Dynamic Response Simulator

Analyze structural response to dynamic loads such as earthquakes or wind. Professional structural engineering tool with real-time calculations and visualization.

Dynamic Response Analysis

The equation of motion for a single-degree-of-freedom system is:

\[m\ddot{u} + c\dot{u} + ku = p(t)\]

Where m is mass, c is damping coefficient, k is stiffness, u is displacement, and p(t) is the dynamic load. For seismic analysis:

\[p(t) = -m\ddot{u}_g(t)\]

Response spectrum analysis uses:

\[S_d = \frac{S_a}{\omega^2}, \quad S_v = \frac{S_a}{\omega}\]
  • Mass (m): Distributed mass of the structure
  • Stiffness (k): Resistance to deformation
  • Damping (c): Energy dissipation mechanism
  • Period (T): Time for one complete cycle

Dynamic Analysis Parameters

Natural Period

0.8 s

Max Displacement

0.45 in

Base Shear

185 kips

Drift Ratio

0.23%

Dynamic Response Analysis

Response Parameters
Displacement History
Peak Response
Vibration Period

Analysis Results

Parameter Value Unit Status

Analysis & Recommendations

Enter dynamic analysis parameters and click "Analyze Response" to see results.

  • Verify dynamic properties match structural system
  • Consider higher mode effects for flexible structures
  • Check local building codes for specific requirements
  • Perform detailed analysis if drift exceeds limits

Q&A

Q: What is the difference between static and dynamic analysis?

A: Static and dynamic analysis differ fundamentally in how they model structural behavior:

Static Analysis:

  • Assumes loads are applied slowly and gradually
  • Inertia and damping effects are neglected
  • Equation: Ku = P (equilibrium only)
  • Appropriate for dead loads, live loads, and slowly applied loads
  • Results in steady-state displacements and forces

Dynamic Analysis:

  • Accounts for inertia and damping effects
  • Considers time-varying loads and structural response
  • Equation: mü + ců + ku = p(t) (motion equation)
  • Required for earthquake, wind, blast, and impact loads
  • Results in time-dependent responses with peaks and valleys

When to Use Each:

  • Static: Permanent loads, gravity loads, slowly applied loads
  • Dynamic: Seismic events, wind gusts, machinery vibrations, impact loads

Dynamic analysis is more complex but necessary for time-dependent loads.

Q: How do I determine the natural period of a structure?

A: The natural period is fundamental to dynamic analysis and can be determined in several ways:

Theoretical Calculation:

  • Single Degree of Freedom: T = 2π√(m/k) or T = 2π√(δ/g)
  • Approximate for Buildings: T = Ct * hn^(3/4) (ASCE 7 method)
  • Where: Ct = 0.02 for steel frames, 0.016 for concrete frames
  • hn: Height of the building in feet

Numerical Methods:

  • Modal Analysis: Solving eigenvalue problem [K - ω²M]φ = 0
  • Finite Element Analysis: Most accurate for complex structures
  • Computer Software: SAP2000, ETABS, STAAD.Pro

Field Testing:

  • Ambient Vibration Testing: Measure response to environmental excitations
  • Forced Vibration Testing: Apply known forces and measure response
  • Microtremor Surveys: Measure soil-structure interaction

For preliminary design, the approximate methods provide reasonable estimates, but final designs should use detailed analysis.

About

Structural Engineering Team
This dynamic response simulator was created with an Calculators and may make errors. Consider checking important information. Updated: April 2026.