DESIGN AND ANALYSIS OF A SIMPLE SUSPENDED CABLE FOOTBRIDGE LOCATED IN A NARROW CANYON CHRISTOS K. DIMOU

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1 DESIGN AND ANALYSIS OF A SIMPLE SUSPENDED CABLE FOOTBRIDGE LOCATED IN A NARROW CANYON CHRISTOS K. DIMOU DEPARTMENT FOR HYDROELECTRIC PRODUCTION PUBLIC POWER COMPANY S.A. AGHISILAOU 56-58, ATHENS, GR-04 36, GREECE C.DIMOU@DEI.COM.GR

2 Outline of Presentation The analysis and design of a slender cable footbridge located in a narrow canyon is presented. The design of the bridge is governed by the Wind Loads The parameters governing the wind profile and their effect on wind speed are identified The wind load distribution and the characteristic Wind Speed are calculated. The resulting Wind Loads are combined with pedestrian, snow, ice and earthquake loads, following the provisions of Eurocodes

3 Location of Bridge

4 Location of Bridge

5 Location of Bridge

6 Location of Bridge

7 Location of Bridge

8 Photorealism

9 Bridge Parameters - Analysis Μέγεθος l 87.40m El 44.70m max El 40.70m min f min h El El 4.00m b d d max (4 b -h) 6 b d l maxpp min 55.70m H m F El f H =9.87m b,max PP min min max PP b H m min F F El f H =7.87m min F T h T Wl C 8b d T h cos tan 4 T c b d h l T N

10 Wind Loads Average Wind Speed Vb c dir c season Vb,0 Vb 7.00 m / sec Vm z cr z ct z Vb Vm z cfunnel cr z ct z Vb Funnel Effect Roughness Orography EN 99--4

11 ENERGY CONSERVATION Wind Loads Funnel Effect dynamic p p static m z c c z c z V funnel r t b

12 CONSERVATION OF MOMENTUM Wind Loads Funnel Effect V V p R T T p R = K

13 Wind Loads Funnel Effect - Assumptions Assumptions Constant Flow Perfect Liquid c funnel Incompressible flow (constant within a fluid parcel - infinitesimal volume - moving with the flow velocity) No significant change in manometric pressure

14 Wind Loads Topography

15 Wind Loads Effect of Water Level 87.4Χ00Χ46.30 z w =375.0m 87.4Χ00Χ46.30 z w =366.0m

16 Μέγιστη Ταχύτητα Ανέμου Wind Loads Characteristic Length s i N V w V i i w i i b ;0; s i b ;0; s s {/00, /5, /.5, /0, /9, /8, /7, /6, /5, /4, /3, /,,, 5, 0} L b Wind Loads Seasonality Wind Directionality Συσχέτιση Μέγιστης Ταχύτητας Ανέμου και Διεύθυνσης (Άρδασσα Κοζάνης) y = x R = y = 6E-07x x x R = Διεύθυνση Ανέμου i 0 i Max of Max Wind Speed 9 8 N w 7 i S????? Max of Average Wind Speed

17 Wind Loads Directionality & Water Level.400 Λόγος V/V.400 Λόγος V/V North Wind South Wind North Wind South Wind V/V S=8.74m V/V S=87.40m Στάθμη Ταμιευτήρα (m) Στάθμη Ταμιευτήρα (m).400 Λόγος V/V.400 Λόγος V/V North Wind South Wind North Wind South Wind V/V V/V S=43.70m.0 S=874.0m Στάθμη Ταμιευτήρα (m) Στάθμη Ταμιευτήρα (m)

18 Wind Loads Average Speed Ταχύτητες Ανέμου και Στάθμη z (Άνεμος από ανάντι) Ταχύτητες Ανέμου και Στάθμη z (Άνεμος από κατάντι) s=87.4m s=87.4m Ταχύτητα (m/sec) z w =366.0m cr x ct x Vb 0.00 Vm 0.00 z Απόσταση Χ του Άξονα της Γέφυρας Στάθμη z (m) Ταχύτητα (m/sec) cr x ct x Vb Vm z z w =366.0m Απόσταση Χ του Άξονα της Γέφυρας Στάθμη z (m) V m NL c z c z c V l c z c z l r, i t, i funnel b i r, i t, i i c NL funnel Vb NL l i NL l i

19 Wind Loads Average Speed Μέση Ταχύτητα Vm Μέση Ταχύτητα Vm Vm (m/sec) S=0.874m S=5.86m S=6.99m S=8.74m S=9.7m S=0.95m S=.485m S=4.566m S=7.48m S=.85m S=9.33m S=43.7m S=87.4m S=74.8m S=437m S=874m Vm (m/sec) S=0.964m S=6.47m S=7.7m S=9.640m S=0.7m S=.05m S=3.77m S=6.07m S=9.8m S=4.0m S=3.3m S=48.0m S=96.40m S=9.8m S=964.0m S=48.0m Στάθμη Ταμιευτήρα (z) (m) Vm 73.0 kmh Στάθμη Ταμιευτήρα (z) (m) 5.00 V k,m (Φόρτιση από Βόρρα - Ανάντι του w =366.0m 5.00 V k,m (Φόρτιση από Νότο - Κατάντι του ποταμού) Ταχύτητα Ανέμου (m/sec) Ταχύτητα Ανέμου (m/sec) Στάθμη Ταμιευτήρα (m) Στάθμη Ταμιευτήρα (m)

20 Wind Loads Wind Pressure Μέσo Φορτίο q m Μέσo Φορτίο q m q m (N/m ) S=0.874m S=5.86m S=6.99m S=8.74m S=9.7m S=0.95m S=.485m S=4.566m S=7.48m S=.85m S=9.33m S=43.7m S=87.4m S=74.8m S=437m S=874m q m (N/m ) S=0.874m S=5.86m S=6.99m S=8.74m S=9.7m S=0.95m S=.485m S=4.566m S=7.48m S=.85m S=9.33m S=43.7m S=87.4m S=74.8m S=437m S=874m Στάθμη Ταμιευτήρα (z) (m) q k,m (Φόρτιση από Βόρρα - Ανάντι του ποταμού) qk w =366.0m Στάθμη Ταμιευτήρα (z) (m) q k,m (Φόρτιση από Νότο - Κατάντι του ποταμού) Ανεμοφορτίο (q(n/m )) Ανεμοφορτίο (q(n/m )) Στάθμη Ταμιευτήρα (m) Στάθμη Ταμιευτήρα (m)

Design Loads (Static & Dynamic) q f, k Static Loads 0.0 kn/m L 30 (Eq. 5. par. 5.3.. EN-99-).5 5.0 kn/m q f, k Q b q 0.70 3.0=.

21 Design Loads (Static & Dynamic) q f, k Static Loads 0.0 kn/m L 30 (Eq. 5. par EN-99-) kn/m q f, k Q b q =.6kN/m f, k Dynamic Loads Stoyanoff, S., Haskett, T., Pridham, B., Hunter, M. and Zoli, T. (007). Pedestrian-induced vibrations on footbridges: advanced response analysis, Bridge Structures, 3:3, 9-45

22 Wind Loads (Q w ) q b V m, eq q [ 7 I ] V k V m, eq Q q max A 0.3 A, 0.3 A A W k p, equiv, Y p, equiv, Z p, equiv, Y p, equiv, Z A c A A c A p, equiv, Y f, s, Y real, Y p, equiv, Z f, s, Z real, Z Q w 3.800kN/m Note: Increased likelihood of the maximum Wind Speed coinciding with low water level of the reservoir

23 Snow Loads (Q s ) s k, A sk,0 A 97 A 500m Q S b s k, A QS, esl cesl b sk, A Q s 0.76kN/m Q s, ecl.453kn/m

24 Ice Loads (Q k,ice ) Wind on Ice (Q k,w ) Q W q k max A 0.3 A, p, equiv, Y, ice p, equiv, Z, ice 0.3 A A p, equiv, Y, ice p, equiv, Z, ice Q k, ice 0.848kN/m Ap, equiv, Y, ice cf, s, Y, ice Areal, Y, ice Ap, equiv, Z, ice cf, s, Z, ice Areal, Z, ice Q kw, 3.875kN/m ISO 494:00 Atmospheric icing of structures

25 Load Combinations (EN 990, EN 997) LC# γ G G+γ Q Q+ψ w γ w Q w LC# γ G G+ ψ Q,w γ Q Q+γ w Q w LC#3 γ G G+ ψ w γ w Q w +γ S Q S,ecl LC#4 γ G G+ γ w Q w + ψ S γ S Q S LC#5 γ G G+ γ k,ice Q k,ice + k k,w ψ k,w γ k,w Q k,w LC#6 γ G G+ ψ k,ice γ k,ice Q k,ice + k k,w γ k,w Q k,w LC#7 G+A Ed,Y LC#8 LC#9 G A Ed,Y G+A Ed,Z A Ed 0.94kN/m LC#0 G A Ed,Z

26 Design Loads q D (kν/m) Value LC # 6.05 LC # 8.37 LC # LC # LC # LC # LC #7.065 LC # LC #9.065 LC #0 0.35

27 Dynamic Response Max Acceleration Human Load Max Acceleration (EN99) a 0.5 fh a 0.70 (m/sec ) Max Bridge Acceleration a N N w c N a p 0.5 R m deck l N ln C C C N C 0.75 C 0.0 Rmin Rmax R R max R min C exp N N R max N max Non associated mass m add N N w c N p a g R Stoyanoff, S., Haskett, T., Pridham, B., Hunter, M. and Zoli, T. (007). Pedestrian-induced vibrations on footbridges: advanced response analysis, Bridge Structures, 3:3, 9-45

28 Free Vibration of Cables dx u u t T m s ds s t dy t T m mg s ds s t w w t T m s s t n Th, n,,..., l m t n l, a, n n l T h m n,,..., 3 4 8bd l bd tan l l l L 8 e l l ThL l e E c Ac Irvine H.M., Caughey T.K. (974). The linear Theory of Free Vibrations of a Suspended Bridge. Proc. R. Soc. Lond A., 34,

Bridge Dynamic Characteristics ω trans =4.80 Hz f 0,h = f t = 0.764 Hz ω l,a =9.60 Hz f l,a =.58 Hz ω l,s =8.99 Hz f l,s = f 0,V =.

29 Bridge Dynamic Characteristics ω trans =4.80 Hz f 0,h = f t = Hz ω l,a =9.60 Hz f l,a =.58 Hz ω l,s =8.99 Hz f l,s = f 0,V =.430 Hz λ =09.9 Irvine H.M., Caughey T.K. (974). The linear Theory of Free Vibrations of a Suspended Bridge. Proc. R. Soc. Lond A., 34,

30 Dynamic Excitation Various Scenarios c a N c f, f, f, f, res, fac 0 res, fac 0, v, v 0 N w c N a f p R 0.5 m f, f, f f deck l f 0 0 a 0.4 f 0.95 a f.8 Hz a 0.065,0.00, h ζ=0.5%, wp=700n (basic scenario) ζ=.0%, wp=700n (optimistic scenario) ζ=0.5%, wp=850n (pessimistic scenario) see «Zivanovic, S., Pavic, A. and Reynolds, P. (005) Review vibration serviceability of footbridges under human-induced excitation: a literature review. J. Sound Vibrat., 79, 74», for P. Young, Improved floor vibration prediction methodologies, ARUP Vibration Seminar, October 4, 00 f

31 Results Accelerations (no Windguys) Κατακόρυφες Επιταχύνσεις Πεζογέφυρας Εγκάρσιες Επιταχύνσεις Πεζογέφυρας ζ=0.5%, wp=700n N= N= 6.0 ζ=0.5%, wp=700n N= N= 0.0 N=3 N=4 N=5 N=0 5.0 N=3 N=4 N=5 N=0 a v (m/sec ) N=5 N=0 N=30 N=40 N=50 N=60 a h (m/sec ) N=5 N=0 N=30 N=40 N=50 N= N=70 N=80.0 N=70 N= (f) Συχνότητα Βάδισης (Hz) (f) Συχνότητα Βάδισης (Hz)

32 Results Dynamic Characteristics (no windguys) Δυναμικά Χαρακτηριστικά Πεζογέφυρας Κυκλική Ιδιοσυχνότητα (Hz) λ ω,v ω,t ω,v,s <ω,v,a Τιμή λ Οριζόντια Δύναμη Καλωδίων (kn) 0

33 Results Accelerations (no Windguys) Κατακόρυφες Επιταχύνσεις Πεζογέφυρας Εγκάρσιες Επιταχύνσεις Πεζογέφυρας.6E+0.0E+0 ζ=0.5%, wp=700n N= N= N= N=.E+0 N=3 N=4 N=5 N=0 8.0E+00 N=3 N=4 N=5 N=0 a v (m/sec ) 8.0E+00 N=5 N=0 N=30 N=40 N=50 N=60 N=70 N=80 a h (m/sec ) 6.0E E+00 N=5 N=0 N=30 N=40 N=50 N=60 4.0E+00.0E+00 N=70 N=80 ζ=0.5%, wp=700n 0.0E (f) Συχνότητα Βάδισης (Hz) 0.0E (f) Συχνότητα Βάδισης (Hz)

34 Effects of Windguys Additional Rigidity in lateral and vertical axes of the Bridge Vibrational decoupling for the lateral and vertical direction Combination of cables with different dynamic characteristics deamplification of dynamic motion Added safety (increase of number of elements contributing to the dynamic stability of the bridge) More complexity Complex Geometry Final Geometry dictated by the topography and geo-technical characteristics of the site.

35 Conclusions The analysis and design of a slender cable footbridge located in a narrow canyon is presented. The effect of the narrow canyon is also considered in the analysis. A complex wind profile is expected. Wind intensity is expected to vary considerably along the axis of the bridge. Wind Loads (with or without ice) are governing the design. Windguys are needed to increase rigidity, induce vibrational de-coupling and de-amplification of stresses/strains and increase the bridge s safety and usability. Windguys increase the complexity of the design and for the particular problem dictated the design shape of the bridge.

36 Thank you for your Attention

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