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

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.

Types of Dynamic Loading (a) Harmonic

load (Machine)

(b) Periodic load (Dancing)

(c) Transient load (Walking)

(d) Impulsive load (Jumping)

Dynamic Resonance

Factors affecting the dynamic amplification: damping, ω and ωn

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.

Dynamic Force – Human Activities

resonance response function

Response to Sinusoidal Force

The time-dependent repeated force can be represented by the Fourier series

Design for Peak Floor Acceleration

(Table 4.1)(Eqs. 4.2, 4.3a, b, 4.4)

(Eq. 2.2)

(Eq. 4.1)

Natural Frequency of Floor System

Combined mode

Floor Evaluation Calculation Procedure

transformed slab moment of inertia per unit width

effective width for joist

effective panel weights for joist

Floor Evaluation Calculation Procedure

effective panel weights for beam

effective width for beam

Floor Evaluation Calculation Procedure

damping ratio

equivalent panel weight

acceleration limit5.7 kips per in.