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icon. Once done, the various options will be come active. The layout of the screen with a vibration case added is shown below.
The vibration design area allows for the response factor analysis of a structure under human induced (footfall) vibration. The response factor design can be carried out in accordance with either:
SCI P354, "Design of Floor for Vibration: A New Approach"
CCIP-016, The Concrete Centre, "A Design Guide for Footfall Induce Vibration of Structures"
The response factor differ in it's approach to human induced vibration from the older rule-of-thumb guidance which involved checks on the deflection of the beam to estimate the natural frequency of individual components of the floor structure. The response factor approach uses the acceleration of the structure under a forcing function which approximates the effect of footfall on a structure and then compares the resulting accelerations against a baseline value. The underlying philosophy is that human perception of vibration is not determined by the frequency of the vibration, but rather by the accelerations. The response factor is given by:
Response Factor = calculated acceleration / baseline acceleration.
A number of factors influence the perception of vibration. These include the activity being undertaken, the level of background noise, the time of day, the period of time a person is exposed to vibration and the source of the vibration. Both the SCI and CC approaches provide a number of mechanisms to attempt to quantify these factors and allow for them in the calculation of the response factor.
Depending upon the nature of the structure, the response of the structure to human induced footfall vibration is classified as either being steady-state or transient. In the steady state response, the amplitude of the vibration is taken to be constant, whereas the transient case has a rapid decrease in the amplitude of each impulsive force of footfall and so the vibration is treated as a series of impulsive forces.
The response factor analysis is carried out on the basis of a single person footfall. The is due to the fact that for higher floor occupation level, the human body tends to act as a damper. Hence the critical response comes from an unoccupied structure. Since the analysis is therefore dealing with a single idealised footfall under serviceability conditions, the resulting magnitude of the deflections of the structure are small. As a result, certain model modifications may be justified, such as taking simple connections in steel beams to be fixed connections (since the rotations under a single footfall are unlikely to overcome the internal friction of the connection). For further guidance on modelling a structure for a response factor analysis, reference should be made to either SCI P354 or the Concrete Centre publication.
In common with the other analysis methods in the dynamic and seismic modules, the first step of the process is to obtain the mode shapes and corresponding natural frequencies for the structure or part of the structure to be analysed. For further information on the Modal Analysis, refer to the Natural Frequencies section of this manual.
In the response factor analysis, frequencies up to the 4th harmonic of the walking frequency are considered important. However since the transient response is critical over 10 Hz, it is recommended that sufficient higher mode shapes are captured. As such, the recommended range of frequencies for a modal analysis would be to include all frequencies in a range from 0 Hz up to 3 to 4 times the 4th harmonic of walking. This gives a suggest modal analysis range from 0 Hz up to 30-40 Hz.
On first entering the Vibration Design area, the options will be greyed out. To add a vibration design, click on the icon. Once done, the various options will be come active. The layout of the screen with a vibration case added is shown below.
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Additional vibration cases can be added by clicking on the icon. However, each analysis has to run for each created vibration case, so adding large umbers of vibration cases should only be done where necessary, since it the number of analysis cases will impact on the analysis time required.
To delete any vibration cases, select the case from the drop down and click on the .png){kind=small}
icon.
Once a vibration case is created, the response factor design approach is selected using the radio buttons. It is possible to have vibration cases which use different approaches. Each approach requires input to determine various design parameters and design options. These are outlined below.
With the SCI P354 Approach option selected, the design parameters reflect those used within the SCI P354 document. The layout of the bottom pane is shown below.
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The SCI P354 specific inputs are as follows:
Weighting factor
The weighting factor is a multiplier on the calculated response factor which aims to take account of the use of the structure. In general the aim of vibration design is to reduce or remove the discomfort of users due to vibration, but in certain cases, it is necessary to reduce the vibration to such a level that it cannot be perceived, or that it does not affect the steadiness of hands or of vision. An example, would be an operating theatre, where the reduction of vibration to levels low enough not to affect hand steadiness or vision is essential. For further information, refer to SCI P354.
Steady State/Transient
The choice of steady state or transient analysis types is selected using the steady state/transient drop down option. For the transient analysis, which analyses the structure under a series of heel strikes, the computation of the response factor is carried out over a time period, which is split into time steps or intervals. SCI advisory note AD 405 recommend that the time period T is taken to be T + 1 / fp such that T is the time taken between steps. However, Section 2.4.1 of SCI P354 suggests taking T = 1 sec.
Forcing function
SCI P354 provides 5 different forcing functions to model 5 different types of activity and activity levels in the Steady State analysis. These are outlined in SCI p354 and include walking (for floor plate analysis), staircases, low and high impact aerobics and jumping. Each forcing function utilises a different Fourier series.
The Transient analysis has only one associated Fourier series.
Frequency range and time steps
Since the frequency of walking will vary from person to person, the response factor is calculated across a range of frequencies. The range used in the calculation is defined in the f1 and f2 input values. The calculations is then carried out at intervals between these two values. The interval is determined by the Steps input value, which determines the number of intervals the frequency range is divided into. The terms Steps here is not related to footsteps.
The frequency range relates to the 1st harmonic of the activity. Subsequent harmonics are determined automatically by the software. For guidance on the range input, refer to tables 3.1 and 3.2 of SCI P354.
Vibration Dose Values
SCI P354 provides an additional analysis option which aims to take into account the frequency of the event causing vibration. The idea is that where the calculated response factors are higher than required, but the frequency of the event causing the vibration is low, account can be taken of this in the analysis. In effect, a VDV allows for a higher response factor but only for short periods of time.
When using the Vibration Dose Values, the required inputs are the duration of the activity causing vibration, Ta, input in seconds, and the number of occurrences which occur during an exposure period. BS 6472 recommends that the exposure periods are taken as a 16 hour day or an 8 hour night.
Vibration dose values can be considered in both the steady state and transient analyses.
Resonance Build-up factor
The steady state analysis assumes that the vibration of the structure has reached a state of constant amplitude. However, this ignores the fact that the vibration will need to build up until is reaches the steady state. Therefore, for vibrations which occur over a short time period, the structure may not have attained it's peak amplitude and accelerations. The aim of the resonance built up factor is account for the build up period needed to attain a steady state response.
The required inputs are the path length, that is, the length over which a person is walking, along with the walking velocity. These values are then used to asses the time period over which the excitation takes place.
The resonance build up factor is not relevant to the transient analysis.
Align Torso
The human body is not equally sensitive to vibration in all axes. In particular, vibrations causing motions which align with the long axis of the body tend to be perceived less so than motions in the other directions. The Align torso allows the alignment of the body long axis to be defined relative to the global axes. This alignment is used to adjust the base acceleration values for human perception, as well as selecting the weighting values, if selected.
The torso alignment is valid in both the steady state and transient analysis methods in SCI P354.
With the Concrete Society Approach selected, the design parameters reflect those used within the CCIP-016 document. The layout of the bottom pane is shown below.
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The inputs are similar to those used in SCP P354. However, no weighting factor is used in CCIP-016. In CCIP-016, the analysis method does not include settings for weighting factors, torso alignment or vibration does values, hence these options are greyed out when using the Concrete Society approach. The CCIP-016 method does include a correction factor, similar to the resonance built up factor in SCI P354.
For the Steady State analysis, the Fourier Coefficient and phase can be checked using the .png){kind=small}
selector. Changing this will display the Fourier coefficient of the selected harmonic, along with the phase angle measured in radians. These are displayed for information purposes only, since the analysis checks the structure for each harmonic required by the selected forcing function.
With a transient analysis, the display will show the Transient times in place of the harmonic information.
The set-up for the analysis is common to steady state and transient analysis, in both of SCI P354 and CCIP-016. The options in this area are outlined below.
Single versus Multiple nodes
The response factor can be calculated for either a single node or a selection of nodes. With a single node selected, the forcing function is applied to a single node in the model. The response can then be measured at either the same node, or at another specific node in the model. A multiple node analysis will apply the forcing function to each selected node in turn and then calculate the response factor at each selected response node. This necessarily means that the multiple node option requires more calculation than for a single node. For each selected response node, the highest response factor will be returned as the analysis result.
In single node analysis mode, to select a node, click on the Loaded Node area and then select the required node number by either clicking on the node in the graphics display or by typing in the node number. For multiple nodes, the click on the .png){kind=small}
icon. This will open an new pop up window. Nodes are selected by clicking on them in the graphics pane. Nodes can be selected or de-selected individually by clicking on them, or, alternatively, multiple nodes can be selected by windowing around the desired nodes. The selected nodes will highlight in red on the model and the node numbers will appear in the Node List pop-up window. If Node Groups have been created, these can be selected from the drop down list to quickly select the nodes in a particular node group.
When the single node option is selected, the results area will display a graph indicating the response at the Response node across the range of frequencies. This can be useful for examining the results when the critical node for vibration design has been identified from using the multi-node option.
Response node = Dynamically Load node
The response factor results are compiled using two sets of nodes; the nodes that the dynamic forcing function is applied to and the nodes where the response is measured at. If the Response node = Dynamically loaded node option is not selected, this means that for each node in the set of loaded nodes, the response has to be measured at all the nodes in the response node set. For example, if the loaded nodes consists of 50 nodes and the response nodes set contains 100 nodes, the software will have to carry out 5000 calculations.
In general, the node with the largest response factor will be the load being dynamically loaded. Therefore, for looking at the results over a large area, involving, therefore, a large number of nodes, setting the Response node = Dynamically loaded node will reduce the amount of calculations required and, hence the time required, since this option only measures the response factor at each loaded node.
In certain circumstances, where vibrations are to be measured in an area that is not subjected to the dynamic loaded node, then the Response nodes = dynamically loaded node should not be used, since the dynamic forcing function is to be applied to one set of nodes while the response is measured at another distinct set of nodes. An example of where this could occur would be in a hospital operating theatre, where footfall in the corridor outside the theatre should be set up significant vibrations in the operating theatre.
Mode selection
The mode selection option allows a suer defined set of mode shapes to be used for the analysis. This can be used to reduce the analysis time. However, care is needed to ensure that sufficient relevant mode shapes are included. This requires an inspection of the mode shapes to identify those which are likely to contribute to the vertical motions of the structure.
The default option is to use all the mode shapes identified in the modal analysis. Given the difficulty of identifying only the relevant modes, this option is the recommended approach.
Once the analysis has been set up, the analysis is run by clicking on the .png)
Single node results
For a single node analysis, the results will be displayed for the single response node. The results will report the peak acceleration, the response factor and, if selected, the vibration does values, for the range of frequencies representing the walking frequency, over the number of input calculation steps. The results will also produce a graph summarising the results over this range. The results shown in the graph are selected using the radio buttons. A typical results screen is shown below, indicating the response factor for node 2575, which is both the loaded and response node.
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Multiple Node results
Where multiple nodes are selected, the results are displayed in the results pane for each node, giving the maximum RMS acceleration, response factor, vibration dose values along with the frequency the loaded node which results in the highest values at the response node. The response factor is also indicated graphically in the graphics pane. The layout of a typical multiple node analysis is shown below.
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Vibration Design of Steel Stairs (technical note)
Stairs differ from floorplates in some key design aspects which can have a significant effect on their design for vibration. For further details see the following technical note Vibration Design of Steel Stairs.