**Advanced Dynamic Analysis And SPACE GASS**

The growing demand for advanced analysis of modern structures means that dynamic analysis solvers, such as those available in SPACE GASS, are becoming more of a requirement.

Four types of dynamic analysis in SPACE GASS that are commonly used by structural engineers include:

- Dynamic Frequency Analysis: Used to determine the natural frequencies of a structure and its modes of vibration.
- Spectral Response (Seismic) Analysis: Used to analyze the effect of a seismic event on a structure in accordance with a number of international seismic loading codes, including IS 1893 (Parts 1 to 4) and IS 16700.
- Harmonic Response Analysis: Used to analyze the effect on a structure of time or frequency dependent load sources that vibrate in a regular sinusoidal manner.
- Transient Response (Time-History) Analysis: Used to analyze the effect on a structure of time-dependent load sources that vary in any regular or arbitrary manner.

**Dynamic Frequency Analysis**

In order to perform a dynamic frequency analysis in SPACE GASS, the structure needs to be input, using the various graphical tools, datasheets or wizards (or a combination of them) together with any masses that affect its inertial properties. The masses usually consist of self-mass, which can be calculated automatically based on the element sizes and their mass densities, plus any extra masses, such as superimposed dead load that vibrate with the structure and affect its dynamic properties.

The SPACE GASS dynamic frequency analysis performs an eigen-analysis that calculates the structure’s natural frequencies (eigenvalues) and corresponding modes of vibration (eigenvectors) for any desired number of modes. Participation factors that indicate the proportion of the mass that contributes towards the solution for each mode are also calculated. A total mass participation factor of at least 90% in each direction indicates that enough modes have been included in the analysis.

**Spectral Response (Seismic) Analysis**

Spectral load cases for each of the two horizontal orthogonal structure directions are usually required for a seismic analysis. A spectral load case can also be defined for vertical shaking, if required. Each spectral load case references a mass load case, response spectrum (acceleration vs time curve), damping percentage and earthquake direction. Spectral load cases for different directions are usually required to be combined using all combinations of ±30% in one direction with ±100% in the other direction, and vice-versa.

Other seismic parameters that must be defined include - scaling of the horizontal base shear, zone factor (based on the structure’s location or its zone classification), damping multiplying factor, importance factor (based on the structure type and its importance), response reduction factor (based on the structure’s frame system), scaling factor (for P-delta effects), signing of the results and mode combination method (SRSS: Square Root of the Sum of Squares or CQC: Complete Quadratic Combination).

*SPACE GASS Dynamic Frequency Analysis - Suspended Slab*

*Mode = 6, Frequency = 5.526 Hz, Period = 0.181 sec*

*Mass Participation = 0.11% (X), 12.77% (Y), 0.09% (Z)*

The SPACE GASS spectral analysis calculates the displacements, forces, moments, stresses and reactions for each mode, in accordance with IS 1893 (or whichever seismic loading code has been specified). It then combines the results for each mode using SRSS or CQC, to form a complete set of results for each spectral load case. If base shear scaling is required, then the results are scaled up accordingly.

**Harmonic Response Analysis**

Typical harmonic load sources include vibrating machines such as crushers, pumps, or vibrating tables, footfall excitation caused by people walking, running or jumping, vehicular excitation caused by moving traffic, imbalance in rotating parts of a machine, etc.

Vibrating load sources can be applied to nodes or as base displacements, velocities or accelerations. Each load source can have its own magnitude, frequency and phase, plus load sources of different types and with different magnitudes, frequencies and phases can be combined. For example, the effect of a vibrating table operating at 40 Hz in one part of the structure can be combined with the effect of an out-of-balance machine operating at 30 Hz, in another part of the structure. Moreover, damping can be specified as Modal (using a constant damping ratio for each mode) or Rayleigh (using a combination of mass-proportional and stiffness-proportional damping).

The harmonic analysis in SPACE GASS can be run, using time or frequency sampling, with any specified number of steps and time or frequency range. Time sampling shows how the structure responds over a period of time, while frequency sampling shows how it responds to a range of frequencies and can be used to produce resonance curves.

**Transient Response (Time-History) Analysis**

Typical transient load sources include wind gusts, seismic events, vibrating machines, blast loads, pulse loads, footfall excitation, moving traffic, etc.

A transient response analysis is similar to a harmonic response analysis in many ways, except that transient loads can vary in any arbitrary manner. For example, a wind gust that rises and falls or a blast load that builds very quickly and then dissipates, or a pulse load that follows a non-sinusoidal but repeatable pattern can all be modelled with a transient analysis.

A transient time-history analysis can also be used to model a seismic event in accordance with IS 1893 (Part 1) : 2016 section 7.7.4, provided that acceptable ground motion data is available for the location of the structure being analyzed.

User-defined factor versus time tables are used to define the time-dependent nature of the transient load sources. These can be defined manually or imported from other programs such as MS Excel.

*SPACE GASS Resonance Curve - Bridge Gantry*

*Peak vertical displacement = 2.94 mm at 4.44 Hz on node 41*

**Dynamic Analysis Results**

After a dynamic frequency, harmonic or transient analysis, the model can be animated to show the modes of vibration, or show how it responds in real-time to the harmonic or transient load sources. This can be done in wireframe or fully rendered modes.

Graphs of displacements, velocities, accelerations and phases versus time or frequency can also be generated from a harmonic or transient analysis for any parts of the structure.

The results of the spectral, harmonic and transient analysis modules can be combined with each other or combined with the results of a static analysis. They can also be used with any of the steel or concrete design modules in SPACE GASS or displayed graphically as displacements, bending moment diagrams, shear force diagrams, axial force diagrams, stress diagrams or reactions.

**For more information,visit: www.spacegass.com**

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