FLOOR VIBRATIONS FREQUENTLY ASKED QUESTIONS AND MORE Presentation is based on AISC/CISC Design Guide 11 and SJI Technical Digest 5 2 nd Ed. Presented by Thomas M. Murray, Ph.D., P.E. Emeritus Professor Virginia Tech, Blacksburg, Virginia thmurray@vt.edu Vibe v2.20 Software for Analyzing s for Vibrations Criteria Based on AISC/CISC Design Guide 11 SJI Technical Digest 5 SEAoT DALLAS CHAPTER Janurary 15, 2015 1/691 SEI Structural Engineers, Inc. 537 Wisteria Drive Radford, VA 24141 540-731-3330 Fax 540-639-0713 tmmurray@floorvibe.com http://www.floorvibe.com 2/69 Questions Concerning Design for Walking Excitation What is the power of Resonance? 3/69 4/69 1
The Power of Resonance Phenomenon of Resonance Response 0 1 2 1-3% Damping 5-7% Damping Natural frequency, f n Forcing frequency, f 5/69 Resonance occurs when a multiple of the forcing function frequency equals a natural frequency of the floor. We are usually concerned with the first natural frequency. Resonance can occur because of walking dancing, or exercising. Note: Walking step frequency range is 1.6-2.2 Hz (96 to 132 bpm) 6/69 Harmonics Footstep = = α i Pcos( 2πif t) 1st Harmonic α 1 P f 1 = 1 step f step Why do some walkers cause more floor motion then other walkers? 2nd Harmonic α 2 P f 2 = 2 f step 3rd Harmonic α 3 P f 3 = 3 f step 7/69 8/69 2
Response from a Lightly Damped Why do some walkers cause more floor motion then other walkers? Because their pace is a sub-harmonic of the floor dominant frequency. That is, a harmonic of their walking speed, i.e. 2 or 3 times their walking speed, matches the floor dominant frequency. Measured Autospectrum (Peak, %g) 0.5 0.4 0.3 0.2 0.1 Walking Speed 100 bpm System Frequency 5 Hz 3 rd Harmonic 2 nd Harmonic 3.33 Hz 9/69 0 0 1 2 3 4 5 6 7 Frequency (Hz) 10/69 What is new in SJI TD5? Peak Acceleration (% Gravity) 25 10 5 2.5 1 0.5 0.25 Rhythmic Activities Outdoor Footbridges........................ Indoor Footbridges, Shopping Malls, Dining and Dancing........................ Offices, Residences........................ DG11 TD5 Use the Modified ISO Scale Considering Resonance 0.1 0.05 ISO Baseline Curve _ 11/69 1 3 4 5 8 10 25 40 Frequency (Hz) 12/69 3
DG11 and TD5 Walking Criterion DG11 and TD5 Walking Criterion a g p Predicted Tolerance = P o exp( 0.35f βw n ) a g o a p = peak acceleration a o = acceleration limit g = acceleration of gravity f n = fundamental frequency of a beam or joist panel, or a combined panel, as applicable P o = a constant force equal to 65 lb for floors and 92 lb for footbridges β = modal damping ratio (0.01 to 0.05) ap Po exp( 0.35fn) ao = g βw g W = effective weight supported by the beam or joist panel, girder panel, or combined panel, as applicable 13/69 14/69 DG11 and TD5 Walking Criterion Tolerance Acceleration Limits Updated Tolerance Occupancy Acceleration Limit a o /g x 100% Offices, Residences 0.5% 0.55% Assembly Areas, Churches, Schools 0.5% 0.55% Shopping Malls 1.5% Indoor Footbridges 1.5% Outdoor Footbridges 5.0% DG11 and TD5 Walking Criterion Improved Approach for Estimating Modal Damping Structural System 1% Ceiling and Ductwork 1% Electronic Office Fit-out 0.5% Paper Office Fit-out 1% Churches, Schools, Malls 0% Dry Wall Partitions in Bay 3% to 5% 15/69 Note: Damping is cumulative. 16/69 4
Fit out Condition: Electronic Office. Limited number of file cabinets. No fullheight partitions, suspended ceiling and ductwork below. Estimated Damping: Structure 1% Ceiling & Ductwork 0% Electronic Office 0.5% Damping 1.5% Fit out Condition: Paper Office. Suspended ceiling or ductwork below. No full height partitions. Estimated Damping: Structure 1% Ceiling & Ductwork 1% Paper Office 1% Damping 3% 17/69 18/69 How accurate are the AISC DG11 and SJI TD5 procedures? 19/69 How accurate is the DG11 procedure? Framing No. of Bays Agreement DG11 Procedure Percent Agreement Hot-Rolled Framing 50 48 of 50 96% Joists w/ Hot-Rolled Girders 27 26 of 27 96% Joists w/ Joist Girders 22 22 of 22 100% Castellated Beams 6 6 of 6 100% ALL 105 102 of 105 97% Data from a study being conducted at the University 20/69 of Kentucky by Dr. Brad Davis. 5
No recommendations are given in DG11 for public areas like airport terminals, lobbies, etc. What do you recommend? No recommendations are given in DG11 for public areas like airport terminals, lobbies, etc. What do you recommend? 1.0%g based on personal experience of spending many hours sitting at airline departure gates. (Recommendation will be included in AISC DG11 2 nd Ed.) 21/69 22/69 Why is the full composite moment of inertia used in the frequency calculations even when the beam, joist or girder is non-composite? Why is the full composite moment of inertia used in the frequency calculations even when the beam or girder is noncomposite? f n = 0.18 g/( b + g ) ( ) = 5wL 4 / 384Es It 23/69 Annoying vibrations have displacements of 0.001-0.010 in. Thus, the interface shear is negligible, so its acts as fully composite for vibration analyses. 24/69 6
Does camber affect beam or girder frequency? Prestressing? 25/69 Does camber affect beam or girder frequency? No! Classical frequency equation: 1/ 2 π ge = s It fn wl 4 is not part of equation. 2 Substituting = 5wL 4 /( 384Es It) Results in = 0.18 g/ fn 26/69 Is there a lower frequency limit? Is there a lower frequency limit? To avoid resonance with the first harmonic of walking and rogue or vandal jumping, the minimum frequency should be greater than 3 Hz, e.g. f n > 3 Hz (Required in the British building code.) 27/69 28/69 7
How do I determine floor width and floor length when calculating effective panel weights, W b and W g? Beam Panel: Wj = (w j / s)bjl Beam Panel Width j ap Poexp( 0.35fn) ao = g βw g j W = + j g W j g + + j g W g W B j = Beam Panel Width B j = C j (D s /D j ) 1/4 L j 2/3 Width 29/69 30/69 Effective Girder Panel Width Girder Panel: W g = (w g /L j,avg )B g L g ) B g = Girder Panel Width B g = C g (D j /D g ) 1/4 L g 2/3 Length A B D C Bay A B C D Width and Length Example Width Length 31/69 32/69 8
Width and Length Example Width and Length Example A B C D A B C D Bay Width Length A 90 90 B C D 33/69 Bay Width Length A 90 90 B 150 90 C D 34/69 Width and Length Example Width and Length Example A B C D A B C D Bay Width Length A 90 90 B 150 90 C 150 30 (45?) D 35/69 Bay Width Length A 90 90 B 150 90 C 150 30 (45?) D 30 90 36/69 9
B g = C g (D j /D g ) 1/4 L g 2/3 Length B g = C g (D j /D g ) 1/4 L g 2/3 Length Bays A & B Bg = 59.9 <2/3 L 37/69 38/69 B g = C g (D j /D g ) 1/4 L g 2/3 Length Bays A & B Bg = 59.9 <2/3 L Bays A: Length = 81 e.g. (32.5 + 16 + 32.5 ) Bg=2/3x81 = 54 < 59.9 a p /g=0.46%g < 0.5% B g = C g (D j /D g ) 1/4 L g 2/3 Length Bays A & B Bg = 59.9 <2/3 L Bays A: B g = 54 ap/g=0.46%g < 0.5% OK Bay B: Length = 48.5 e.g. (32.5 + 16 ) 2/3x48.5 =32.3 < 59.9 ap/g=0.61%g > 0.5%g NG 39/69 40/69 10
How do I modify a design that does not satisfy the criterion? How do I modify a design that does not satisfy the criterion? Increase stiffness of the element with the lower frequency to improve performance. 41/69 42/69 W21 44 W14 22 W18 35 S W14 22 W21 44 4 SPA @ 7-6 =30 = L g L = 45 j Example: Bay D of previous example. W14 22 W24 55 d = 3.50 + 2.00 e = 4.50 2 W18 35 Section 3.50 2.00 Width = 30 ft Length = 90 ft Paper Office 43/69 Original Design W18x35 f b = 3.76 hz f n = 3.08 Hz W24x55 f g = 5.37 hz a p /g=0.74%g Improved Design Increase Concrete Thickness 1 in. W18X35 f b = 3.75 hz f n = 3.04 Hz W24x55 f g = 5.28 hz a p /g=0.65%g 44/69 11
Original Design W18x35 f b = 3.76 hz f n = 3.08 Hz W24x55 f g = 5.37 hz a p /g=0.74%g Improved Design Increase Girder Size W18X35 f b = 3.76 hz f n = 3.33 Hz W24x84 f g = 7.17 hz a p /g=0.70%g 45/69 Original Design W18x35 f b = 3.76 hz f n = 3.08 Hz W24x55 f g = 5.37 hz a p /g=0.74%g Improved Designs Increase Beam Size W21x50 f b = 4.84 hz f n = 3.57 Hz W24x55 f g = 5.29 hz a p /g=0.58%g W24x55 f b = 5.22 hz f n = 3.71 Hz W24x55 f g = 5.28 hz a p /g=0.50%g 46/69 Question Concerning Design for Rhythmic Excitation I am designing a floor in a health club that will be used for aerobics. Why are my required members so large? 47/69 48/69 12
I am designing a floor in a health club that will be used for aerobics. Why are my required members so large? Resonance with the first, second and third harmonics of the activity must be avoided. Footstep = α i P cos ( 2π if t) step f step = 1.5 Hz to 2.5 Hz (90 bpm to 150 bpm) i = 1, 2, 3 which means f n > 7.5 Hz Vibrations s and More (as in current research) 49/69 50/69 Long Span (> 25 ft)eck s Long Span (> 25 ft)eck s Single 30 ft by 30 ft bay constructed and tested at the Virginia Tech. Supported only at the perimeter with W21x44 girders an W14x22 beams. 51/69 52/69 13
Long Span (> 25 ft)eck s Long Span (> 25 ft)eck s If the deck is supported by beams, it will probably be a low frequency floor (f n < 9-10 Hz) and provisions in DG11 or TD5 can be used. If the deck is supported by walls, it will probably be a high frequency floor (f n > 9-10 Hz) and further analysis will not be necessary. Low Frequency : Provisions in DG11 or TD5 can be used. Analyze assuming 1 ft width of slab is equivalent to a beam. 1 ft 53/69 54/69 Long Span (> 25 ft)eck s Low Frequency Analysis Model Analysis of Slender Stairs 55/69 56/69 14
Analysis of Slender Stairs Loading is much more severe than walking on floors: Much faster. More synchronization. If linear or near linear model as a beam. Linear Near Linear 57/69 Analysis of Slender Stairs How do I evaluate a slender stair design? 1/2 Frequency: π ge = s It 2 wl 4 Predicted Acceleration: f n 2 L = Stringer Length a p R α Qcos φ (1 exp( 100 β )) a o = g βw g Tolerance Acceleration: 1.7 to 4.6%g 58/69 Analysis of Slender Stairs References Davis, B. and Murray, T.M. (2009). Slender Monumental Stair Vibration Serviceability. J. Architectural Engineering, 15(4), 111 121. Alternate Bay Framing Davis, B. and Avci, O. (2015 In Press) Simplified Vibration Serviceability Evaluation for Slender Monumental Stairs. Journal of Structural Engineering. 59/69 60/69 15
Alternate Bay Framing Alternate Bay Framing Advantages: Eliminates back-to-back connections Improved speed of erection Shallower Girder Depth Added space for MEP Systems Lower floor-to-floor height Improved Vibration Performance Improved occupant satisfaction 61/69 62/69 Alternate Bay Framing Alternate Bay Framing Disadvantages: May be Added Tonnage Minor increase in overall weight Increased Amount of Deck Closure Strips Increased material and labor Odd Shear Stud Layout at Girders Potential for improper layout Coordination of Deck Layout 63/69 64/69 16
Alternate Bay Framing Disadvantages: Better with Bays with Aspect Ratios Close to 1:1 Current AISC DG11 Procedures Over Predict Vibration Response Alternate Bay Framing Modified DG11 Analysis Procedure: ap Poexp( 0.35fn) ao = g βw g f n =min (beam and girder frequencies) Width = Girder Span Length = Beam Span + 1/2 Adjacent Beam Spans 65/69 66/69 Alternate Bay Framing Combined Mode Panel: Strength is essential but otherwise unimportant. Hardy Cross 67/69 68/69 17
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