Source: https://jmrplens.github.io/phonometry/vibration/immission/people-in-buildings/ # Vibration and people in buildings (DIN 4150-2) A [vibration meter](https://jmrplens.github.io/phonometry/vibration/immission/vibration-meter/) turns a record into two numbers, the maximum weighted vibration severity `KB_Fmax` and the clock maximum r.m.s. `KB_FTm`, and stops. DIN 4150-2 is where those numbers are judged for the people who live or work where the vibration arrives: a table of guide values by kind of area and time of day, a procedure that reads them in a fixed order, and a set of rules for the sources that most often shake a house, from a hammer in the workshop next door to the railway at the end of the street. It is not a standard of limits, and it says so. The guide values are "not to be applied mechanically", the annex that explains them calls them recommended values rather than binding ones, and one of its own worked examples finds a reading 13 % above the lower value and calls the requirement met, because a measurement of `KB_F` is uncertain by about that much. What the standard does fix is the procedure, and the procedure is what this page implements. ## 1. Two quantities, and the order they are read in `KB_Fmax` says how bad the vibration was at its worst. The **assessment vibration severity** `KB_FTr` says what it added up to over the whole **assessment period**, 16 h by day (6:00 to 22:00) and 8 h by night. Both are formed for the three directions and the largest is assessed. Clause 6.2 reads the guide values of Table 1 in a fixed order, which its Figure 2 draws as a flowchart: - `KB_Fmax` at or below the **lower value** `A_u`: the requirement is met, and nothing else is asked. - `KB_Fmax` above the **upper value** `A_o`: not met, however short the exposure. - In between: up to three short events a day are met as they are; anything else is decided by `KB_FTr` against `A_r`. ```python from phonometry import vibration guide = vibration.guide_values("commercial") print(guide) # GuideValues(a_u=0.3, a_o=6.0, a_r=0.15, time_of_day='day', edition='1999') # Annex C, Example 1: a sawmill's stationary 5 Hz vibration at KB_Fmax = 0.25. verdict = vibration.assess_people_in_buildings(0.25, guide) print(verdict.complies, verdict.criterion) # True A_u # Above A_o the question ends the other way, unless the events are rare. print(vibration.assess_people_in_buildings(6.5, guide).criterion) # A_o blast = vibration.assess_people_in_buildings(2.0, guide, rare_short_events=True) print(blast.complies) # True ```

Figure code

```python import matplotlib.pyplot as plt import numpy as np from phonometry import vibration areas = list(vibration.GUIDE_VALUES) x = np.arange(len(areas)) fig, axes = plt.subplots(1, 2, figsize=(11.5, 5.6), sharey=True) for ax, time_of_day in zip(axes, ("day", "night"), strict=True): values = [vibration.guide_values(a, time_of_day=time_of_day) for a in areas] ax.bar(x - 0.19, [v.a_u for v in values], 0.38, label="$A_u$") ax.bar(x + 0.19, [v.a_r for v in values], 0.38, label="$A_r$") ax.plot(x, [v.a_o for v in values], "v", label="$A_o$") ax.set_yscale("log") ax.set_xticks(x, areas) ax.set_title(time_of_day) axes[0].legend() ```

The verdict compares at the decimals the guide value is printed with, half up as a hand rounds, because that is what the standard does: its Example 4 forms a `KB_FTr` of 0,154, writes it as 0,15 and finds it at the `A_r` of 0,15, met. And it follows Example 3 on a `KB_Fmax` above `A_u` by less than the 15 % a measurement of `KB_F` is uncertain by: the requirement "can as a rule still be regarded as met", the standard concludes, and the verdict says so, with `within_uncertainty` set for anyone who wants to read it more strictly. **How the measurement goes.** Use a DIN 45669-1 meter, checked before and after, and measure on the floor of the room itself: `z` usually at the middle of the floor panel, `x` and `y` along the outer walls with `x` towards the source where possible, the three at once unless the vibration is steady, and a fourth channel near the source. Set down loose, a transducer holds while the peaks stay at or below 3 m/s², its horizontals only to 40 Hz; on a carpet it stands on the spiked device, about 2,5 kg with the transducer, pressed and tapped through the covering. Capture the characteristic exposure, form `KB_Fmax` and, where it is needed, `KB_FTr` by day and by night with the rest hours apart, and report the positions, the coupling, the meter and its settings. ## 2. The assessment vibration severity `KB_FTr` is the clock maximum r.m.s. of each stretch of exposure, weighted by the share of the assessment period it lasts for (Formula (4a); with one stretch, Formula (4b)): ```text KB_FTr = √( (1 / T_r) · Σ_j T_e,j · KB²_FTm,j ) ``` A stretch that falls in the **rest hours** of the day, 6:00 to 7:00 and 19:00 to 22:00 on working days and the whole day on Sundays and public holidays, carries the weight 2 (Formula (5)). Annex C works the same two forging hammers through both formulas: hammer a) for 6 h at a `KB_FTm` of 0,16 and hammer b) for 1,5 h at 0,39, first with both outside the rest hours and then with hammer b) moved into them. ```python from phonometry import vibration hour = 3600.0 hammers = [0.16, 0.39] hours = [6 * hour, 1.5 * hour] # Annex C, Example 4: Formula (4a), both hammers outside the rest hours. kb_ftr = vibration.assessment_vibration_severity(hammers, hours) print(f"KB_FTr = {kb_ftr:.3f}") # 0.154, which the standard writes as 0.15 # Example 5: hammer b) runs 19:00 to 20:30, in the rest hours, Formula (5). evening = vibration.assessment_vibration_severity( hammers, hours, in_rest_time=[False, True] ) print(f"KB_FTr = {evening:.2f}") # 0.20 guide = vibration.guide_values("commercial") print(vibration.assess_people_in_buildings(0.47, guide, kb_ftr=kb_ftr).complies) # True print(vibration.assess_people_in_buildings(0.47, guide, kb_ftr=evening).complies) # False ``` The same formula turned around says how long a source may act before `KB_FTr` reaches `A_r`, which is what Example 2 asks: the sawmill of Example 1 in a residential area instead, where `A_r` is 0,07, may run for 1,48 h of the 16 h day. ```python from phonometry import vibration exposure = vibration.admissible_exposure_s(0.23, 0.07) print(f"{exposure / 3600:.2f} h") # 1.48 h ``` ## 3. The sources that have their own rules Clause 6.5 adds a rule per kind of source, and each is one argument: - **Rare short events**, up to three a day, blasting among them: `KB_Fmax` is compared with `A_o` alone, which `rare_short_events=True` asks for. Quarry blasting has more: blasts in immediate succession may count as one event, at most fifteen a week if they do; and blasts on working days with the neighbours warned, between 7:00 and 13:00 or 15:00 and 19:00, one a day, are held in a mixed or residential area to the `A_o` of an industrial one, 6, which `source="quarry_blasting"` asks for, with a `KB_Fmax` of 8 allowed a few times a year in exceptional cases. - **Road traffic** uses the procedure as it stands, without the rest-time weighting. - A **railway** is judged on `A_u` and `A_r` only, with the rest-time weighting not applied either, which `source="railway"` asks for; `A_o` is not a verdict for it, and 6.5.3.5 sets its own thresholds instead, a night-time clock maximum above 0,6 on a surface line or 0,3 underground being a reason to look into the cause, flat spots on wheels for one, and to put it right. An **urban surface line**, a tram, light rail or S-Bahn, gets `A_u` and `A_r` raised by the factor 1,5 with `source="urban_railway"`. A new line is held to Table 1; an existing one often exceeds it, and the standard leaves that case to judgement. - A **construction site** has its own Table 2, by how many working days it shakes the neighbours and by the stage the operator is held to, stage I below which no considerable annoyance is expected, stage II which needs the measures of 6.5.4.3, and stage III above which the exposure is unreasonable. The values for two to six days are interpolated between the one-day column and the column that starts at seven, as Figure 3 draws them; at night Table 1 applies; and the site's blasting is held to an `A_o` of 8. ```python from phonometry import vibration for days in (1, 3, 6, 7, 30): guide = vibration.construction_guide_values(days, stage="I") print(f"{days:2d} working days: A_u {guide.a_u:.2f}, A_r {guide.a_r:.2f}") # 1 working days: A_u 0.80, A_r 0.40 # 3 working days: A_u 0.67, A_r 0.37 # 6 working days: A_u 0.47, A_r 0.32 # 7 working days: A_u 0.40, A_r 0.30 # 30 working days: A_u 0.30, A_r 0.20 urban = vibration.guide_values("residential", time_of_day="night", source="urban_railway") print(urban) # GuideValues(a_u=0.15, a_o=0.2, a_r=0.075, time_of_day='night', edition='1999') ``` ## 4. A railway, class by class The trains of a railway occupy a few clock intervals each and leave the rest quiet, so Annex A forms `KB_FTm` for each **class** of train over the intervals its trains occupied (Formula (A.1)), puts a standard deviation on its square (Formula (A.2)), and weights each class in `KB_FTr` by the intervals it occupies in the period, 1920 by day and 960 by night (Formula (A.3)). Example 8 does it for a ten-minute record with three passages, the third of which takes three intervals: the peak interval of each train is one class and the two flank intervals of the third train another, extrapolated to a day of 288 and 192 occupied intervals: ```python from phonometry import vibration class_1 = [0.92, 0.6, 0.9] # the clock maxima trains of class 1 occupied class_2 = [0.2, 0.24] kb_ftm = [vibration.railway_takt_maximum_rms(c) for c in (class_1, class_2)] spread = [vibration.railway_takt_spread(c) for c in (class_1, class_2)] print([round(v, 2) for v in kb_ftm]) # [0.82, 0.22] railway = vibration.railway_assessment_severity(kb_ftm, [288, 192], spread=spread) print(f"KB_FTr = {railway.kb_ftr:.3f}") # 0.325 print(f" from {railway.lower:.3f} to {railway.upper:.3f}") # 0.253 to 0.384 guide = vibration.guide_values("residential") verdict = vibration.assess_people_in_buildings( 0.92, guide, kb_ftr=railway.kb_ftr, source="railway" ) print(verdict.complies, verdict.criterion) # False A_r ``` Annex D turns Formula (A.3) around into a figure: with one class of train and each train occupying one clock interval, how many an hour keep `KB_FTr` at `A_r`. It reads off 7 trains for the 0,05 of a dwelling at night and 14 for the 0,07 of a mixed area, both at a `KB_FTm` of 0,2, and the formula behind the figure is `120 (A_r / KB_FTm)²`.

Figure code

```python import matplotlib.pyplot as plt import numpy as np from phonometry import vibration trains = np.geomspace(0.5, 100.0, 200) fig, ax = plt.subplots(figsize=(10, 6.2)) for a_r in (0.2, 0.15, 0.1, 0.07, 0.05): ax.loglog(trains, a_r * np.sqrt(120.0 / trains), label=f"$A_r$ = {a_r:g}") for a_r in (0.05, 0.07): n = vibration.admissible_trains_per_hour(0.2, a_r) ax.plot([n], [0.2], "o") ax.set_xlabel("Trains an hour") ax.set_ylabel("$KB_{FTm}$") ax.legend() ```

```python from phonometry import vibration print(int(vibration.admissible_trains_per_hour(0.2, 0.05))) # 7 print(int(vibration.admissible_trains_per_hour(0.2, 0.07))) # 14 ``` ## 5. From an unweighted record Where only an unweighted velocity record exists, Clause 7 estimates `KB_Fmax` from its peak and its frequency: Formula (6) is what the KB weighting would leave of a sine of that peak, with the 5,6 Hz corner of the meter, and Formula (7) scales it by an empirical factor of Table 3 for the kind of vibration, 0,9 for a clean harmonic signal down to 0,6 for a single short event with no resonance in the floor. The standard marks the result with an asterisk because it is an estimate, and puts the factors at about 15 % either way. ```python from phonometry import vibration # Annex C, Example 7: a blast on a ceiling, 4 mm/s peak at 14 Hz. estimate = vibration.kb_fmax_from_peak_velocity(4.0, 14.0, kind="single_event_resonant") print(f"KB*_Fmax = {estimate:.1f}") # 2.1, against an A_o of 3 ``` ## 6. A formula printed wrong Formula (A.1b) prints `KB_FTm,j` equal to a mean of squares with no root over it, while Formula (A.1a) beside it takes the root, Formula (A.2) beneath them uses `KB²_FTm,j` for the mean square, and Example 8 applies (A.1b) with the root. The library takes the root, the tests hold it to the example, and the [errata page](https://jmrplens.github.io/phonometry/reference/errata/) has the reading. ## 7. The draft of 2023 E DIN 4150-2:2023-08 is to replace this edition, and the library reads it with `edition="2023"` on `guide_values` and `assess_people_in_buildings`. It changes one cell of Table 1, the night `A_u` of a mixed area down to 0,1; no longer excuses a `KB_Fmax` within the 15 % above `A_u`; compares a railway with `A_o` and forms its numbers by category of train, with a weighting factor per kind of train, and a road by night not; and adds an existing road whose neighbours must put up with 50 % more, and an induced seismic event held to the daytime `A_o`. The guide values carry the edition they were read for and the verdict follows it. The railway and the rest of the changes have [their own page](https://jmrplens.github.io/phonometry/vibration/immission/railway-categories/). ```python from phonometry import vibration print(vibration.guide_values("mixed", time_of_day="night", edition="2023")) # GuideValues(a_u=0.1, a_o=0.3, a_r=0.07, time_of_day='night', edition='2023') ``` ## What this guide covers The **guide values** of Table 1 by area, time of day and kind of source, the **procedure** of Clause 6.2 as a verdict with the criterion that decided it, and the **assessment vibration severity** of Formulae (4a), (4b) and (5) with the exposure `A_r` allows. The **source rules** of Clause 6.5: rare short events on `A_o` alone, the railway on `A_u` and `A_r` with the factor 1,5 of an urban surface line, and the construction site's **Table 2** by duration and stage with the interpolation of Figure 3. **Annex A** in full: the clock maximum r.m.s. of a class of train, the spread of its square, the assessment severity by classes and the interval the spread puts on it; and **Figure D.1**, trains an hour against `A_r`. And **Clause 7**, the estimate of `KB_Fmax` from a peak velocity with Table 3. **No judgement of the cases the standard leaves open.** An existing railway line, a construction site beyond 78 working days, a hospital next to one, and whatever 6.2 sends to an individual assessment are decided case by case in the standard, and are not decided here. **The measurement is described, not checked.** Where the transducers go, how they are coupled and how long a measurement runs are Clause 5 and DIN 45669-2, set out above for the person measuring. Of all that, the library puts a number only to the loose-mounting limits, the wax limit of Table 1 and the mass loading of 7.2.4, on the meter's page; the quantities themselves come from the meter of DIN 45669-1, which forms them from a record. ## See also - [Measuring vibration immission (DIN 45669-1)](https://jmrplens.github.io/phonometry/vibration/immission/vibration-meter/): where `KB_Fmax` and the clock maxima come from, and the numbers of DIN 45669-2 a measurement is planned by. - [Vibration next to a railway (DIN 45672)](https://jmrplens.github.io/phonometry/vibration/immission/railway-vibration/): the same passages reduced for comparison rather than for assessment. - [Vibration damage to structures (DIN 4150-3)](https://jmrplens.github.io/phonometry/vibration/structural/structural-damage/): the other half of DIN 4150, what the building itself may take. - API reference: [`vibration.immission.people`](https://jmrplens.github.io/phonometry/reference/api/vibration/people/). ## References - Deutsches Institut für Normung. (1999). *Erschütterungen im Bauwesen — Teil 2: Einwirkungen auf Menschen in Gebäuden* (DIN 4150-2:1999-06). The assessment quantities of 6.1, the procedure of 6.2 with Figure 2, the guide values of Table 1, the assessment vibration severity of Formulae (4a), (4b) and (5), the rules by source of 6.5 with Table 2 and the interpolation of Figure 3, the estimate of Clause 7 with Formulae (6) and (7) and Table 3, and Annex A with Formulae (A.1) to (A.4). Annex C is the oracle of the conformance rows. Clause 5 on the measurement and the report of Clause 8 are prose, set out in the measurement section. - Deutsches Institut für Normung. (2010). *Messung von Schwingungsimmissionen — Teil 1: Schwingungsmesser — Anforderungen und Prüfungen* (DIN 45669-1:2010-09). The meter whose KB_Fmax and clock maxima this standard judges, and the 5.6 Hz corner frequency Formula (6) carries. The three simultaneous channels and the fourth near the source of 5.1.2, the interruption and back-erasure of the clock maxima of 5.1.6.4, and the check before a measurement of 6.5. - Deutsches Institut für Normung. (2005). *Messung von Schwingungsimmissionen — Teil 2: Messverfahren* (DIN 45669-2:2005-06). The floor positions of 5.1.3, the directions of 5.2, the couplings of 5.3.2 and 5.3.3 with Table 1, the measuring time of 6.1, the disturbances of 7.2.2 and the report of Clause 9, as the measurement section describes them. The loose-mounting limits, the wax limit and the mass loading are implemented on the meter's page; the rest is prose.