Single/Multi-Story Benchtop Structural Shear Frame Model
Rigid aluminum floor plates supported by high-yield spring steel column strips.
Civil Engineering / Shear Frame Free Vibration
FREE TO EXPLORELABORATORY 47 · CIVIL ENGINEERING
Natural Frequency & Viscous Damping Ratio of Multi-Story Shear Frame Structures (Free Vibration)
Investigate dynamic characteristics of single- and multi-story building shear frames subjected to initial displacement release, determine fundamental natural frequency (f_n) and logarithmic decrement damping ratio (ζ) using accelerometers. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.
STRUCTURAL MATERIALS · MECHANICS · GEOTECHNICAL · HYDRAULICS · HIGHWAYS · SURVEYING
Your virtual civil engineering laboratory.
NATURAL CIRCULAR FREQUENCY SQUARED Ω_N²—
CIVIL INFRASTRUCTURE TELEMETRY
Ready to sample with Floor Mass m = 6.0 kg.
Adjust Floor Mass m, then execute civil engineering measurement.
Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.
Civil engineering assumptions and boundary condition limits
The civil engineering physical models apply within the specified calibrated operational window (2.0 to 12.0 kg). Evaluated on a precision benchtop aluminum building shear frame. Inverse-mass formulation correlates natural frequency squared ω_n² directly to 1/m with lateral stiffness slope k = 1850.0000 N/m.
Laboratory apparatus & testing equipment.
High-Precision Piezoelectric Triaxial Accelerometers
Low-mass ICP accelerometers (sensitivity 100 mV/g) mounted at floor level.
Multi-Channel Dynamic FFT Signal Analyzer & DAQ
High-speed USB data acquisition system capturing time-history ring-down signals at 1 kHz.
Calibrated Stackable Floor Surcharge Masses
Machined brass weights (1.0 kg increments) bolted symmetrically to floor plates.
Quick-Release Mechanical Initial Displacement Trigger
Solenoid catch releasing frame smoothly from initial displacement without imparting initial velocity.
Laser Displacement Optical Sensor
Non-contact triangulation sensor recording floor drift to 0.01 mm precision.
FOLLOW THE METHOD
A reason behind every step.
Investigate dynamic characteristics of single- and multi-story building shear frames subjected to initial displacement release, determine fundamental natural frequency (f_n) and logarithmic decrement damping ratio (ζ) using accelerometers. Standardized parameter settings: 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 kg.
01
Shear Frame Assembly & Column Alignment
Mount spring steel columns into heavy clamping base; bolt rigid aluminum floor plate at top (L = 400 mm); verify column verticality and symmetry.
02
Accelerometer Mounting & Sensor Zeroing
Mount piezoelectric accelerometer on floor plate along lateral motion axis; connect to DAQ interface; zero baseline noise.
03
Initial Floor Mass Configuration
Bolt calibrated surcharge masses to floor plate to establish target mass m (2.0 kg); verify mass on digital scale.
04
Initial Displacement & Free Release Triggering
Displace top floor plate laterally by exactly 10.0 mm using manual screw; engage quick-release trigger; release frame into free vibration.
05
Time-History Acquisition & FFT Processing
Record decaying acceleration time-history; identify successive peak amplitudes x_1, x_2, ..., x_n; execute Fast Fourier Transform (FFT) to extract peak natural frequency f_n (Hz); compute ω_n = 2π·f_n.
06
Mass Escalation & Damping Computation
Increment floor mass across six systematic levels (2.0, 4.0, 6.0, 8.0, 10.0, and 12.0 kg); plot ω_n² versus 1/m to calculate stiffness k; compute logarithmic decrement δ and damping ratio ζ.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into civil engineering insight.
Points are your recorded observations. The solid regression line validates Shear Frame Free Vibration mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
ω_n² = 1850.0000 / m
| # | Total Structural Floor Mass m (kg) | Natural Circular Frequency Squared ω_n² (rad²/s²) | Inverse of floor mass 1/m (kg⁻¹) | Natural circular frequency squared ω_n² (rad²/s²) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the civil engineering metrics mean.
The theoretical undamped natural circular frequency of a single-degree-of-freedom structure is:
If the lateral stiffness of a shear building frame is quadrupled while keeping mass constant, its natural frequency will:
The damping ratio ζ for welded structural steel building frames during elastic vibration is typically:
In a free vibration decay record, the ratio of successive displacement peaks is measured as x_1 / x_2 = 1.20. The logarithmic decrement δ is:
THEORY AND STRUCTURAL CONTEXT
Civil engineering background & physical principles.
In structural civil engineering, earthquake engineering, and wind engineering, all buildings, bridges, and infrastructure towers undergo dynamic oscillations when excited by transient seismic ground motions, hurricane gusts, or mechanical machinery. The fundamental dynamic parameter governing structural response is the fundamental natural circular frequency ω_n = √(k / m), where k is the lateral structural stiffness (N/m) and m is the effective floor mass (kg). For an idealized single-degree-of-freedom (SDOF) shear frame—composed of rigid floor slabs supported by flexible vertical column cantilevers—the lateral stiffness provided by two parallel fixed-guided elastic columns of height L and flexural rigidity EI is k = 2 · (12EI / L³). When released from an initial lateral displacement x_0, the structure executes free damped harmonic oscillations: x(t) = x_0 · e^(-ζ·ω_n·t) · cos(ω_d·t - φ), where ζ is the dimensionless viscous damping ratio (typically 1% to 5% for welded steel and concrete structures) and ω_d = ω_n · √(1 - ζ²) is the damped natural frequency. The damping ratio is quantified experimentally via the Logarithmic Decrement method: δ = (1/n) · ln(x_i / x_{i+n}) ≈ 2πζ, where x_i and x_{i+n} are successive peak displacement amplitudes recorded by accelerometers. In this laboratory investigation, floor mass m is systematically varied from 2.0 to 12.0 kg to calibrate lateral frame stiffness slope k = 1850.0000 N/m, verify the inverse-mass frequency relation ω_n² = k/m, and determine structural damping ratio ζ.
ω_n² = 1850.0000 / m
Evaluated on a precision benchtop aluminum building shear frame. Inverse-mass formulation correlates natural frequency squared ω_n² directly to 1/m with lateral stiffness slope k = 1850.0000 N/m.