vibration.structural.building_damage

Effects of vibration on structures (DIN 4150-3:1999-02).

A pile driver, a passing tram or a blast puts vibration into the ground, and the question the neighbours ask is whether the building will crack. DIN 4150-3 answers it the way an engineering practice can afford to: not with a stress calculation, but with guideline values (Anhaltswerte) for one measured quantity, the peak particle velocity, drawn from a large body of measurements on real buildings. Keep under them and damage of the kind the standard defines has not been observed; exceed them and it does not follow that damage occurs, only that the cheap check no longer settles the question and Clauses 4.2 to 4.4 have to be done properly.

What is measured (5.1). At the foundation, the largest of the three components $v_x$, $v_y$, $v_z$ of the particle velocity, as a peak, each treated on its own; the standard calls it $|v_i{|}_{\max }$ and then writes it $v_i$. In the topmost floor plane, the larger of the two horizontal components, measured at the outside wall, which is the building’s horizontal answer to the foundation excitation rather than a new excitation.

Short-term vibration (Clause 5) is vibration that does not occur often enough for resonance to build up in the structure. Table 1 gives its guideline values by building class, and at the foundation they depend on frequency: a building tolerates a fast wiggle better than a slow one, so the value rises from 1 Hz to 100 Hz. Between the printed frequencies the guideline is read off Bild 1, which joins the corner values by straight lines on a linear frequency axis; above 100 Hz the 100 Hz value may be used. In the topmost floor plane one value covers all frequencies.

Long-term vibration (Clause 6, Dauererschütterungen) is the opposite case: often enough for the structure to respond at its own frequencies. Table 3 drops to a single value per class in the topmost floor plane, roughly a quarter of the short-term one, and prints no frequency dependence at all.

Buried pipelines (5.3) are judged on their own Table 2 by pipe material, measured on the pipe, and long-term vibration halves those values (6.3).

Three sizing rules travel with the tables and are here because a reader who has the tables needs them in the same breath:

• Ceilings and floors (5.2) are separately covered by a vertical $v_z\le 20$ mm/s at the point of largest vibration, usually mid-span.
• Massive engineering structures such as reinforced-concrete abutments and block foundations may take twice the row 1 values of Table 1 (5.1).
• The lowest horizontal natural frequency of a building of five storeys or more is roughly $f_i\approx 10/n$ with $n$ the storey count (6.4), which is the estimate that tells you whether the topmost floor plane will be excited at all.

Clause 6.2 turns a measured velocity into a bending stress for a beam or a one-way slab vibrating in one mode, which is the bridge from this guideline check to the stress calculation of 4.2:

The guideline values are not limits in the legal sense and not an acceptance specification. They are where experience says the question stops being worth asking.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

assess_building_vibration(
    velocity_mm_s: float,
    *,
    building_class: BuildingClass | str,
    frequency_hz: float | None = None,
    location: MeasurementLocation | str = 'foundation',
    duration: VibrationDuration | str = 'short_term',
    massive_structure: bool = False,
) -> DamageAssessment

Compare one measured peak velocity with its guideline value.

Parameters

Returns: The comparison, as a DamageAssessment.

Raises

bending_stress(
    peak_velocity_m_s: ArrayLike,
    *,
    dynamic_modulus_pa: float,
    density_kg_m3: float,
    load_ratio: float = 1.0,
    mode_factor: float = 1.0,
) -> np.ndarray | float

Peak bending stress from a peak velocity, Formula (1) of 6.2.

For a beam or a one-way slab of full rectangular section, constant stiffness and uniform mass, vibrating in one mode, the peak bending stress follows from the peak velocity alone:

The system dimensions do not enter, which is the point of the formula: a velocity measured where the amplitude is largest is enough. The mode factor $k_n$ lies between 1 and 1,3 in the technically important cases, so it moves the answer by less than a third.

Parameters

Returns: The peak bending stress, in pascals; a float unless the velocity was an array.

Raises

Constant (float).

BENDING_STRESS_CONSTANT = 1.73

Constant (tuple).

BUILDING_CLASSES = ('commercial', 'residential', 'sensitive')

A DIN 4150-3 rule is used outside the range the standard offers it for.

Raised by storey_fundamental_frequency below STOREY_FREQUENCY_MIN_STOREYS. The estimate is still returned: the standard offers 10 / n from about five storeys up, and below that it says nothing, so the number is an extrapolation rather than the rule.

DamageAssessment(
    velocity_mm_s: float,
    guideline_mm_s: float,
    building_class: str,
    location: str,
    duration: str,
    frequency_hz: float | None,
)

One measured velocity against the guideline value it is judged by.

Attributes

DamageAssessment.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw Bild 1 with this measurement on it.

The three foundation curves of Table 1 against frequency, and the measured velocity as a point, so the margin is read rather than computed.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

property

The measured velocity as a fraction of the guideline value.

property

Whether the measured velocity keeps to the guideline value.

True is the whole of what the standard promises: damage of the kind 4.5 defines has not, in the experience the tables are drawn from, been observed. False is not the converse, and 5.1 says so: exceeding a guideline value does not mean damage occurs, it means the question has to be answered by 4.2 to 4.4 instead.

Constant (float).

FLOOR_VERTICAL_MM_S = 20.0

Constant (tuple).

FOUNDATION_FREQUENCIES_HZ = (1.0, 10.0, 50.0, 100.0)

foundation_guideline_curve(
    building_class: BuildingClass | str,
    frequency: ArrayLike | None = None,
) -> tuple[NDArray[np.float64], NDArray[np.float64]]

Bild 1 as two arrays: frequency and guideline velocity.

The corner points of Table 1 by default, which is the polyline Bild 1 draws; pass frequency to sample the same polyline elsewhere.

Parameters

Returns: (frequency_hz, guideline_mm_s).

Raises

guideline_velocity(
    building_class: BuildingClass | str,
    frequency: ArrayLike | None = None,
    *,
    location: MeasurementLocation | str = 'foundation',
    duration: VibrationDuration | str = 'short_term',
    massive_structure: bool = False,
) -> np.ndarray | float

The guideline peak velocity of Table 1 or Table 3, in mm/s.

At the foundation for short-term vibration the guideline is a function of frequency, read off Bild 1: constant below 10 Hz, then two straight segments joining the corner values of Table 1 on a linear frequency axis, and constant again above 100 Hz, since 5.1 allows the 100 Hz value to be used for anything faster. Everywhere else Table 1 and Table 3 print one number for all frequencies, and frequency is then not needed.

Parameters

Returns: The guideline peak velocity, in millimetres per second; a float unless frequency was an array.

Raises

Constant (mapping).

LONG_TERM_TOP_FLOOR_MM_S = {'commercial': 10.0, 'residential': 5.0, 'sensitive': 2.5}

Constant (float).

MASSIVE_STRUCTURE_FACTOR = 2.0

pipeline_guideline_velocity(
    material: PipelineMaterial | str,
    *,
    duration: VibrationDuration | str = 'short_term',
) -> float

The guideline peak velocity on a buried pipeline (Table 2), in mm/s.

Measured on the pipe itself; a substitute measurement at the ground surface above it only estimates the value (5.3, D.1). Long-term vibration halves the table, which is what 6.3 allows without further evidence.

Parameters

Returns: The guideline peak velocity, in millimetres per second.

Raises

Constant (float).

PIPELINE_LONG_TERM_FACTOR = 0.5

Constant (tuple).

PIPELINE_MATERIALS = ('welded_steel', 'concrete_or_flanged_metal', 'masonry_or_plastic')

Constant (mapping).

PIPELINE_MM_S = {'welded_steel': 100.0, 'concrete_or_flanged_metal': 80.0, 'masonry_or_plastic': 50.0}

Constant (mapping).

SHORT_TERM_FOUNDATION_MM_S = {'commercial': (20.0, 20.0, 40.0, 50.0), 'residential': (5.0, 5.0, 15.0, 20.0), 'sensitive': (3.0, 3.0, 8.0, 10.0)}

Constant (mapping).

SHORT_TERM_TOP_FLOOR_MM_S = {'commercial': 40.0, 'residential': 15.0, 'sensitive': 8.0}

Constant (int).

STOREY_FREQUENCY_MIN_STOREYS = 5

Constant (float).

STOREY_FREQUENCY_NUMERATOR_HZ = 10.0

storey_fundamental_frequency(storeys: int) -> float

The rough lowest horizontal natural frequency of a building (6.4).

f_i ~ 10 / n, offered for buildings from about five storeys up. It is a rough estimate and the standard says so; its use is to tell whether the excitation is anywhere near the frequency at which the topmost floor plane will answer.

Parameters

Returns: The estimated lowest horizontal natural frequency, in hertz.

Raises

Warns