Dynamic modeling in structural analysis has become increasingly relevant as standards have become more and more rigorous in the subject. Furthermore, the extensive use of economical, lightweight buildings requires increasingly accurate dynamical analysis. These topics are addressed by the dynamic and footfall modules in AXISVM.
In the case of dynamic analysis, the program determines the displacements and internal forces of the structure for each time step, corresponding to the defined dynamic loads. The analysis can be carried out by considering linear or nonlinear material behavior. Geometric nonlinearity can also be considered.
The following dynamic actions can be applied:
- dynamic point load acting on a node, domain, or load panel
- distributed surface load on a domain or load panel
- node or nodal support acceleration
With these dynamic loads, the DYN module is able to conduct time-history analysis (e.g. earthquake), shock wave analysis (e.g. blast), and forced vibration analysis (e.g. machinery).
Requirements / recommendations
- in order to perform nonlinear dynamic analysis, the nonlinear (NL) basic package is needed
The DYN module is independent from design codes/standards.
- the time integration is carried out by the Newmark-beta implicit numerical method
- geometric and material nonlinearity can be taken into account
- the dynamic load functions can be defined by either numerical data at sampling points, or by analytical functions
- the intermediate points of the load function can be determined with linear or Whittaker-Shannon interpolation
- the accelerograms can be corrected in order to obtain zero end speed and displacement
- the internal forces can be used in standardized design procedures, with caution
THE PARAMETERS OF DYNAMIC ANALYSIS
THE INTERPOLATION OF LOAD FUNCTIONS
If the sampling points of the load function are not coinciding with the time steps, the program interpolates the function value at a given instance of time with linear interpolation or with the Whittaker-Shannon formula. The latter can approximate a continuous function, which is better discretised with uniform time steps.
Nowadays, the cost-efficiency and ease of assembly of buildings and bridges have become more important. A possible consequence of this is a considerable decrease in structural weight. However, the dynamic effect of moving masses is typically larger on lightweight buildings. As a result, the buildings’ serviceability can be significantly restricted, due to disconcertingly large accelerations. In order to restrain the large accelerations, it is inevitable to control the vibrational serviceability limit state, for which the footfall analysis is a modern approach. A corresponding procedure has been implemented into the AxisVM software.
Further information: Footfall Analysis Guide >>
Requirements / recommendations
- a basic package with surface elements is required (e.g. L3S, NL3P)
The FFA module is independent from design codes/standards.
- the following two recommendations are built into the software:
- Willford, M.R., Young, P. A Design Guide for Footfall Induced Vibration of Structures, Concrete Society, 2006
- Smith, A. L., Hicks, S. J., Devine, P. J. Design of Floors for Vibration: A New Approach, The Steel Construction Institute, Ascot, 2009
- the analysis can only be performed on floors (the angle between the domain’s normal vector and the direction of gravitation is less than 10°), and stairs (the angle between the domain’s normal vector and the vertical direction is between 10°-70°)
- only linearly elastic structures can be considered
- before the calculation, a vibration analysis must be performed
- the footfall load excites only the nodes of surface elements; the nodes of line elements are not considered in the procedure
- the method does not consider the horizontal component of the footfall load, which can have significant effect on the vibration of bridges. Therefore, the process is only capable of handling the vibration of buildings’ floors and stairs
In the case of footfall induced vibrations, the response of the system consists of two parts, namely: the transient part and the steady-state part. Fundamentally, the characteristic shape of the vibration can be one of these two types. For the most part, the stiffness of the structure and the duration of the excitation determine which type of vibration is dominant.
The user can choose between these two recommendations:
- SCI P354