Several areas of research regarding floor vibrations were studied during the process of this research. A basic literature review of previous work in the field of floor vibrations is presented along with a summary of the study. The first area of study involved a comparison of finite element models with field tests for a suspended floor system. The suspended floor system underwent several retrofits to determine which retrofit reduced annoying vibrations the most. Comparisons were also made to see how well a finite element model could be used to predict the effectiveness of the retrofits. The attempt to make accurate finite element models was successful. The second area of study involved an experimental modal analysis (EMA). The experimental mode shape was compared with that from the finite element model (FEM). The research done in this area of study also involved measuring damping for a suspended floor system. The floor system was also subjected to a known input force and the response of the system was compared to the theoretical response based on the finite element model and the hand calculations prescribed by AISC Design Guide 11–Floor Vibrations Due to Human Activity (Murray et al., 1997). The findings helped provide useful information for the third area of study. The third area of this study focused on finding a method for performing a quick and inexpensive field test on a floor system to determine its acceptability. No good method found. The fourth area of this study was to find a way to accurately model complex floor systems with finite element modeling programs. Previous research yielded good results in the area of frequency prediction. However, the main focus of this study was to find a way to accurately predict peak acceleration of a complex floor system. This portion of research did not find a way to model complex floor systems in a finite element program for producing accurate peak accelerations. However, the source of error between the finite element program and the hand calculations was accurately defined. / Master of Science

The scope of this study is divided into three topics. To begin, more accurate methods for estimating the fundamental natural frequencies of floors were explored. Improvements for predicting the behavior of floor systems using several criteria were also investigated. The final topic compared the AISC and SCI methods for analyzing vibrations acceptability. Natural frequency prediction was studied by examining 103 case studies involving floor systems of various framing occupied or being constructed in the United States and Europe. Based on the results from these comparisons, it was reasonably concluded that the predicted bay frequency using Dunkerly's estimate (fn2) is not the most accurate method for predicting the system frequency using the AISC Design Guide for all types of framing analyzed. The predicted beam frequency using AISC methods provided sound correlations with the measured bay frequencies. On the other hand, with the exception of floor systems with joist girders and joists, the results showed that the SCI methods provided more accurate predictions of bay frequency despite a fair amount of data scatter. Evaluations based on the AISC Design Guide 11, the SCI criteria Murray Criterion, and Modified Reiher-Meister scale were compared with subjective field analyses for each case study in the second part of this study. The AISC Design Guide criterion is the most consistent method for predicting floor behavior. The SCI criterion is the next most consistent method for floor acceptability, followed by the Murray Criterion then the Modified Reiher-Meister scale. In the final part of this study, predicted accelerations and floor behavior tolerability for 78 case studies were evaluated using the AISC and the SCI criteria. The two prediction methods are in agreement for 82 % (64 of 78) of the case studies, and strongly disagree for only 12 % (9 of 78) of the case studies. / Master of Science

The possibility of using a commercially available structural analysis program to predict the response of a floor system due to walking excitation as given in AISC Design Guide 11, Floor Vibrations Due to Human Activity (Murray, et al., 1997) was explored. This research included ideal floors that did not have measured values as well as several case study floors that do have measured values for the fundamental frequency. First, multiple model set-ups and loading protocols are applied to the ideal floors and the results compared to results from the Design Guide procedure. A recommendation of the best combination of a model set-up and loading protocol that best matches the Design Guide procedure results is made. Then, case study floors are modeled with the recommended model set-up and loading protocol, and the results compared to the results from the Design Guide procedure and to measured fundamental frequencies. The peak accelerations are also compared to subjective evaluations as to the acceptability of the system. Next, multiple systems were analyzed using five different modeling techniques, including the Design Guide Method, an alteration of the Design Guide Method, the Rayleigh Method, the Analytical Method, and the structural analysis program method, in an attempt to determine the source of discrepancies between the structural analysis program method and the Design Guide method. Finally, conclusions are drawn regarding the structural analysis program procedure as well as possible sources of differences. In general, the structural analysis program procedure reliably predicts the fundamental frequency of a floor system, but does not predict the Design Guide peak acceleration under dynamic loading. The difference in the effective mass of a system between the two methods is a source of discrepancy. / Master of Science

Experimental and analytical research was conducted to address the vibration properties of Long Span Deck Floor Systems (LSDFS). The research comprised three stages. In the first part, experimental in-situ tests were conducted on thirteen bays of buildings under construction. The natural frequencies and acceleration responses were captured to observe the vibration behavior of the tested floors. In the second part, a laboratory footbridge was constructed to determine the fixity level attained at the supports when a LSDFS is supported by CMU walls. For this purpose, the footbridge was tested with three support conditions, and a number of experiments were carried out to determine the dynamic properties of the structure. Static tests using both point and distributed loadings were conducted to measure the deflections at the footbridge midspan. The static test results were compared to the theoretical deflections for a pinned-end beam and a fixed-end beam. Dynamic tests using experimental modal analysis techniques were conducted to determine the natural frequencies and mode shapes of the structure. The measured fundamental natural frequency of the footbridge was compared to the frequencies calculated for a simply supported beam and a beam with fixed ends, to determine the degree of fixity attained in the connection between the LSDFS and the supporting walls. In the last part of the research, three analytical procedures to predict modal characteristics of long span deck floor systems are studied. Floor frequencies are calculated using finite element analyses. Two design guides for floor vibration analysis were used to calculate natural frequencies and response accelerations. The predicted results obtained from the analytical methods are compared to the experimental results to determine their accuracy. Recommendations for the use of the analytical methods are provided. / Master of Science

Master of Science / Department of Architectural Engineering and Construction Science / Bill Zhang / Vibration has been a consideration in many types of structures, and as the advancement of technology has allowed steel and concrete sections to become lighter, vibration has become more of a consideration in the design of structures. This report focuses on occupant induced vibration of steel framed floors due to running as the vibration source. The history of vibration analysis and criteria in structures is discussed. However, lack of research and experimentation on running as the source of vibration exists; therefore, the history section focuses on walking as the source of vibration. The current design criteria for vibration of steel framed floors in the United States of America is the American Institute of Steel Construction (AISC) Design Guide 11: Vibrations of Steel Framed Structural Systems Due to Human Activity. This design guide discusses vibration due to walking, running, and rhythmic activities as well as gives design criteria for sensitive occupancies and sensitive equipment. In order to apply the Design Guide 11 analysis procedure for running as the source of vibration, the Kansas State University Chester E. Peters Recreation Complex is used as a case study. The recreation complex includes a 1/5-mile running track that is supported by a composite steel framed floor. Based on the Design Guide 11 criterion, the running track is deemed acceptable. Lastly, this report discusses remedial procedures in the case of annoying floor vibration specific to floors that have running as a source of vibration. In addition, areas of further research are suggested where running is a source of vibration on steel framed floors.

Studies on the effective moment of inertia of girders that support concrete slabs using joist seats as the horizontal shear connections, and a cost efficiency analysis comparing composite and non-composite floor systems that meet vibrations design standards, were conducted. The first study was undertaken because over-prediction of girder effective moment of inertia was the suspected cause of several recent vibration problems in floors supported by widely spaced LH-series joists. Eight purpose-built floors of the type in question were subjected to experimental tests of girder effective moment of inertia and girder frequency. Frequencies were tested for two live loading cases. Three separate test configurations were made with each floor by changing the seat-to-girder connections between bolted, welded, and reinforced. In the study, 1) the accuracy of the current design practice is assessed, 2) a new relationship was proposed, and 3) suggestions for finite element modeling are made. In recent years, composite construction has been used to improve cost efficiency by reducing structural weight and in some cases by reducing story height. However, vibration problems are a design consideration in composite floors because lighter floors tend to be more lively. It is not clear if cost savings can be made with composite construction if vibrations are considered in the design. To compare the cost of composite and non-composite floors that satisfy AISC/CISC Design Guide criterion for walking excitation, four typical size bays were analyzed using commercial design software that finds the least expensive member configuration for a given bay size. All acceptable bay configurations of member sizes and spacing were evaluated for least non-composite and composite costs, then these results were compared. The findings show that composite construction can be more economical when initial dead load deflections do not control the design. / Master of Science

A new modular steel floor system, named FastFloor, is proposed for commercial buildings. The system is conceptualized to be prefabricated at the shop and ready to be installed on a previously erected skeleton frame structure consisting of girders and columns or connected to core shear walls. The system configuration aims to increase the speed of design, fabrication, and erection of a steel project by eliminating concrete pouring and curing times. Other advantages include reducing the weight of the building and its carbon footprint. Several module configurations were considered and evaluated based on a series of interviews with experts in steel fabrication and erection engineering. The selection relied not only on addressing the issues related to fabrication, transportation, and erection but also on satisfying floor vibrations, as it was determined to be the governing limit state of the plate thickness, section sizes, and beam spacing due to the presence of an unstiffened bare plate acting as a slab. Observations were performed regarding fabrication sequence and transportation on the chosen configuration. The dynamic properties of the module are particularly important because DG11 was developed for composite concrete-steel floor systems, and its applicability to all steel-floor systems needs to be evaluated. In parallel, a vibration testing program was conducted to determine the dynamic properties of the module, including natural frequencies and mode shapes. Lastly, the acceptability of the modular system for floor vibrations was evaluated by both a calculation method and a modeling approach. The analysis results suggest that the module will not satisfy floor vibrations criteria, but a modified module with added stiffeners is shown to be acceptable. Upcoming tests, by others, on specimens with a raised access floor will be necessary to refine the predictions and determine if the stiffeners are actually required. / Master of Science / FastFloor is an innovative modular all-steel floor system that aims to revolutionize the construction of commercial buildings, with benefits including enhanced efficiency in design, fabrication, and erection, as well as reduced environmental impact, by eliminating the need for concrete pouring and curing and full prefabrication in shops. Several module configurations were evaluated based on insights from industry experts in steel fabrication and erection engineering. It was observed that the main challenge in the early phases was to address issues related to fabrication, transportation, and erection while ensuring optimal performance in terms of floor vibrations. This thesis project focused on a preliminary assessment of the vibration behavior of the system by conducting dynamic tests and evaluating the compatibility with the analytical and computational procedures in Design Guide 11, which is not calibrated for an all-steel system like FastFloor. Based on the results, it was concluded that the initial configuration did not fully satisfy the floor vibrations criteria. However, through further computational evaluation, a modified module, based on the initial configuration with added stiffeners, was predicted to be satisfactory. Thus, future research will continue to refine the system behavior and predictions and evaluate the contributions of Raised Access Floor to the vibration performance.

The report aims to investigate norms, standards, guidelines and experience within the industry for how to design CLT (cross-laminated timber) regarding vibrations induced from humans. The following is being researched, ISO137, KL-trähandboken, Eurocode 5 and a new unpublished working draft of Eurocode 5 final working draft, Canadian CLT handbook and Cross-laminated timber structural design according to Eurocode from Austria.The conclusion is that the literature for CLT is non-existent in the current Eurocode 5 which only addresses timber floors with joists, however the new Eurocode draft suggests an update to include CLT which is similar to the norm CLT from Austria.The report contains a calculation part in which an analysis is conducted for a real project with calculations based on Eurocode 5 and the Eurocode 5 final working draft, the design tool Calculatis and FEM program RFEM. The calculations are compiled and evaluated.The calculation results show differences between the different standards. The natural frequencies are typically the same. The biggest difference is between the accelerations which is in direct relation to the modal mass, and the modal mass differs a lot between the calculations. It is understandable how Eurocode 5 final draft and RFEM calculate the modal mass, but not so for Calculatis as it doesn’t show any calculations in the technical documentation.There is a difference of the modal mass between Eurocode 5 final draft and RFEM, likely because EK5 calculate the modal mass for a rectangular floor simply supported at two or four sides. Whereas the RFEM model is not strictly rectangular nor is it simply supported everywhere, instead there are beams in some places. This suggests that caution should be regarded in calculations where floor structures have been simplified. / I denna rapport undersöks hur ett KL-träbjälklag dimensioneras med hänsyn till vibrationer. Vibrationerna som beaktas är vibrationer från steg på bjälklaget. Rapporten är uppdelad i två delar. Del 1 är en litteraturstudie av normer och standarder. Del 2 är en beräkningsdel. Beräkningarna som utförs är handberäkningar från två av normerna, en beräkning med hjälp av Calculatis samt beräkningar med FEM-programmet RFEM. Alla beräkningar jämförs med varandra för att undersöka likheter och skillnader i resultaten.Slutsatsen från litteraturstudien är att det i dagens svenska dimensioneringsstandard (Eurokod 5) saknas bestämmelser för hur KL-trä ska dimensioneras, alla regler är anpassade för träregelbjälklag. Det kommer en uppdatering på Eurokod 5 om några år, ett slutgiltigt utkast på vibrationsdelen har studerats. Utkastet har regler som är anpassade för både KL-träbjälklag och träregelbjälklag.I beräkningsdelen är resultatet att det finns både skillnader och likheter mellan de olika beräkningsmetoderna. Egenfrekvenserna är relativt lika mellan de olika beräkningsmetoderna. Störst skillnad blir det för accelerationerna. Detta eftersom modalmassorna skiljer sig mellan de olika beräkningarna och accelerationsberäkningarna bygger på modalmassan. I Eurokod 5 final draft och RFEM är det tydligt hur modalmassan beräknas medan det är svårt att förstå hur den beräknas i Calculatis.En av anledningarna till att det blir så stor skillnad mellan egenmoden mellan Eurokod 5 final draft och RFEM är för att i Eurokod 5 final draft beräknas modalmassan enbart för rektangulära bjälklag som är fritt upplagda på 2 eller 4 sidor. Medan beräkningarna i RFEM har skett på ett bjälklag som inte riktigt är rektangulärt samt att delar av bjälklaget inte är fritt upplagt utan placerat på en balk. I detta fallet blir det stor skillnad på egenmoden vid förenkling av strukturen, förenklingar av strukturen bör därför beaktas med försiktighet för beräkningar.

Since their invention in the early 1900s, Tuned Vibration Absorbers (TVAs) have shown to be effective in suppressing vibrations of machines and structures. A vibration absorber is a vibratory subsystem attached to a primary system. It normally consists of a mass, a spring, and a damper. Mounted to the primary system, a TVA counteracts the motions of the primary system, "absorbing" the primary structure's vibrations. A conventional passive TVA, however, is only effective when it is tuned properly, hence, the name "tuned" vibration absorber. In many practical applications, inevitable off-tuning (or mistuning) of a TVA occurs because of the system's operating conditions or parameter changes over time. For example, the mass in a building floor could change by moving furnishings, people gathering, etc., which can "off-tune" TVAs. When TVAs are off-tuned, their effectiveness is sharply reduced. Moreover, the off-tuned TVAs can excessively amplify the vibration levels of the primary structures; therefore, not only rendering the TVA useless but also possibly causing damage to the structures. Off-tuning is one of the major problems of conventional passive TVAs. This study proposes a novel semiactive TVA, which strives to combine the best features of passive and active TVA systems. The semiactive TVA in this study includes a Magneto-Rheological (MR) damper that is used as a controllable damping element, for providing the real-time adjustability that is needed for improving the TVA performance. This study is conducted in two phases. The first phase provides a numerical investigation on a two-degree-of-freedom (2-DOF) numerical model in which the primary structure is coupled with a TVA. The numerical investigation considers four semiactive control methods for the MR TVAs, in addition to an equivalent passive TVA. These numerical models are optimally tuned using numerical optimization techniques to compare each TVA system. These tuned systems then serve as the basis for numerical parametric studies for further evaluation of their dynamic performance. The parametric study covers the effects of damping, as well as system parameter variations (off-tuning). The results indicates that semiactive TVAs are more effective in reducing the maximum vibrations of the primary structure and are more robust when subjected to off-tuning. Additionally, the numerical study identifies the "On-off Displacement-Based Groundhook control (on-off DBG)" as the most suitable control method for the semiactive TVA among control methods considered in this study. For the second phase of this study, an experimental study is performed on a test setup, which represents a 2-DOF structure model coupled with an MR TVA. Using this setup, a series of tests are conducted in the same manner as the numerical study to evaluate the performance of the semiactive TVA. The primary purposes of the experiment are to further evaluate the most promising semiactive control methods and to serve as a "proof-of-concept" of the effectiveness of this MR TVA for floor vibration applications. The results indicate that the semiactive TVA with displacement-based groundhook control outperforms the equivalent passive TVA in reducing the maximum vibrations of the primary structure. This confirms the numerical result that identifies on-off DBG control method as the "best" control method for the MR TVA among four semiactive control schemes considered. The experimental robustness study is also conducted, focusing on the dynamic performance of both the passive and the semiactive TVAs when the mass of the primary system changes (mass off-tuning). The mass of the primary system varied from -23 % to +23 % of its nominal value by adding and removing external masses. The experimental results show that the semiactive TVA is more robust to changes in the primary mass than the passive TVA. These results justify the benefits of the use of semiactive MR TVAs in structures, such as building floor systems. The off-tuning analysis further suggests that, in practice, semiactive TVAs should be tuned slightly less than their optimum in order to compensate for any added masses to the structure. Additionally, the lessons learned from the experimental study have paved the way for implementing the semiactive MR TVA on a test floor, which is currently in progress under a separate study. / Ph. D.

The purpose of this study was to examine the effect of bottom chord extensions on deflections and vibration characteristics of joist supported floor systems when joist bottom chord extensions are installed. To understand the effect of bottom chord extensions on deflections, natural frequency, damping, mode shape and effective mass, extensive analytical and experimental studies were conducted on single span and three span joist supported laboratory footbridges with different bottom chord extension configurations. Finite element computer models were created to simulate and compare the results of stiffness and vibration tests. Testing was done with a) the bottom chord extensions in-place before the concrete was placed, b) with all or part of the bottom chord extensions removed, and c) after the bottom chord extensions had been reinstalled with jacking for the single span footbridge and without jacking for the three-span footbridge. Results from the stiffness tests indicate that re-installing the bottom chord extensions to the joists of the single span footbridge with cured concrete with the center of the span raised helps to reduce the uniform load deflections to some extent, but not as much as placing the bottom chord extensions before the concrete placement. Likewise, for the three span footbridge, placing the bottom chord extensions before the concrete placement is observed to be a better solution. Results from the dynamic tests indicate that the effect of bottom chord extensions on the single span footbridge is consistent for natural frequency, 20 psf live load deflections, sinusoidal excitations with high amplitudes, quarter point heel drop excitations, walking excitations, and effective mass values. The effect of bottom chord extensions on the three span footbridge is consistent for the natural frequency and 20 psf deflections. However, the FRF (Frequency Response Function) peaks of chirp, heel drop, sinusoidal excitations, accelerations from walking data, and the MEScope and Finite Element model effective mass results do not follow a common trend. It can be concluded that even though the footbridge was stiffened by the bottom chord extensions, that does not necessarily mean that the acceleration levels, and hence the frequency response function peaks, decrease. However, bottom chord extensions do increase the natural frequencies for all the three governing bending modes. / Ph. D.