controlling human induced vibrations on structural slab supported

8/12/2019 Controlling Human Induced Vibrations on Structural Slab Supported

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Earl P. Bonita,M.Sc.

Controlling Human Induced Vibrations

on Structural Slab Supported by Long

Span Castellated Steel Beams Using

American and European DesignGuidelines


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Goal

Provide basic principles on analytical tools

to evaluate steel framed floor systems

using American and European DesignGuidelines


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Outline

Theory of Floor VibrationRelationship between Resonance and Damping

American Design Guidelines Evaluation Flowchart Simple Method

European Design Guidelines Evaluation Flowchart Simple Method

Acceptance Criteria for Human ComfortFinite Element Method

Mitigating Measures

Case Study


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Walking Excitation

Causes of Floor Vibration

Footfall


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Discomfort

Structural Damage

Effects of Floor Vibration

Inelastic response overload

Bouncy floors


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Response to Harmonic Loading


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Human Induced Vibration

Beam line

- Footfall


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m + c + k = P o sin t

Damped Forced Vibration

Equation of motion

Steady-state and transient response

U(t) = e -nt (A cosdt + B sindt) + C sindt + D cost


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Response for Underdamped System


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Forcing Function = Footfall

F = P [1+ icos(2 i f step t + i) ]

By Fourier series

a/g = RP o cos(2 i f step t) / W

Resonance response function

Simplified

a/g = P o exp (-0.35 f n ) / W < ao /g


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Resonance: 1 st harmonic

Sinusoidal Vertical Force


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Resonance


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Resonance and Damping


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Damping

Underdamped

Critically damped

Exponential decay of the response


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SAP2000: Modal Time-History


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Two Methods of Footfall Analysis

Simple Method direct formulas

numerical techniqueFinite Element Method


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Simple Method

Footfall Analysis


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American Design Guidelines


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Recommended Peak Acceleration (% of g)

(3.62, 0.16)


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European Design Guidelines


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Design Chart for D = 3% damping

(17220 Kg, 7.1 Hz)

OS-RMS = One-Step Root Mean Square


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American Design Guidelines

European Design Guidelines

Acceptance Criteria for HumanComfort

f n and OS-RMS 90

f n and a o /g (% of g)


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Finite Element Method

Footfall Analysis


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OASYSSteps

1.Obtain natural frequency of floor system

2.Dynamic time response from footfall3.Footfall response contour

4.Peak acceleration

5.Displacement, velocity and acceleration over time.


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ADAPT Floor Pro

1. Natural frequency from ADAPT floor pro

2. Excitation force of vibration

3. Appropriate damping factor4. Effective weight of the panel and SDL

5. Peak acceleration ratio

6. Acceptability of vibration

Steps


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Vibration results - ADAPT floor pro


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SAP2000

Steps

1.Load case for each footfall

2.Point load corresponding to footfall location

3.Modal time-history that represents footfall sequence

4.Modal time-history based on Ritz modes

5.Impulse function, scale factor and arrival time

6.Time steps to cover duration of time-history


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Mitigating Measures

Floor Vibration Solutions


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Reduction of Effects

Increase Mass

Increase Damping

Stiffening

Passive Control


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Case Study Simple Method


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Case Study Results


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Conclusion

American and European Design Guidelines case studyresults are both Satisfactory.

Simple Method is a good floor vibration evaluation tool, butFinite Element method can be used for more intricate

analysis.

Increasing the Damping Ratio is the best option for theMitigating Measures presented.


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QED

controlling human induced vibrations on structural slab supported

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