# DYNAMIC ANALYSIS 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.

## MODULES

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
• 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

# CHARACTERISTICS

• 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

# DETAILS

## THE PARAMETERS OF DYNAMIC ANALYSIS

In the dynamic analysis, a static and a dynamic load case can be considered. The results are stored at every time step, or at specified time steps. In addition, the correction of the load function and interpolation method, as well as the nonlinearity and convergence criteria, can be set.

## RUN-TIME MONITORING

The movement (displacement, velocity, acceleration) about a nodal degree of freedom can be monitored during analysis, which can reveal certain structural behavior during the 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.

## THE CORRECTION OF EARTHQUAKE ACCELEROGRAMS

The real (recorded) accelerograms can be modified. Due to measurement error, the recorded acceleration data does not result in zero end speed. The applied algorithm modifies the original acceleration in order to obtain zero end velocity and displacement.

## DAMPING

The structural damping is taken into account using proportional, Rayleigh-damping. Nodal damping can be taken into account with spring and dashpot elements. Bilinear characteristic can be considered according to the Maxwell or Kelvin model.

## PRESENTATION OF THE RESULTS

The computed kinematic results (displacements, velocities, accelerations) and internal forces and moments can be presented (plotted) as a function of time or as a function of any other time-dependent result.

## ANIMATION

Animations can be displayed for time-dependent changes of any result component and can be saved as a GIF or AVI file type. The speed of replay can be adjusted and arbitrary subdomains can be chosen for the animation.

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)

# CHARACTERISTICS

• 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

# DETAILS

## PARAMETERS OF FOOTFALL ANALYSIS

The analysis can be adjusted with different parameters, depending on the nature of the problem. The user can select the modes, type of excitation, damping ratio, and the footfall parameters.

## VIBRATION TYPES

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:

• CCIP-016
• SCI P354

## "R" RESPONSE FACTOR RESULT COMPONENT

The vibration response factor result shows the envelope function of the response factor due to human induced vibration. The response factor is proportional to the maximum of the structural acceleration, thus the user can find the location and value of the largest acceleration.

## NODAL RESULTS

Once the results are available, the user can obtain the response factor, the location of the critical excitation (index of the node) and the critical frequency for each node.