Steel Pipe Bridges in Sweden Detailed Design Procedures

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1 Steel Pipe Bridges in Sweden Lars Pettersson, Skanska Sweden AB, Major Projects

2 In Sweden Steel Pipe Bridges are structurally designed according to a andbook developed by te oyal Institute of Tecnology (KTH) in Stockolm. Te bridge codes require te andbook to be used in te design of steel pipe bridges

3 Te design metod is based on te following important parts: Duncan: Soil Culvert Interaction metod Klöppel & Glock: buckling calculations Andréasson: soil modulus for frictional materials Te design metod as been verified by several full scale test results many of wic ave been performed in Sweden

4 In te bridge codes requirements for te design of steel pipe bridges are given. Te Swedis andbook complement te bridge code requirements by adding structural design requirements. a 3 D a 3 a 5 4 c a H 1 Border for natural soil 1:n 1 1:n 2 a 2 a 1 D a

5 Backfilling soil requirements in te bridge codes may serve as an example of ow te codes and te andbook complement eac oter:

6 Steel Pipe Bridges Seven different steel pipe profiles, wic cover most of te profiles available on te market, are defined in te andbook: t c b c D H c H D c H D c t s b D H c s t b H D s t c c H D H c t s ak del Straigt section equirements for te relation between different radii are indicated.

7 Two types of load are of importance in te structural design of steel pipe bridges; soil load and live (traffic) load. Live load; example from te Swedis bridge code

8 Te radial soil pressure will result in normal forces in te corrugated pipe wall. In case tese radial soil pressures were constant all around te culvert profile no bending moments would arise in te culvert wall. But since tat is not te case and backfilling operations will lock-in certain bending moments te culvert will not be free from bending moments. c=0 c

9 Te effect of so called arcing is included in te design model. Negative arcing, wic occurs at low eigts of cover, and positive at iger eigts of cover are calculated. Te diagram sows te normal force in te culvert wall as a portion of te overburden load. Normal force (kn) Arcing, example, D = 6 m, circular profile ,0 2,0 4,0 6,0 8,0 10,0 12,0 Heigt of cover (m) N,j (arcing not included) N,j (arcing included) N,j (ring-compression-metod)

10 Te live load is converted into an equivalent line load. Tis is done using te Boussinesq equations for loads acting on an elastic alfspace. A line load is calculated tat will produce te same vertical pressure at a dept equal to te dept of cover as te maximum vertical pressure tat will be produced by te live load itself. v 2 s 3 c 5 3 P Vertical pressure Point loads v 2 p z Y lcases "Ekv. load 2" lcases "Klass Last a" lcase lcasef X max v 85.5kPa at te point: x vmaxi y vmaxi ( 0 2.2)m loops

11 In te diagram below calculated equivalent line loads at different eigts of cover for live loads in te Swedis bridge code Bro 2004 are sown: Equivalent load type 1 Equivalent load type 2 Equivalent load type 4 p traffic/(kn/m) c/m

12 ailroad live loads can be treated te same way as road live loads. Te distribution of te concentrated axle loads troug te sleeper is elpful to reduce te load on te pipe. An equivalent line load is calculated according to te same principles as for live load on a road. 200,0 180,0 160,0 c b Equivalent line load /kn 140,0 120,0 100,0 80,0 60,0 40,0 Single track Double track H Sleeper Ballast 20,0 0,0 0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00 c /m Engineered soil D

13 Te radial soil pressure will introduce normal forces into te pipe but at te same time te soil will stabilize te culvert wall. It is quite easy to realize tat a soil tat will give a ig resistance against culvert wall movements will also lead to a iger load bearing capacity for te soil pipe structure. Terefore it is important tat te structural design procedures take te soil quality into account. Load at calculated failure (kn) P (%) c = 0.75 m c = 1.0 m Te diagram sows a calculated axle load at failure (witout safety factors) for a 6 m span structure at two different eigts of cover for different degrees of compaction (std P)

14 Using a large number of FEM-calculations and te results from full scale tests te following equations for calculating normal forces and bending moments as been developed: Soil load Live (traffic) load Normal forces H H N D S D D D D D 2 c,red c,red 2 j 0, 2 1 ar 0,9 0,5 cv Nt ptraffic ( D/2) q N (1,25 / D) p ( D/ 2) q t c,red traffic N 0,5 p ( D/ 2) q t traffic Bending moments 0,75 3 cv c t j / ,surr ar 1 2,cover 1 D s M D f f f S f f 0,75 IV t t traffic ar 1 2,cover s M f f f f Dp S f f qd

15 Bending moments are dependent on te relative stiffness between te pipe and te surrounding soil. A stiffness ratio is used in te calculation according to te following equation: 3 f EjdD /( EI) s Since te soil is non-linear it is necessary to define a soil modulus tat is representative for te structure at and. Tis is done by calculating te soil modulus at a stress level equal to te stress at te quarter points

16 Te structural design is done as a limit state design. Design cecks are performed in te ultimate, serviceability and fatigue limit state according to te following principles: In te ultimate limit state te pipe wall capacity is cecked using an interaction formulae. In te serviceability limit state te stress in te pipe is cecked not to exceed te yield point of te steel. In te fatigue limit state te plates and te bolts are cecked for te stress range tat is created by te live load

17 EUOCODE It sould be noted tat in te Englis translation of te tird edition of te andbook an adaptation of te design principles to Eurocode 3 are given. Also, te equivalent line load for te Eurocode load pattern is calculated at different eigts of cover as sown below: p traffic/(kn/m) c /m

18 In te ultimate limit state te capacity of te pipe wall is cecked using te following equation: N f yd d,u A s1 c M M d,u u 1,0 Were te denominator in te first term is te critical force of te pipe wall. If te normal force in te pipe wall is large enoug te wall will fail by buckling. If te soil modulus is low te pipe wall will buckle at a lower force and vice versa. Here te soil modulus is used to calculate te critical load of te pipe wall

19 In te serviceability limit state te stress in te pipe wall is not allowed to exceed te yield stress of te steel: N A d,s s1 M W d,s 1 f yd It sould be noted tat te live load will produce negative moments as well as positive: c c

20 Te bolted connections ave to be cecked bot in te ultimate limit state as well as in te fatigue limit state: Te bolted connections are used to transfer bot normal forces as well as bending moments. Terefore te sear capacity of te bolts as well as te bearing stress in te plates ave to be cecked (n is te number of bolts per unit lengt of te pipe): uls d vd bd N min( n F ; n F ) In order for te bolted connections to be able to transfer bending moments tey ave to fulfill te following equation: a n 2 F td W f yd

21 Equations to calculate section parameters as well as tabulated values are given for four (4) typical corrugations ( mm corrugation sown): c =200 =55 corr a t m t =53 Equations are also given for te designer to be able to calculate if a certain corrugation is prone to local buckling: 1/2 ucr (1,429 0,156ln(( t / ) ( yk / 227) )) u M m t f M Also, te effect on te capacity of so called cross corrugation can be calculated

22 Summary: In Sweden a andbook for te structural design of steel pipe bridges as been developed by te oyal Institute of Tecnology. Te andbook allows te designer to perform a steel pipe bridge design in te ultimate, serviceability and fatigue limit states. Te design metod allows te designer to use any live load and also allows te designer to calculate te soil modulus on condition tat te gradation and te degree of compaction for te backfill soil are known. An adaptation to te Eurocode as been included in te Englis translation of te tird edition of te Swedis andbook. Te effect of using different eigts of cover, corrugations, soil types etcetera can easily be cecked. Terefore designers are encouraged to use te design metod not only in te detailed design pase but also wen performing preliminary designs