Brad Davis

This paper explains the vibration evaluation methods for floors supporting sensitive equipment in the second edition of the AISC Design Guide 11, Vibrations of Steel-Framed Structural Systems Due to Human Activity. It presents new experimentally verified equations that are simplified for practical implementation. Sensitive equipment tolerance limits are stated in numerous forms, including peak acceleration and various spectral acceleration and velocity. For this reason, response predictions are given in terms of all tolerance limit forms that are commonly used. The most severe responses of lower frequency floors to walking are due to resonant build-ups whereas the most severe responses of higher frequency floors are due to a series of individual footsteps impulses, so equations are given for both. Because the sensitive equipment tolerance limit is objective, each equation includes a calibration factor that results in a high probability that the predicted response will exceed the actual response.

With the use of lighter construction materials, more slender architectural designs, and open floor plans resulting in low damping, vibration serviceability has become a dominant design criterion for structural engineers worldwide. In principle, assessment of floor vibration serviceability requires a proper consideration of three key issues: excitation source, system, and receiver. Walking is usually the dominant human excitation for building floors. This paper provides a comprehensive review of a considerable number of references dealing with experimental measurement and mathematical modeling of dynamic forces induced by a single pedestrian. The historical development of walking force modeling—from single harmonic loads to extremely complex stochastic processes—is discussed. As a conclusion to this effort, it is suggested that less reliance should be made by the industry on the deterministic force models, since they have been shown to be overly conservative. Alternatively, due to the random nature of human walking, probabilistic force models seem to be more realistic, while more research is needed to achieve enough confidence to implement in design practice.

Ultimate shear strengths of 20 unstiffened I-girder specimens from the literature and seven new specimens designed to fill gaps in the experimental data are compared with predictions from models recommended by Basler, Höglund, and Lee and colleagues. Basler’s model, which is based solely on an idealized web shear buckling resistance, is shown to be accurate for webs with slenderness between 60 and 100. However, it is very conservative for members with typical plate girder web slenderness ratios. Höglund’s methods, which aim to characterize the shear postbuckling capacity of unstiffened webs, are found to be accurate to conservative. The method by Lee and colleagues, which aims to predict the shear postbuckling strength of webs with widely spaced stiffeners, is accurate on average. However, this method significantly overpredicts the strength of several specimens. A proposed adaptation of Höglund’s recommendations from a 1997 article matches the current AISC shear buckling strength equations for sto...

Slender monumental stairs are major architectural features in many high-end building structures. Architectural requirements for these are usually very aggressive, with long spans and slender stringers being the norm. The resulting low natural frequencies are often within reach of the lower harmonics (which have high amplitudes) of the vertical force caused by a person descending the stair. Also, some configurations with very low frequency lateral vibration modes might allow high lateral accelerations. Because the potential for annoying vibrations is high, it is critical that stair designers have access to evaluation methods. Current evaluation methods rely on finite-element analysis-based response prediction methods that are outside the reach of many structural engineering firms. This paper presents a simplified vertical acceleration prediction method, based on the fundamental natural mode of the stair, which is suitable for manual calculations. Response predictions are compared to experimental measurements to calibrate the prediction method for design use. Lateral vibrations are discussed, and an evaluation method is proposed. Finally, a numerical example is provided.

High-frequency steel and concrete floors are often used to support sensitive equipment to minimize vibration response to walking. Equipment vibration tolerance limits are sometimes expressed as waveform peak acceleration, and are more often expressed as narrowband spectral acceleration, or one-third octave spectral velocity. Current methods predict the waveform peak response after a footstep. However, postprocessing beyond what is practical for typical design office usage is often required to predict responses directly comparable to spectral tolerance limits. Also, current methods are not calibrated to provide a specific level of conservatism. This paper presents new methods for predicting the waveform peak acceleration, narrowband spectral acceleration maximum magnitude, and one-third octave spectral velocity maximum magnitude. A total of 89 walking vibration tests were performed on five high-frequency floor bays. The measurements are used to assess the precision of the proposed methods and to calibrate the prediction methods to provide a specific probability that the actual response will exceed the predicted response. The measurements are compared to predictions by the proposed method and five established methods.

When occupants complain of lively floor motion due to human activity, it is often necessary to estimate the dynamic properties of the floor and ascertain the form and level of vibration response toward the goal of designing an effective retrofit solution. The most detailed and accurate experimental method is to determine the natural vibration modes using full experimental modal analysis, which requires substantial equipment including at least one floor shaker, and then determine the acceleration due to walking. However, due to cost and time constraints and possible unacceptable occupant disruption, it may not be possible to perform a full experimental modal analysis. An alternative testing procedure is to use a handheld spectrum analyzer to record floor accelerations due to heel drop and timed walking excitations. These measurements are then used to estimate the natural frequencies and vibration response level, respectively. This paper describes the procedure and compares results with experimental modal analysis techniques. The method is illustrated by a case study of an in-service floor and is shown to be economical, convenient, and effective.

Slender monumental stairs are major architectural features in hotels, condominiums, hospitals, and other high-end building structures. Architectural requirements for these are usually very aggressive, with long spans and slender stringers being the norm. Slender stairs often have fairly massive treads and guardrails which, combined with slender stringers, results in natural frequencies within reach of the very large lower harmonics of the force caused by a person descending the stair. Stair designers must be able to predict the vertical vibration response of a stair during the design phase. Current prediction methods rely on finite element analysis-based response prediction methods which are outside the reach of many structural engineering firms. This paper presents a simplified response prediction method based on the fundamental natural mode of the stair, which is suitable for manual calculations. Response predictions are compared to experimental measurements to show that the predictions are accurate enough for design use.

High-strength steel reinforcement in buildings had previously been limited to specialized applications, but recently published design guidance allows expanded use. A case study, conducted to investigate productivity benefits of using 690 mpa (100 ksi) versus 414 mpa (60 ksi) reinforcement, found that there was little to no benefit in using 690 mpa (100 ksi) steel in slabs, post-tensioned girders, and columns, but the beam reinforcement weight was reduced by 36%. The 2010 material cost ratio of 690 mpa (100 ksi) to 414 mpa (60 ksi) reinforcement was two, outstripping the weight reduction. However, labor cost is a function of weight, bringing the overall cost of 690 mpa (100 ksi) reinforcement to within 35% of 414 mpa (60 ksi) reinforcement cost. The material cost ratio will presumably decrease over time; if it drops by 30% or more, 690 mpa (100 ksi) reinforcement will be more economical. Labor costs, which vary by location, strongly influence the productivity benefits of 690 mpa (100 ksi) reinforcement. The use of 690 mpa (100 ksi) reinforcement is more favorable in expensive labor markets and it appears to be currently competitive in some. The paper’s primary contribution to the overall body of knowledge is the quantitative understanding of the economic factors that influence the ability of 690 mpa (100 ksi) steel reinforcement to have a productivity advantage over the use of conventional 414 mpa (60 ksi) steel reinforcement. Practitioners, designers, and researchers can use this information to understand the cost and productivity impact of high-strength reinforcing steel.

Floor vibration serviceability is a primary design consideration for steel framed floors and numerous evaluation methods have been proposed over the last 35 years or so. However, there is relatively little information available on the accuracy of the methods. Therefore, the objective of this study is to investigate the accuracy of the following five well-known methods: Modified Reiher-Meister, Murray Criterion, Hugo Bachmann's Method, AISC Design Guide 11 Chapter 4, and the SCI P354 Simplified Method. The methods listed above were used to evaluate the bays in an extensive 122 bay database to determine the accuracy of prediction of natural frequencies and overall acceptability. The SCI P354 most accurately predicted the natural frequency, with an average measured-to-predicted ratio of 1.01 (24% COV). The AISC Design Guide 11 most accurately predicted floor bay acceptability, with a 91% agreement with observations.

It is sometimes necessary to provide retrofit solutions to objectionable floor vibrations due to human activity. Because such problems are usually detected after the design and construction phases are complete, and the owners have occupied the building, the evaluation of retrofit options must be fast and economical. This paper describes a framework for evaluating retrofit options and presents a case study.