Introduction of Floor Vibration for Steel Structures
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Transcript of Introduction of Floor Vibration for Steel Structures
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Introduction of Floor Vibration
for Steel Structures
ENCE710 – Advanced Steel Structures
C. C. Fu, Ph.D., P.E.Department of Civil & Environmental
EngineeringUniversity of Maryland
College Park, MD
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Background The first criteria in designing floor for service ability starts nearly
180 years ago. Tredgold (1828) wrote that girders over long spans should be made “deep” to avoid the inconvenience of not being able to move on the floor without shaking everything in the room.
Traditionally, soldiers "break step" when marching across bridges to avoid large, potentially dangerous, resonant vibration.
The example of the millennium bridge. A traditional stiffness criterion limits floor deflection due to live
load = span/360. This limitation has limited success in controlling floor vibration.
Resonance has been ignored in the design of floors and footbridges until recently.
Dynamic amplification. Rhythmic activities, such as aerobics and high-impact dancing, can cause
serious floor vibration problems due to resonance.
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Types of Dynamic Loading (a) Harmonic
load (Machine)
(b) Periodic load (Dancing)
(c) Transient load (Walking)
(d) Impulsive load (Jumping)
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Dynamic Resonance
Factors affecting the dynamic amplification: damping, ω and ωn
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Peak Acceleration for Human
Comfort for VibrationsAcceptance criteria for peak floor acceleration with frequency ranges from 4 Hz to 8 Hz.Office (0.005 g).
Gym (0.05 g) ~ 10 times office acceptance.
Shopping mall (0.015 g) ~ 3 times office acceptance.
Acceptance criteria for peak floor acceleration increases outside thefrequency range from 4 Hz to 8 Hz.
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Dynamic Force – Human Activities
resonance response function
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Response to Sinusoidal Force
The time-dependent repeated force can be represented by the Fourier series
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Design for Peak Floor Acceleration
(Table 4.1)(Eqs. 4.2, 4.3a, b, 4.4)
(Eq. 2.2)
(Eq. 4.1)
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Natural Frequency of Floor System
Combined mode
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Floor Evaluation Calculation Procedure
transformed slab moment of inertia per unit width
effective width for joist
effective panel weights for joist
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Floor Evaluation Calculation Procedure
effective panel weights for beam
effective width for beam
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Floor Evaluation Calculation Procedure
damping ratio
equivalent panel weight
acceleration limit5.7 kips per in.