Over the last decade it has become increasingly popular to provide large public areas with gracefully designed 'flexible' staircases. One inherent characteristic of this type of construction is a low stiffness to mass ratio and hence a low natural frequency when compared to more traditional designs. A number of staircases have been found to be dynamically responsive to pedestrian traffic resulting in costly repairs. The objective of this thesis was to investigate the differences between human induced loading on floors with that on stairs. Experimental work carried out on a purpose built staircase showed that forces up to 3 times the static body weight were generated during fast descents while forces up to 2.5 times the static body weight were generated during fast ascents. The work also showed that first harmonic values generated while ascending were slightly higher than for descending whilst second harmonic values were up to 3 times greater for fast descents than for fast ascents. When compared with floor testing, stair testing produced first harmonic values nearly 2.5 times greater with second, third and fourth harmonic values nearly 3 times greater. The harmonic results for the flat testing were also incorporated into a new mathematical expression to predict peak accelerations on simply supported floors and footbridges. The experimental results were duplicated analytically by developing a computer program to calculate the vertical ground reaction forces from body segment positional data. Following a Newtonian approach, the predicted first harmonic values were 20% to 30% lower than actual while the second harmonic values were approximately the same. Monte Carlo simulation techniques were also used to model the effects of group loading on stairs. The simulations predicted enhancement factors (a multiplier on single subject loading) of 3 to 6 for smaller groups(< 9 people) and 4 for larger groups(> 25 people). If the experimental/analytical results are combined with the group loading predictions, the harmonic values for groups ascending or descending flexible staircase could be substantially increased. These results demonstrate that loading data from floors is highly inappropriate for staircase design.

The flexibility of the floor slabs is quite often ignored in the seismic analysis of structures. In general, the rigid behavior assumption is appropriate to describe the in-plane response of floors. For seismic excitations with vertical components, however, the flexibility of the floor slabs in the out-of-plane direction may play a significant role and it can result in an increase in the seismic response. The simplified procedures used in the current practice to include the floor flexibility can lead to highly conservative estimates of the slab and supported equipment response. To include floor flexibility, a detailed finite element model of the structure can be constructed, but this procedure leads to a system with large degrees of freedom the solution of which can be time consuming and impractical. In this study, a new dynamic condensation approach is developed and proposed to reduce the size of the problem and to calculate the seismic response of structures with flexible floor slabs. Unlike other currently available dynamic condensation techniques, this approach is applicable to classically as well as nonclassically damped structures. The approach is also applicable to structures divided into substructures. The approach can be used to calculate as many lower eigenproperties as one desires. The remaining higher modal properties can also be obtained, if desired, by solving a complementary eigenvalue problem associated with the higher modes. The accuracy of the calculated eigenproperties can be increased to any desired level by iteratively solving a condensed and improved eigenvalue problem. Almost exact eigenproperties can be obtained in just a few iterative cycles. Numerical examples demonstrating the effectiveness of the proposed approach for calculating eigenproperties are presented. To calculate the seismic response, first the proposed dynamic condensation approach is utilized to calculate the eigenproperties of the structure accurately. These eigenproperties are then used to calculate the seismic response for random inputs such as a spectral density function or inputs defined in terms of design response spectra. Herein, this method is used to investigate the influence of the out-of-plane flexibility of the floor slabs on the response of primary and secondary systems subjected to vertical ground motions. The calculated results clearly show that inclusion of the floor flexibility in the analytical model increases the design response significantly, especially when computing acceleration floor response spectra. This has special relevance for secondary systems and equipment the design of which are based on the floor response spectra. The accuracy of the results predicted by two of the most popular methods used in practice to consider the floor flexibility effects, namely the cascade approach and the modified lumped mass method, is also investigated. The numerical results show that the cascade approach overestimates the seismic response, whereas the modified lumped mass method underestimates the response. Both methods can introduce significant errors in the response especially when computing accelerations and floor response spectra. For seismic design of secondary systems supported on flexible slabs, the use of the proposed condensation approach is thus advocated. / Ph. D.