Lightweight structures such as steel floors, steel-concrete composite floors (Deck floors), etc. can easily cause discomfort and insecurity due to vibration when walking or working, even though they are safe (not collapsed). How do engineers calculate by numbers to ensure that the floor does not vibrate without wasting money for the Investor and limiting the “fait accompli” – when the construction is completed and only discovered when it is used? The following is a practice in construction consulting.

🏐The load-bearing structure of the project is designed to ensure safety (materials are not damaged when working under the load used), and must also ensure comfort: aesthetics, psychology (concrete does not crack beyond the limit, the floor does not sag too much …). The feeling of vibration is also a type of comfort used, depending on each person’s perception, one person finds the vibration unbearable while another finds it normal. If the majority or the boss feels the vibration, it is not okay 🤣

Causes of vibration

Vibration sources due to impacts during the use of the structure:

– Repetitive: walking, jumping, …

– Forced vibration sources: machinery

– Sudden impact: collision

As a physical object, the structure always has its own vibrations. The frequency of natural vibrations is inversely proportional to the mass and directly proportional to the stiffness. The lighter and thinner the structure, such as steel, the lower the frequency.

How much vibration is allowed

In addition to the intuition based on each person’s feelings (when the matter has already happened), it is necessary to rely on reason (when designing and constructing new structures), there must be a numerical limit when the feeling of vibration is uncomfortable. This number is specified in the design standards. The Eurocode standard specifies clearly, in detail and is easier to practice, so it will be used.

This limit depends on the function of use: office, house, medical, dance floor, machine room, etc.

Design Practice

⛳️Vibration Forms

The determination of familiar vibration forms uses structural design analysis software, using the finite element method. The point to note is that only the vertical vibration forms, which are the direction of vibration, are determined.

Mass participating in oscillation in ETABS calculation diagram

Therefore, declare the mass participating in oscillation according to:

– The weight of the structure itself, the finishing layers, the load used (live load) according to the ratio of participation in oscillation.

– Only take the mass component in the vertical direction.

⛳️Method 1: Traditionally according to Eurocode

The conventional steel floor structure system consists of main beams and secondary beams made of shaped steel in 2 directions. Determine the natural frequency of each individual beam according to the simple beam diagram, this value must not be less than 4Hz.

The frequency formula determined according to the beam stiffness and load includes: self-weight, weight of finishing layers, suspended ceiling, plus 10% of the load used (live load). With the explanation of the number 10% considered as the long-term component of the loads used (such as furniture..)

$$f=\frac{1}{2\pi}\sqrt{\frac{K}{M}}=\frac{18}{\sqrt{\delta_{max}}}$$

With $\delta_ {max} (mm) $ is the maximum deflection of the beam caused by the above load combination.

However, this limit frequency value is too safe, in fact, in many cases the calculation does not reach the number but when used, there is no problem with vibration from residents. Moreover, separating the beam from the floor structure is also too safe because the floor itself also prevents the beam from oscillating.

⛳️Method 2: refer to ArceloMittal’s “Design Guide for Floor Vibration”

(Attached file)

The simple practice process for steel floors is as follows:

– Determine the frequency and the specific oscillation mass. According to the software results.

Determine the Oscillation Frequency (f) from the ETABS software: in the Analysis Results/ Structure Output/ Modal informations/ Modal Periods and Frequencies table.

Specific oscillation mass (ms): in the Model Definition/ Other Definitions/ Mass Data/ Table: Mass Summary by Story. Take the UZ value (vertical oscillation component) as the oscillation mass of the floor corresponding to the floor under consideration.

Take the UZ value in the Analysis Results/ Structure Output/ Modal information/ Modal Participating Mass Ratios table, which is the mass coefficient participating in the oscillation of each oscillation mode (r).

Specific oscillation mass mm = ms.r

Determine the damping of the structural system (D)

In the example, the concrete-steel composite floor (D1=1%), the furniture is in the form of an open office (D2=1%), the finish has a suspended ceiling below (D3=1%) so D = D1+D2+D3 = 3%

Look up the chart to get the OS-RMS90 value according to the values ​​f (Eigen Frequency of the floor), mm (Modal mass of the floor). Use the chart corresponding to the value D.
This chart also helps to determine which vibration zone the floor structure belongs to: from A to F. The meaning of the chart: the lighter the floor (smaller mm) and the thinner (smaller stiffness, leading to small f) will belong to the zones with more vibration (towards the orange and red sides of the chart)

Vibration limit test
According to table 2 of the document. Depending on the function of the floor, it is a machine room, medical, school, house, office, meeting room, commercial, hotel, industrial, sports.

Each A-F zone of the floor determined in the above step will be comfortable (Recommended), acceptable (Critical), or uncomfortable (Not recommended, the feeling of vibration is obvious, causing insecurity for the user).

This method is simple in construction design. Should be used in quick assessment situations, basic design…

Actual design consulting situation

The office building project in Hai Ba Trung district, Hanoi uses steel Deck floor structure. After construction, it was found to be shaking according to the feelings of the majority of users. To handle the problem, the design consultant needs to find a location to reinforce to eliminate vibration.

Survey the status quo,

The most vibrating position that needs structural reinforcement is in the middle of the longest span floor as marked.

The solution is to hang the H-shaped steel column on the concrete ceiling above, the reason is because the large space requirement cannot support the column down. Connect the steel column through bolts drilled into the concrete and the bracket.
Calculation data from the structural diagram:

– Current diagram (attached file):

Mode 1 vibration pattern: f=4Hz, r=0.0822, ms=12.170kg => mm = 1.000kg. Look up the chart in zone F, which is an uncomfortable vibration area for office use. Consistent with the actual feeling.

– Additional column reinforcement diagram:

Mode 1 vibration pattern: f=28Hz, r=0.053, ms=12.200kg => mm = 650kg. Look up the chart in zone D, which is a comfortable vibration area for office use. Consistent with the actual feeling after construction, everyone no longer feels the vibration.

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(continued) 🎁The next section will present how to calculate and evaluate vibration according to the document SCI Publication P354: Design of Floors for Vibration: A New Aproach, 2009. In which, the nature of the response of floor beam structures to the agents causing vibration sensation is more clearly stated and detailed data can be calculated more convincingly.