A study of the influence of different types of timber footbridges on the natural frequency of vibration. Vanessa Baño

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1 Vanessa Baño Vanessa Baño, J.Carlos Santos, Julio Vivas, Soledad Rodríguez, Abel Vega and Keith Crews A study of the influence of different types of timber footbridges on the natural frequency of vibration

2 In recent years in Spain demand for timber footbridges has increased considerably

3 In recent years in Spain demand for timber footbridges has increased considerably

4 In recent years in Spain

5 Normative SERVICIABILITY LIMIT STATE OF VIBRATION IN FOOTBRIDGES IAP-11. Regulation relating to loads in the design and planning of road bridges, 2011 VIBRATIONS Frequencies of risk of resonance (Hz) Vertical and longitudinal Verification by appropriate dynamic studies of the vibrational response when the bridge is of a new structural type or uses new materials (different to steel or concrete) SÈTRA, Service d Études techniques des routes et autoroutes Vertical natural frequency range classification Frequency (Hz) >5 Range 1 Range 2 Range 3 Range 4 Classification of pedestrian comfort and risk or resonance cuased by pedestrian traffic: Range 1. maximum risk of resonance Range 2. medium risk of resonance Range 3. low risk of resonance Range 4. negligible risk of resonance

60 Verification by appropriate dynamic studies of the vibrational response when the bridge is of a new structural type or uses new materials (different to steel or concrete) SÈTRA, 2006.

6 Objectives To evaluate the numerical and experimental frequencies of vibration of several timber footbridges To analyse the lower experimental frequencies of vibration in order to classify the footbridges by risk of resonance and comfort criteria To study the influence of span in natural frequency for first modal shape in bending To analyse the design of simple supported timber footbridges in relation to serviceability limit state of vibration

resonance and comfort criteria To study the influence of span in natural frequency for first modal shape in

7 Timber footbridges. design Design of simple supported timber footbridges studied Deck Joists Diagonals Main girders Secondary beams

8 Timber footbridges. dimensions Dimensions, cross section of main girders and mass L w w g h g m [m] [m] [mm] [mm] [kg] L (m) w (m) Determination of mass of bridges: volume (m 3 ) * Density (Kg/m 3 ), considering a general density of 550 Kg/m 3 (Pinus sylvestris) h g L=span of the bridge (m) w=width of the bridge (m) wg=width of main girder (mm) hg=height of main girder (mm) m=mass of bridge (kg) W g Eurocode 5 (UNE EN :2006) IAP-11 ROBOT Software

5 185 462 1601 7 5.8 1.5 185 330 974 w (m) 8 21.6 1.

9 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

10 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

11 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

12 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

13 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

14 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

15 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

16 Timber footbridges. dimensions L w w g h g m [m] [m] [mm] [mm] [kg]

17 Methodology Experimental tests Theoretical calculations Numerical calculations f1a f1b f1c Experimental natural frequency of first bending mode (Hz) Theoretical natural frequency of first bending mode (Hz) Numerical natural frequency of first bending mode (Hz) Dynamic tests Equation derived from closed-form solutions for pinned-pinned single span beams Using structural analysis software ROBOT

bending mode (Hz) Numerical natural frequency of first bending mode (Hz) Dynamic tests Equation

18 Dynamic tests

19 Dynamic tests CONFIGURATION PCB 3711B112G accelerometers: -sensibility: 1000 mv/g -measurement range: ±2g impact hammer accelerometers Data logging Cronos IMC Equipment IMC Devices software PCB 086D20 impulse force test hammer

range: ±2g impact hammer accelerometers Data logging

20 Dynamic tests CONFIGURATION impact hammer accelerometers Data logging Cronos IMC Equipment IMC Devices software

21 Dynamic tests CONFIGURATION impact hammer accelerometers Data logging Cronos IMC Equipment IMC Devices software Data processing IMC Famos FFT (Fast Fourier Transformation) LMS Test Lab Analisys of FRF: selection of modal shape and natural frequency

22 Dynamic tests MODAL SHAPES FRF

23 Dynamic tests CONFIGURATION

24 Dynamic tests

25 Results Evaluation of the numerical and experimental vibrational frequencies N. of Bridge EXP. THEOR. NUM. H g f 1a f 1b f 1c [%] [Hz] [Hz] [Hz] Hg = humidity of beams f1a = experimental natural frequency of first bending mode f1b = theoretical natural frequency of first bending mode calculated by Equation (1) f1c = numerical natural frequency of first bending mode calculated by ROBOT r= correlation coefficient r=0.995 r=0.994 High correlation coefficient between: experimental and theoretical results (0.995) experimental and numerical results (0.994)

26 Results Evaluation of the numerical and experimental frequencies of vibration EXP. THEOR. NUM. EXP.-THEOR. EXP.-NUM. THEOR.-NUM. f 1a f 1b f 1c Relative Error Relative Error Relative Error [Hz] [Hz] [Hz] % % % The relative error between experimental and theroretical results was of 19.1% The relative error between experimental and numerical results was of 17.5% The relative error between theroretical and numerical results was of 2.0% r=0.995 r= % 17.5% 2.0% There has not been a good estimation of the mass of footbridges in order to predict the theoretical and numerical natural frequencies.

27 Results Classification of the footbridges by comfort criteria and risk of resonance span EXP. Resonance Risk N. of Bridge [m] f 1a [Hz] IAP-11 SETRA (>4.6 Hz) No risk (>5 Hz) Range (>4.6 Hz) No risk (>5 Hz) Range (>4.6 Hz) No risk (2.6-5 Hz) Range (>4.6 Hz) No risk (>5 Hz) Range (>4.6 Hz) No risk (2.6-5 Hz) Range (>4.6 Hz) No risk (>5 Hz) Range (>4.6 Hz) No risk (>5 Hz) Range (<4.6 Hz) Low risk (2.6-5 Hz) Range 3 Range 3. low risk of resonance Range 4. negligible risk of resonance All footbridges studied presented no risk or low risk of resonance in vertical vibrations for pedestrian walking

28 Results Influence of span in natural frequency for first modal shape in bending There was a decreasing relationship between the natural frequency of the first bending mode and the span for the experimental results of these 8 timber footbridges. The simple supported and straight timber footbridges with a span longer than 20 m and a width between 1.5 and 2 m presented first frequencies of vibration lower than 5 Hz. A span between 20 and 25 m could be the limit of manufactured timber footbridges with this design according to serviceability limit state of vibration (comfortability).

29 Thank you for your attention Vanessa Baño J.Carlos Santos Julio Vivas Soledad Rodríguez Abel Vega Keith Crews

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