The structure is on the 1st floor (one storey height aboveÂ ground) of a purpose-built office building. It has steel primaryÂ beams spanning 12m at 6m centres, secondary beams at 3mÂ centres and steel columns approximately on a 6x12m grid.

Composite steel-concrete slabs span between the secondaryÂ beams. The floor is based on sets of bays totalling 72x24m withÂ additional voids for staircases. In general the primary cellularÂ beams are constructed from an upper Tee 457x191x89UB andÂ a lower Tee 610x229x113UB, with voids of diameter 550mm atÂ 750mm centres. Secondary beams are 254x146x31UB and theÂ columns are 254x254x73UC. Photographs taken on-site haveÂ provided an estimate for the concrete slab as being 130 mmÂ deep, with 60 mm trapezoidal decking.

The floor is considered by its occupants to be quite lively. TheÂ floor was chosen as the test bed for a new active vibrationÂ control system1 requiring creation of a modal model forÂ simulations, evaluation of structural contributions to dynamicÂ performance through finite element modelling and correlation

and measurements of vibration response to walking with andÂ without active control in operation.

**Location: Leeds, UK**

ANSYS commercial FE software was used to model the floor.Â Composite slabs were modelled using orthotropic SHELL63Â elements, where the slab thickness and density were constantÂ throughout but the orthotropic behaviour of the slab inÂ directions of the primary and secondary beams (due to theÂ trapezoidal steel decking) were modelled by reduced Youngâ€™sÂ modulus (nominally 38MPa) in the secondary beam direction.

The primary and secondary beams were modelled usingÂ BEAM44 elements which allow for taper and centroidal offsetsÂ (Figure 1). Composite connections between the beams andÂ slabs were modelled using offset centroids of the beams andÂ slab (Figures 2 & 3). Columns were modelled (without offsets)Â using the relatively simple BEAM4 elements. Both BEAM44 andÂ BEAM4 elements incorporate tension, compression, bendingÂ and torsion capabilities.

The columns were assumed to be fixed one storey above andÂ below the floor under consideration. All other internalÂ connections were assumed to be fixed, an assumptionÂ generally taken as valid because the very small deflectionsÂ resulting from walking-induced vibrations are not sufficient toÂ cause significant rotation at joints, even if those joints areÂ designed to be pinned with regards to ultimate limit stateÂ analysis. Imposed loads and non-structural dead loads wereÂ modelled as additional mass on the slab elements. Figure 4Â shows the initial FE model.

Test Point (measurement) locations for the modal test areÂ shown Figure 5, with vertical accelerometers located atÂ column and mid-bay locations wherever possible. AttentionÂ was paid to TP04 and its surroundings because it wasÂ perceived to be a particularly lively location on the floor.Â Because the vibration perception was particularly acute at thisÂ point, this was a good initial candidate for the installation ofÂ the shaker for the subsequent active vibration control studies.

Modal testing was carried out using artificial excitation suppliedÂ by two APS Dynamics Model 400 electrodynamic shakersÂ operated in inertial mode. Four excitation points were used (TPsÂ 04, 07, 31 and 36) and responses were measured at all TPs,Â resulting in 4 columns of the frequency response function (FRF)Â matrix. The modal testing was carried out using continuousÂ uncorrelated random excitation with two excitation points at aÂ time (i.e. multi-input multi-output or MIMO modal testing). TimeÂ domain data blocks were of duration 20 s giving a frequencyÂ resolution of 0.05 Hz. The number of averages was 80 with 75%Â overlapping and a Hanning window was applied to all dataÂ blocks.

The magnitudes of the driving point mobility FRFs acquired areÂ shown in Figure 6 where force and response are measured atÂ the same point. From a visual inspection, there areÂ approximately nine modes between 4 and 10 Hz. The lowestÂ mode occurs at 4.86 Hz and the highest peak occurs at TP04 atÂ approximately 6.4 Hz. TP04 is the point on the structure whereÂ the response was subjectively assessed to be highest.

On-site modal parameter estimation was carried out on the fullÂ set of acquired FRFs using the MEâ€™scope suite of software. InÂ particular, mode indicator functions were first calculated toÂ give an indication of the locations of vibration modes and thenÂ the multiple reference orthogonal polynomial algorithm wasÂ used to estimate the modal properties, including modal massÂ for mode shape scaling. Between 4.86 and 9.19 Hz, 13 modesÂ were estimated. Fig. 7 shows the estimated vibration modesÂ which were dominant at TP04. The vibration mode atÂ approximately 6.37 Hz is the most likely to be excited byÂ pedestrian excitation; this mode has a damping ratio of 3%Â and a modal mass of approximately 20 tonnes.

The primary aim of the experimental modal analysis (EMA) wasÂ to generate an experimental modal model for designing andÂ simulating the performance of the active vibration controlÂ system. Such a model represents reality in operationalÂ conditions and is chosen for performance simulations wherever

possible and with access to the full-scale structure. For a-prioriÂ simulations only finite element analysis (FEA) is available andÂ modelling technology for floors engages a different set ofÂ uncertainties. Both FEA and EMA can produce modal modelsÂ that are suitable for performance simulations for assessment of

vibration serviceability.

For this floor limited model calibration was undertaken in orderÂ to improve understanding of the performance of the structuralÂ system. Since this type of flooring system is common in the UK,Â such a correlation study has benefits for a-priori analysis ofÂ similar structures that may be problematic. Figure 8 showsÂ matching of selected FEA and EMA modes, not necessarily theÂ same as the critical modes for the AVC study, but intended forÂ manual updating. An independent modal analysis wasÂ performed using a different mode estimation technique,Â explaining the slight difference in frequencies to the EMA results

presented in Figure.

Figure 8 shows a reasonable correlation between the FE andÂ EMA shapes for the first six modes, with the exception of theÂ second FE mode which was not picked up by the EMA study.Â One area of uncertainty is the additional stiffness andÂ additional mass from non-structural elements such as storage

areas and office equipment. The natural frequencies from theÂ preliminary FE study are noticeably higher than those from theÂ EMA study, indicating a lack of mass or excessive stiffness in theÂ model which could derive from differences in slab depth orÂ effects of non-structural components. Other possibilities are

incorrect assumption about concrete modulus and the degreeÂ of composite action.

Increasing the slab depth causes lower modes to decrease inÂ frequency (because these modes are global with concreteÂ behaving more as added mass) while higher modes increaseÂ in frequency (because the stiffness of the slab dominates withÂ more local bending in higher modes). Factors such as material

modulus and member geometric properties could not be inÂ error enough to explain the differences so possible reasons forÂ a lack of composite action were explored. Adjusting shear lagÂ in the slab and cracking in the concrete above hoggingÂ regions resulted in insignificant changes in natural frequencies.

So, some mechanism exists in the real structure through whichÂ stiffness is lost.

The best improvement was obtained by a change in the offsetÂ for the beams and a small reduction in the Youngâ€™s Modulus ofÂ the concrete. The updated FEA model frequencies are given inÂ italics in Figure 8.

Figure 9 shows a comparison of the FRF obtained from EMAÂ with that from updated FEA for TP04, the location of most livelyÂ response, assuming a damping value of 2.5% in the FEA in lineÂ with average of values from the modal test. The importantÂ features of the EMA in the frequency range of concern are recreatedÂ acceptably by the FEA.

For this type of structure the major concern is with vibrationÂ serviceability due to footfall-induced vibrations. Both FEA andÂ EMA results can be used for performance simulations usingÂ either published design guidance2, referred to as CSTR43, or byÂ direct simulation using measured ground reaction force (GRF)Â time histories as moving dynamic loads.

For a prototype structure, whose design may have beenÂ adjusted on the basis of such simulations using a-priori FEA,Â walking response measurements can be made as the finalÂ proof test of actable performance.

Figure 10 shows simulations using the updated FE modelÂ showing the response hotspot around TP04 for walking at 1.6Hz,Â exciting response in modes around 6.5Hz by the fourthÂ harmonic of the walking force fundamental frequencyÂ component. The simulations use first principles approaches ofÂ CSTR43 implemented using bespoke MATLAB software VSATs.Â The numerical values are â€˜R factorsâ€™ referenced to a RMSÂ acceleration value of 0.005m/sec2 calculated with a 1 secondÂ averaging time and with ISO-standard frequency weighting.

The structure is classed as a â€˜low frequency floorâ€™ because itsÂ performance with respect to footfall forces generated isÂ dominated by modes in which resonance can be generatedÂ by strong components of the walking force occurring at lowerÂ multiples of the pacing rate. High-performance (i.e. lowÂ response) floors typically found in hospitals and micro-chipÂ plants are classed as â€˜high frequency floorsâ€™ since their

response is dominated by rapid transient decay of modes withÂ frequencies above 10Hz due to the impulse-like forceÂ characteristic of individual footfalls.

Vibration tests as described in this study are often required toÂ demonstrate compliance of an as-built structure with designÂ specifications (i.e. a maximum R-factor, according to usage),Â while a-priori modelling, influenced by experience ofÂ model/test correlations of similar structures seeks to use bestÂ practice to predict performance capability beforeÂ construction, giving an opportunity to adjust a poor design.

The maximum R-value for the floor (over all pacing rates andÂ response points) is 7.3. This is just within acceptance limits for anÂ office floor.

With the main objective for this particular study being theÂ development of an active vibration control, the outcome ofÂ the experimental study has been generation of an appropriateÂ modal model for design of the AVC. Figure 11 shows on-siteÂ evaluation of the AVC designed using the EMA results. AVCÂ performance was assessed for controlled excitation, drivingÂ with one shaker and controlling with another, and for moreÂ usual (design) scenario of footfall loads due to a singleÂ pedestrian.

Figure 12 shows the success of the AVC in controlling responseÂ at the most lively point, TP04. The figure also shows the in-situÂ measured response to walking. The red lines are the RMSÂ envelope, and for the uncontrolled floor, the values are aÂ good match the predictions of Figure 10. The exerciseÂ demonstrates the capability of AVC system for significantÂ improvement in floor vibration performance.

Thanks go to Mr Jeremy Wells of WSP for providing access toÂ the test structure and for his assistance in the test logisticalÂ arrangements.

1. Diaz, I.M. and Reynolds, P. (2010) Acceleration feedbackÂ control of human-induced floor vibrations. EngineeringÂ Structures, Vol. 32, No. 1, January, pp. 163-173.

2. Pavic, A. and Willford, M. (2005). Vibration Serviceability ofÂ Post-Tensioned Concrete Floors. Appendix G in Post-TensionedÂ Concrete Floors Design Handbook, 2nd Edition. TechnicalÂ Report 43. Concrete Society. Slough, UK.

3. Brownjohn, J. M. W., Pavic, A. and Omenzetter, P. (2004) AÂ Spectral Density Approach for Modelling Continuous VerticalÂ Forces on Pedestrian Structures Due to Walking. CanadianÂ Journal of Civil Engineering, Vol. 31, No. 1, pp. 65-77.

4. Pavic, A., Brownjohn, J.M.W. and Zivanovic S. (2010). VSATsÂ software for assessing and visualizing vibration serviceabilityÂ based on first principles. ASCE Congress 2010, Orlando, Florida,Â USA, 12-15 May.

Author: | FSDL |

Category: | Case Study |

Date: | January 11, 2015 |

Author: | FSDL |

Category: | Case Study |

Date: | January 11, 2015 |

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