Spectral response analysis results

The results of a spectral response analysis include normal deflections, forces, moments, stresses and reactions that can be displayed graphically, printed or used in a design in the same way that the results of a static analysis are used. In addition, spectral load cases and static load cases can be combined in combination load cases.

The output results also include a summary of the analysis input parameters and details of the governing mode shapes, total static forces, total masses and mass participation factors. The key output results are explained in more detail as follows:

Spectral curve multiplier

This factor depends on a number of code-specific factors related to the site location, structure importance, return period, ductility, etc. It is used to scale the accelerations from the spectral curve so that they are appropriate for the structure being analysed. For AS1170.4-2007 for example, the spectral curve multiplier (SCM) = KpZSp/m, where Kp is the probability factor, Z is the hazard design factor, Sp is the structural performance factor and m is the structural ductility factor. Other loading codes have similar factors.

Mass participation factors

A mass participation factor (MPF) represents what proportion of the mass contributes to the dynamic response of the structure for each mode and for each direction. The total MPF in a particular direction is simply the sum of the MPFs for all the modes being considered. The total MPF for each direction is a reliable indicator of the number of modes required in the spectral analysis. If all modes are considered then the sum of the MPF’s (the total MPF) will be 100%. In reality, we only consider a finite number of modes and the total MPF should be at least 90% for a good result. If the total MPF is less than 90% then more modes should be included in the analysis.

Usually, an earthquake is applied along the two horizontal axes, as defined by the direction vector. For example, an earthquake acting in the X direction would have a direction vector of Dx = 1.0, Dy = 0.0 and Dz = 0.0. In this case, the total MPF in the X direction should be greater than 90%.

A MPF that exceeds 100% indicates that the mode shapes from the dynamic frequency analysis are not accurate enough. If this happens, you should repeat the dynamic frequency analysis using a smaller tolerance.

The table in the output report showing the mass participation factors for each mode gives a good indication of the contribution of each mode to the overall dynamic response of the structure. From it you can quickly see which modes are dominant and which ones contribute very little.

Dominant mode

The dominant mode in each direction is the one with the largest MPF.

Total static force

The total static force for the two horizontal directions is calculated from the total mass multiplied by the acceleration obtained from the spectral curve. The period used to get the acceleration is usually the fundamental period of the structure (ie. the one with the largest translational period in the direction being considered). You can control this via the base shear scaling settings from which you can choose between: (a) the period from the dominant mode (ie. the one with the largest mass participation factor), (b) the period from a user specified mode or (c) a user defined period. If base shear scaling is turned off then the period from the dominant mode is used.

Base shear

The base shear is calculated by obtaining the sum of the reactions for each mode and then combining those sums using SRSS or CQC. This is done separately for each direction to give a base shear for each direction. The base shear is shown in the "Reac" line at the end of the normal reactions report. Note that it is rarely equal to the sum of the individual reactions in the reactions report due to the SRSS or CQC mode combination step.

Base shear % of SFce (static force)

This is the percentage of the base shear to the total static force after any base shear scaling has been performed.

Total mass

The total mass (including self mass if self weight is included in the mass load cases) applied to the model for each direction.

Base shear % of Mass

This is the percentage of the base shear to the total mass after any base shear scaling has been performed.

MPF for dominant mode

This is the mass participation factor for the dominant mode (ie. the highest MPF from all the modes being considered).

Total mass participation factor

The MPFs for each mode are summed to give the total mass participation factor.

Spectral accel (acceleration)

The spectral acceleration for each mode is obtained from the spectral curve and is based on the period of the mode. It is expressed in gravity units (g's) and is essentially equal to the acceleration from the spectral curve multiplied by the spectral curve multiplier.

Mode factor

The mode factor is calculated from La/w^2, where L is the excitation factor, a is the acceleration (obtained from the spectral curve and converted to length/sec^2 units) and w is the circular frequency of the mode. The actual deflections for each mode are obtained by multiplying the mode factor by the mass normalized mode shape.

Storey shear and storey drift

After the analysis, graphs of storey shear and storey drift can be obtained by right-clicking anywhere in the graphics area and then selecting "Storey Shear" or "Storey Drift" from the popup menu that appears.