrid building in Växjö, Sweden, has been monitored for three years to understand the variation in global dynamic parameters over time.The SHM-system monitors the natural frequencies of the building and hygrothermal parameters, including temperature and RH inside and outside the building as well as within a CLT slab at different depths.
The collected data shows clear seasonal variations in the natural frequencies of the building; for example, the first frequency varies between 3.04 Hz and 3.41 Hz during the measurement period, which corresponds to ± 5.7 % around the mean value.The highest frequencies are observed in the early autumns (September/October) and the lowest in early spring (March/April) each year.This behavior is similar to what has been reported in other buildings with other construction materials, such as modern concrete buildings [15], as well as adobe masonry buildings [17,20].As also seen in [17], no apparent seasonal variation was observed for the corresponding damping ratios.
In addition to the seasonal variations, an overall decrease in the natural frequency was detected and derived from the dry-out that occurs in structural elements during the first years of service after construction.These trends are also visible in the actual measured MC for the CLT slab.
A high correlation suggests that the MC in the CLT slab significantly affects the natural frequencies.The structural system also indicates a possible influence from the concrete shear walls, the steel bracings, and non-structural walls on the eigenfrequencies.As no measurements were taken in these elements, no direct conclusions can be made about their influence.The results above highlight the importance of monitoring the MC within structural elements in SHM systems in addition to environmental parameters.
Based on the measurement data, a model is presented for predicting the natural frequencies using three parameters: seasonal changes, dryout of the CLT slab, and a balancing frequency.The model provides a good approximation of how the natural frequencies of House Charlie vary over time, providing results over the influence the seasonal effects have along with estimations when a dry-out of the structural materials is to be expected.The prediction model can be used as the baseline for damage assessment through vSHM as it provides significantly better predictions than the average values of the natural frequencies.
This study demonstrates that considering the variations in hygrothermal parameters when monitoring the global dynamic parameters in a vSHM system improves the predictability and narrows the error margin for potential damage detection.For newly constructed buildings using timber, dry-out is an additional factor that should be considered.Therefore, it is recommended to conduct further research within this area, both in terms of carrying out more long-term SHM campaigns as well as producing theoretical models to develop reliable models for predicting the seasonal variations of the dynamic parameters in different types of structures.This applies particularly to buildings using a combination of structural materials, such as timber-concrete hybrids.

Table 2
Parameters from the curve-fitting performed in Fig. 18

Table 3
Parameters from the curve-fitting performed in Fig. 19 and coefficients for determinations.

Fig. 1 .
Fig. 1.House Charlie, (a) during construction in 2018 and (b) the finished building in use in 2021.

Fig. 2 .
Fig. 2. Structural system of House Charlie.Yellow/orange elements are in timber, grey in concrete and red elements are steel columns and bracings.

Fig. 4 .
Fig. 4. The slab layout of the first floor in House Charlie and the placement of the temperature/RH sensors numbered 1 to 3.

Fig. 3 .
Fig. 3. Locations of the measurement equipment placed in House Charlie.

4. 1
Fig. 10 presents external (T ext ), internal (T int ), and mean slab temperature (T slab , the mean value from the three reading within the slab), showing a clear seasonal trend only for the exterior readings.On the other hand, both the interior and slab temperatures are more or less constant due to the active heating and ventilation system of House Charlie that keeps the indoor temperature around 21 • C. To visualize short-term readings, Fig. 10b shows the daily variation of temperature readings during the first week of April 2019.The daily day and night variations are significant in the case of T ext but very limited for T int and T slab .

Fig. 5 .
Fig. 5. Histograms of the RMS acceleration values at the top floor in the X and Y direction.

Fig. 6 .
Fig. 6.The first three mode shapes obtained by an OMA performed on a data set from 2019 to 08-31.The red lines show the deformed mode shape, and the blue lines show the undeformed structure.The first mode is at 3.31 Hz, the second mode is at 3.55 Hz, and the third mode is at 4.00 Hz.The three mode shapes appear torsional but are unclear due to the limited number of geophones.

Fig. 7 .
Fig. 7. Evolution of the first three natural frequencies of House Charlie over a) the complete measurement period and b) for a single week.

Fig. 8 .
Fig. 8.The variation in frequency during the measurement period (left) along with the corresponding histogram (right) for the first three natural frequencies of House Charlie.

Fig. 9 .
Fig. 9.The variation in damping during the measurement period (left) along with the corresponding histogram (right) for the first three natural frequencies of House Charlie.

3 c
are equivalent to ± 15 % of the corresponding balanced value MC 3 a .Variations on the open side are clearly more pronounced than on the protected side, where the seasonal changes are only ± 5.6 % of the long-term MC for position 1.

Fig. 10 .
Fig. 10.Exterior, interior, and slab temperature complemented with the SMHI data for exterior temperature are shown for a) the entire measurement period and b) a single week.

Fig. 11 .Fig. 12 .
Fig. 11.Exterior-, interior-and slab RH for (a) a period of 3 years complemented with the SMHI data for exterior RH and (b) for a single week.

Fig. 13 .
Fig. 13.Observations from the three sensors through the CLT slab on the first floor where a) shows the temperature, b) the observed RH, and c) the calculated MC.

Fig. 14 .
Fig. 14.First natural frequency of House Charlie co-plotted with (a) temperature, (b) relative humidity, (c) absolute humidity, and (d) moisture content.A moving average with a window size of one month is used for all curves.

15 .
Linear regression models between interior and exterior environmental parameters and the natural frequencies.C.Larsson et al.

Fig. 16 .
Fig.16.Linear regression models between the MC within a CLT slab at different embedment depths and the natural frequencies.

Fig. 17 .
Fig. 17.Derived approach of the relationship between the RH within a CLT slab over time.

Fig. 18 .
Fig. 18.MC measurements in a CLT slab in House Charlie along with the curve fitting and a 3-year prediction.

Fig. 19 .
Fig. 19.Curve fitting and a 3-year prediction of the three natural frequencies.

Table 1
Structural elements and dimensions.
and coefficients for determinations.
C.Larsson et al.
Deviations of the observed natural frequencies from the mean (light colors) and predicted (dark colors) frequencies of House Charlie during the measurement period August 1st, 2018, and August 31st, 2021.