Structural systems for glulam arch bridges

Transcription

1 ICTB Lillehammer, September 12-15, 2010 Structural systems for glulam arch bridges Kolbein Bell professor emeritus The Norwegian University of Science and Technology Trondheim, Norway 1

2 Types of arch bridges preferable 2-hinge or 3-hinge most common 2

3 Some typical glulam arch bridges built recently in Norway in the 25 to 40 m span range 3

4 Nybergsund 4

5 Tynset 5

6 Flåm 6

7 Måsør 7

8 Horne bru 8

9 All these bridges were designed to meet the requirements of the Norwegian Timber Code NS 3470 However, NS 3470 is now history From April 2010 our timber bridges will have to meet the requirements of Eurocode 5 (EC5) 9

10 and EC5 is not kind to the typical Norwegian arch bridge design kmod and Major issues γ M k h kvol kdis volume effects (,, ) k m k cr bending and shear ( and ) combined τ d and σ τ σ d t,90, d t,90, d + 1 fv, d kdiskvol ft,90, d the quality of glulam L40 from GL36c to GL28c 10

11 Example 11

12 Short term loading in service class 3 Capacity ( κ ), in % of ultimate limit strength Numbers in parentheses are the ratio NS EC5 κ κ 12

13 Cont. Capacity ( κ ), in % of ultimate limit strength Numbers in parentheses are the ratio NS EC5 κ κ 13

14 Hanger arrangements for medium span length m 14

15 13,0 kn/m additional 19,5 kn/m Light timber deck 300 kn 2D 2-hinge fails miserably EC5 apparently OK 15

16 However hangers relax and become up to 50 mm shorter buckle with an amplitude of approx. 500 mm Not acceptable! unless 16

17 17

18 Heavy concrete deck tie rod 18

19 2D analyses the winner No relaxing hangers Most unfavorable load positions with respect to sections A, B, C and D 19

20 3D analyses of design C No rotation No additional transverse stiffening free rotation MODEL 20

21 Buckling analysis dead load only (no load factor) 1 st buckling mode buckling factor = 5,25 21

22 Buckling analysis Traffic load only (dead load constant) (including load factor) 1 st buckling mode buckling factor = 5,15 2 nd buckling mode buckling factor = 7,80 22

23 Nonlinear static analysis for full traffic and wind loading Max. horizontal displacement 1,5 kn/m δ H = 95 mm Displacements 23

24 Findings - design C A cross section of b x h = 800 x 600 mm is only slightly overstressed (105%) in combined bending and axial compression (shear and tension perp. to grain is OK) EC5 with γ M = 1,15 This statement also applies to a 3-hinge arch design 24

25 Hanger arrangements for large span length 100 m Network arches 25

26 Glulam: GL28c Concrete deck: x 350 (two lanes) Loading : Additional dead load: 10 kn/m per arch (asphalt & railing) Distributed traffic load: 13 kn/m per arch Three concentrated traffic loads, each 300 kn, per lane Wind load: 1,0 kn/m per arch 26

27 Hanger arrangements 2D model constant α = 60 deg 29 arch segments; two lengths x 29 equal arch segments 27

28 Preliminary 2D analyses Alternative a : ample capacity Alternative b : sufficient capacity Alternative c : sufficient capacity continue with c 28

29 3D analysis one arch MODEL Buckling analysis same BC as before dead load only buckling factor = 0,91 29

30 Full 3D model 30

31 Buckling analysis only traffic load varies mode # 1 # 2 buckling factor = 7,7 buckling factor = 13,3 (dead load only: buckling factor = 4,9 ) 31

32 Design check based on 3D nonlinear static analysis of bridge subjected to short term loading consisting of dead load (with load factor = 1,2) wind load (with load factor 1,0) traffic load (with load factor = 1,3) and Eurocode 5 for service class 3 and stage 1 stage 2 γ M = 1,15 ULS capacity: combined bending and compr. 103 % shear 40 % tension perp. to grain 30 % 32

33 Stiffness Deformations from nonlinear ULS analysis with critical loading arch: 50 mm arch: 120 mm deck: 155 mm 33

34 Free vibration analysis 34

35 Free vibration analysis, cont. 35

36 The proposed design, which is in no way optimized, is believed to be feasible but there are many challenges: the casting of the concrete deck the tie rod (tension of 8000 kn!) the hangers (change of length) the arch (glued or mechanically joined?) connection between arch and foundation joint between hanger and arch 36

37 Standard connection 37

38 Proposed connection (in principle) 38

39 Thank you for your patience 39