Vibration, Resonance and Fatigue
Steel, being flexible, is an excellent conductor of vibration. Dynamic activity in one part of a structure can be transmitted through the structure itself by means of the horizontal and vertical components to any other adjacent part. Even dynamic activity outside of the structure such as road or rail traffic can be transmitted through the ground into the building causing disturbing, or even dangerous vibrations to the detriment of the people or activities taking place.
Generally, tall structures, or those with large horizontal spans are more susceptible because the taller the vertical columns, and/or the greater the horizontal span, the lower will be the natural frequency of the building, and the lower the natural frequency, the more it’s susceptible to unacceptable levels of vibration.
Here, we'll look at:
Vibration is measured in terms of Frequency, Amplitude and Acceleration:
Frequency: is the number of cycles and object completes when moving from one extreme position to another, and back again. The unit of measure for frequency is Hertz (Hz). One Hertz is equal to one cycle per second.
The natural frequency of a steel beam or floor can be calculated for design estimate purposes by the simple formula: fn= 18 / √d . Where fn= the natural beam or floor frequency, and d= the deflection of the beam or floor.
Therefore, a beam or floor deflecting 100 mm will have a natural frequency of fn= 18 / √d = 1.8 Hz
Amplitude: is the distance from the stationary position to the extreme position on either side and is measured in metres (m). The intensity of vibration depends on Amplitude
Acceleration: is the speed of the vibrating object as it varies from its stationary position to its extreme position. The object slows down as it reaches its extreme position and eventually stops, then moves in the opposite direction accelerating until it reaches its maximum velocity as it passes through its neutral or stationary position.
Acceleration is measured in terms of metres-per-second (m/s)
Vibration limits, or acceptable thresholds are expressed in terms of acceleration as a percentage of acceleration due to gravity (g), where 1g = 9.8 m/s.
Types of Vibration and the Causes
Vibration caused by the effects of Wind Pressure and the ‘buffeting’ effects of Vortex Shedding has already been touched upon, as has the potential of being generated by Seismic Activity. But vibration due to Live-Load conditions is equally disruptive.
Types of vibration match those of the varying types of Live-Loads, i.e. Transient, Periodic, Harmonic, and Impulsive.
Vibration as a result of Transient Live loads is generally caused by human activity in public access areas. In residential or commercial buildings, the conducting of day-to-day activities is not generally considered a major factor as the accepted design criteria for such buildings will generally accommodate this.
Vibration as a result of Periodic Live Loads can be more problematic. If you imagine a person walking across a simply supported beam (supported at each end), the deflection will increase as the person approaches the center-span and decreasing as the person continues toward the end. This deflection is a function of the beam size, its span, and the mass of the applied load (the person’s weight). Reducing the beam size, and/or increasing the beam span, and/or increasing the load, will increase the deflection.
If that person reaches the center-span of the beam and stops, the beam will still deflect under the (now) static load but will cease to bounce, the beam is now in equilibrium. If that person now jumps up and down the beam will again bounce, and if the frequency of the activity, which is known as the ‘step’ or ‘forcing’ frequency’ matches the natural frequency of the beam, the deflection will amplify resulting in the phenomenon of Resonance
Vibration as a result of Harmonic Live Loads generated by rotating or vibrating equipment and machinery is usually at a higher frequency and its effects can be mitigated by local energy isolation, usually in the form of anti-vibration mountings. Ideally, if possible, the best solution is to locate the offending equipment on the lower levels of the structure, or in a basement, thereby isolating the equipment from the structure entirely.
Vibration as a result of Impulsive Loads as a result of sudden, non-rhythmic impacts are generally at a lower frequency, and like Harmonic loads, are best mitigated at source.
Acceptable Levels of Vibration
Levels of vibration depend on whether they are continuous or intermittent, and on the nature and intended use of the structure, they may be either:
This actually means: imperceptible to the human senses, and though it may not cause discomfort to people, it may affect sensitive scientific equipment as may be found in laboratories, hospital operating theatres, observatories, and other such environments
Light vibrations, though not necessarily causing structural damage can be very disturbing to people, the level of disturbance depending on what the person is doing at the time. If the person is active, light vibrations should not cause a major problem, but if the person is at rest, trying to concentrate, or trying to sleep, they can be disturbing to the point of affecting the person’s well-being
Strong vibrations will be disturbing to people whether they are active or at rest. Such disturbance may be caused by being in close proximity to a dance studio, mechanical plant and equipment, or heavy road or rail traffic. In residential or commercial buildings, strong vibrations would be considered outside of the human tolerance level
Severe vibrations are rarely caused by a live load condition, except perhaps in an industrial environment provided it is intermittent. Unless taken into account at the design stage, severe vibrations may threaten the integrity of the structure itself.
Violent vibrations will almost certainly be the result of wind or seismic activity and if not considered at the design stage could cause irreparable damage to the structure. However, such vibrations usually only affect older buildings, modern design and analysis can, to a great extent, mitigate these affects.
The Effects of Vibration on a Structure
The main consequences of uncontrolled vibration on a structure are Resonance and Fatigue:
Resonance occurs when the forcing frequency matches that of the natural frequency of the structure. If the forcing frequency is synchronized, that is to say if the load is steady and rhythmic more energy is fed into the system, amplifying at each cycle of loading. As a consequence, the magnitude of the vibration will increase until a maximum is reached, at which time the consequences may be severe leading to a possible catastrophic structural collapse.
Fatigue occurs where there is a repeated cyclic loading, usually at the joints or connections between the steel members. Fatigue stress is progressive depending on the number and intensity of load cycles, and once fatigue stress is evident by visible cracks or deformations it’s usually too late, and the member or joint must be repaired or replaced. Unattended evidence of fatigue will lead to ultimate failure or collapse.
Controlling the Effects of Vibration
To control the effects of vibration, the beam or floor must have a natural frequency greater than that of the forcing frequency, if the natural frequency is less than the forcing frequency, then there are a number of steps that can be taken to improve the situation:
- Increase the beam or column size, thereby reducing its deflection
- Decrease the beam or column span. In the case of a column, this can be done by adding additional cross-members, thus reducing the effective length, or in the case of a beam, add additional vertical supports in the form of columns or posts, or alternatively, introduce vertical ‘Vee’ or Chevron’ bracing. (Refer to Stabilizing a Steel Structure)
- Reduce of relocate the applied load
There are two other means of controlling the effects, which are discussed briefly under the heading Stabilizing Systems - they include