Introduction to Dynamic Analysis in Structural Engineering

Modern structures are rarely static. They must withstand time-varying forces from wind, earthquakes, machinery, traffic, and human activity. Dynamic analysis is the branch of structural engineering that studies how structures respond to such loads, focusing on vibrations and oscillations. RISA (Rapid Interactive Structural Analysis) offers a comprehensive suite of dynamic analysis tools that enable engineers to predict and mitigate these effects. This article explores the core capabilities of RISA for vibration and oscillation analysis, explains the theory behind each method, and provides practical guidance for applying these tools in real-world projects.

Core Dynamic Analysis Features in RISA

RISA's dynamic modules are built on the same finite element engine as its static analysis tools, ensuring consistency in modeling and results. The three primary analysis types—modal, response spectrum, and time history—are integrated into RISA-3D, RISAFloor, and RISAFoundation. Each serves a different purpose but together form a complete dynamic design workflow.

  • Modal Analysis: Determines natural frequencies and mode shapes.
  • Response Spectrum Analysis (RSA): Estimates peak responses from earthquake spectra without a full time-history.
  • Time History Analysis (THA): Computes actual structural response over time to recorded or synthetic input motions.

Additionally, RISA supports moving load analysis for bridge and crane loads, and harmonic (steady-state) analysis for rotating machinery vibrations. These tools share a common interface for defining masses, stiffnesses, and damping.

Natural Frequencies and Mode Shapes

Every structure has inherent vibration characteristics – its natural frequencies and the corresponding deformed shapes (mode shapes). When a dynamic load’s frequency matches a natural frequency, resonance occurs, potentially amplifying displacements and stresses many times over. RISA’s modal analysis solves the eigenvalue problem (K – ω²M)φ = 0 to extract these frequencies and modes.

Engineers use this information to:

  • Identify potential resonance with known excitation frequencies (e.g., 1–10 Hz for wind, 0.5–5 Hz for earthquakes).
  • Calculate modal participation factors to determine which modes contribute most to response in a given direction.
  • Design vibration serviceability for floors, footbridges, and stadiums to avoid discomfort from human-induced oscillations.

RISA allows users to specify the number of modes to extract (typically covering 90–95% of the effective mass) and displays mode shapes graphically with animation. This visual feedback is invaluable for identifying weaknesses such as soft stories or torsional irregularities.

Mass Modeling for Accurate Modal Results

The quality of modal analysis depends on correct mass distribution. RISA provides options for self-weight mass, added dead loads, live load mass (with reduction factors per ASCE 7), and point masses from equipment. Engineers can also define seismic mass as the total dead load plus a percentage of live load. RISA automatically lumps mass at nodes, but users can refine the mesh in areas of high mass concentration.

For structures with significant diaphragm flexibility, RISA can model semi-rigid diaphragms that affect mode shapes. The software supports mass eccentricity to account for accidental torsion in seismic design.

Response Spectrum Analysis: Seismic Design Workhorse

How RISA Implements RSA

Response Spectrum Analysis (RSA) is the most common method for earthquake-resistant design of building structures. Instead of running a full time-history, RSA uses a design spectrum (e.g., from ASCE 7, IBC, Eurocode 8) that gives the maximum acceleration, velocity, or displacement for a range of periods. RISA applies the spectrum to each mode and combines the contributions using the Square Root of the Sum of Squares (SRSS) or Complete Quadratic Combination (CQC) methods. The CQC method is recommended when modes are closely spaced (natural frequencies within 10% of each other).

The software outputs:

  • Maximum base shear, story shears, overturning moments.
  • Peak member forces, displacements, and drifts for each load direction.
  • Accidental torsion effects when mass eccentricity is specified.

RISA handles multi-directional excitation (e.g., 100% in X + 30% in Y per orthogonal combination rules) and automatically generates load combinations for strength design according to the selected code.

Practical Considerations for RSA

RSA is efficient but has limitations. It provides peak values without phasing information, so it cannot capture the exact time sequence of yielding or cumulative damage. Engineers must still check ductility and detailing requirements per code. RISA allows users to define multiple response spectra (e.g., for different soil sites or risk categories) and to scale the spectrum to match a target base shear if the computed base shear is less than the code minimum (typically 85% of the empirical base shear).

For tall or irregular buildings, RISA supports modal response spectrum analysis with rigid modes to account for high-frequency contributions that are not amplified by the spectrum. The software also includes options for vertical seismic effects on cantilevers and long-span beams.

Time History Analysis: Capturing Real-Time Behavior

Linear vs. Nonlinear Time History

Time History Analysis (THA) is the most detailed dynamic analysis, simulating the structural response at every time step for a given acceleration record. RISA offers two types:

  • Linear THA: Assumes the structure remains elastic. Useful for base-isolated buildings or for verifying RSA results. RISA can process long-duration records efficiently through its direct integration solver (Newmark-β method).
  • Nonlinear THA: Accounts for material yielding, geometric nonlinearity (P-Delta), and connection nonlinearity. This is essential for performance-based design where energy dissipation through inelastic behavior is explicit.

Nonlinear THA in RISA utilizes plastic hinges defined on frame elements and nonlinear springs for isolators and dampers. Users can specify hinge properties from ASCE 41 (backbone curves) or from section analysis results. The software outputs quantities like ductility demands, cumulative plastic rotations, and residual drifts.

Selecting and Scaling Ground Motions

One of the most critical steps in THA is selecting appropriate ground motion records. RISA supports importing acceleration time histories in common formats (e.g., SMF, PEER NGA, simple ASCII). Engineers should select at least three to seven records for design. When fewer than seven records are used, the maximum response governs; with seven or more, the average response can be used (per ASCE 7).

RISA automates the scaling process: users can target a spectrum and scale motions in the time domain (amplitude scaling) or frequency domain (spectral matching). The software can also generate artificial accelerograms using user-defined response spectra.

Post-Processing Time History Results

After running THA, RISA provides extensive output:

  • Time plots of displacement, velocity, acceleration at any node.
  • Hysteresis loops for nonlinear elements to visualize energy dissipation.
  • Envelope values (max/min) for forces, moments, and drifts across all time steps.
  • Animations of the deformed shape over time – ideal for client presentations and peer review.

The ability to export time-history data to Excel or MATLAB for further spectral analysis is a significant advantage for researchers and advanced practitioners.

Damping in RISA Dynamic Analysis

Accurate damping modeling is essential for realistic dynamic results. RISA supports several damping options:

  • Modal (Rayleigh) Damping: Expressed as αM + βK. Users enter two damping ratios at two frequencies (typically 1% and 5% critical for steel and concrete, respectively). RISA computes the coefficients automatically.
  • Constant Modal Damping: Assigns the same damping ratio to all modes (e.g., 5% for seismic).
  • Hysteretic Damping from Hinges: In nonlinear THA, damping is inherent through plastic deformation. RISA additionally allows defining viscous dampers (fluid, friction, or viscoelastic) as nonlinear link elements with force-velocity relationships.

The software also permits frequency-dependent damping for systems with damping materials like viscoelastic layers in composite beams. Proper damping specification can reduce resonance amplitudes by 50–80%, making structures both safer and more economical.

Application to Specific Vibration Problems

Floor Vibrations Due to Human Activity

Annoying floor vibrations in offices, gyms, and auditoriums are a common serviceability issue. RISA’s modal analysis can compute floor natural frequencies and mode shapes. To evaluate comfort, engineers typically compare the peak acceleration against criteria from AISC Design Guide 11 or SCI P354. RISA supports impulse loading from a heel drop and can compute peak acceleration using the modal mass and participation factor. By adjusting beam depths, slab thicknesses, or adding damping, the software helps optimize designs to meet stringent vibration criteria.

Wind-Induced Oscillations of Tall Buildings

For tall and flexible structures, wind-induced vibrations (buffeting, vortex shedding) can govern strength and occupant comfort. RISA can import wind time-histories from wind tunnel data or from code-based gust effect factors. The dynamic response to wind is then analyzed via linear THA or simplified as a gust response factor per ASCE 7. RISA’s mass and stiffness modeling, combined with its modal output, allows engineers to check acceleration serviceability limits (e.g., 10–15 milli-g for office buildings). Tuned mass dampers can be modeled as spring-mass systems connected to the structure.

Machinery and Equipment Foundations

Rotating and reciprocating machinery impart harmonic forces at the operating speed. RISA’s harmonic (steady-state) analysis computes the steady-state response at the forcing frequency. Engineers can design foundation blocks to avoid resonance and limit displacement amplitudes to values recommended by manufacturers (e.g., 0.001 in/s peak velocity). RISA also models impact loads from presses and crushers as impulse time histories.

Verification and Validation of Dynamic Results

Any dynamic analysis software must be validated. RISA provides benchmarks for common structures (e.g., simple cantilever, multi-story frame) that can be compared to closed-form solutions. Engineers should always check:

  • That the total effective modal mass approaches the total mass (typically 90% per code).
  • That the fundamental period matches approximate methods (e.g., ASCE 7 equation for masonry/steel frames).
  • That the base shear from RSA is not less than 85% of the empirical base shear.
  • That nonlinear THA results are stable with respect to time step size (e.g., Δt ≤ 1/10 of the highest mode period).

RISA includes a dynamic check wizard that flags common errors like insufficient modes, unrealistic damping, or missing mass.

External Resources for Deeper Learning

To master RISA’s dynamic analysis capabilities, consider these external references:

  1. RISA-3D Official Dynamic Analysis Documentation – Provides technical details and example models.
  2. ASCE Seismic Design Resources – Covers the design spectra and combination rules used in RISA.
  3. PEER Ground Motion Database – Source for downloading and scaling acceleration records for THA.
  4. AISC Design Guide 11: Floor Vibrations – Guidance for serviceability assessment using modal analysis.
  5. ScienceDirect Structural Dynamics Overview – Theoretical background.

Conclusion: Integrating RISA into Practice

RISA’s dynamic analysis capabilities are not just theoretical – they are essential tools for designing safe, serviceable, and economical structures. From modal analysis that reveals a building’s natural tendencies, through response spectrum methods that drive code-compliant seismic design, to full nonlinear time history analysis for performance-based applications, RISA empowers engineers to address vibrations and oscillations with confidence. By properly modeling mass, damping, and loading, and by validating against code requirements, engineers can reduce construction costs, improve occupant comfort, and ensure resilience against earthquakes and wind. Whether you are a student learning the fundamentals or a seasoned practitioner handling complex projects, RISA provides the precision and flexibility needed to master dynamic design.