1. Introduction of Floor Vibration for Steel Structures ENCE710 – Advanced Steel Structures C. C. Fu, Ph.D., P.E. Department of Civil & Environmental Engineering University of Maryland College Park, MD

2. 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.

3. Types of Dynamic Loading (a) Harmonic load (Machine) (b) Periodic load (Dancing) (c) Transient load (Walking) (d) Impulsive load (Jumping)

4. Dynamic Resonance Factors affecting the dynamic amplification: damping, ω and ω n

5. Peak Acceleration for Human Comfort for Vibrations Acceptance 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 the frequency range from 4 Hz to 8 Hz.

6. Dynamic Force – Human Activities resonance response function

7. Response to Sinusoidal Force The time-dependent repeated force can be represented by the Fourier series

8. Design for Peak Floor Acceleration (Table 4.1) (Eqs. 4.2, 4.3a, b, 4.4) (Eq. 2.2) (Eq. 4.1)

9. Natural Frequency of Floor System Combined mode

10. Floor Evaluation Calculation Procedure transformed slab moment of inertia per unit width effective width for joist effective panel weights for joist

11. Floor Evaluation Calculation Procedure effective panel weights for beam effective width for beam

12. Floor Evaluation Calculation Procedure damping ratio equivalent panel weight acceleration limit 5.7 kips per in.