Integral Bridge Design to EN

Transcription

1 Integral Bridge Design to EN ge Integral Bridge Design to EN Paul Jackson

2 Integral Bridge Design to EN ge Preacst beam and slab bridge chosen to illustrate as much of the code as practical To UK NA and PD but made clear where things come from. Bridge is integral: brings in EN 1997PD which held it up! Format: calc. sheets + text Today, I will say a bit about the design calcs. concentrating on areas most different from BS 5400!

3 Image option 1 Detail of Bridge 2 span integral bridge, each span 20m long 7.3m wide c/way + 2m wide footways either side Superstructure 8 standard precast, pretensioned concrete Y beams with a 160mm deep insitu rc deck slab; insitu diaphragms at abutments and pier Substructure precast concrete piles with pile caps

4 Materials Concrete EN 1992 uses cylinder strengths C50/60 used for precast beams C35/45 used for deck slab, diaphragms, pier, pilecap & precast piles Prestressing steel BS 5896 (EN10138 was voted down so BS has been brought into line with ENV and current practice!) Reinforcement Uses BS EN & BS 4449:2005. Latter specifies required properties for standardised grades

5 Analysis: Not much changed from BS 5400 Image option 1 Grillage model of bridge deck Structural Model & Analysis Global analysis deck (grillage model) Piers & abutment stiffness (rotational springs) 8 longitudinal 1.5m c/c (precast beam + slab) Transverse 1.85m c/c Possible to model superstructure & substructure together in a single 3D model (practicalities of design process means that they are normally considered separately)

6 Cover This bridge example is assumed to be passing over a c/way, hence Class XD3 exposure (exposed to spray containing chlorides) The bridge soffit (> 5m above c/way) XD3 classification not required (BS 8500), so XD1 (exposed to airborne chlorides) applies Top of deck (protected by waterproofing) XC3 Min. cover requirements (BS 85001:2006) Nominal cover = Min. cover + allowance for deviation

7 Cover Element Surface Concrete Grade Exposure class c min mm c dev mm c nom mm Slab Deck C35/45 XC Soffit C35/45 XD Beam C50/60 XD Diaphragm Deck C35/45 XC Soffit / Side C35/45 XD Pier wall C35/45 XD Stringcourse C35/45 XD Dc dev currently given in IAN 95: final HA position not yet fixed.

8 Actions 1) Permanent Actions 2) Variable Actions 3) Accidental Actions

9 Permanent Actions Selfweight DL of beam & slab Differential settlement 20mm max. assumed Differential shrinkage (SLS only) deck is cast after precast beams, hence causes tension within the deck slab, compression within the beams & an overall sagging within the deck

10 Variable Actions Wind Thermal Construction loads Traffic loads

11 EN Traffic Actions 1 2 α q 1ψ 1, q q1 α q 2ψ 1, q q2 α qrψ 1, q q r α Q ψ 1 1, Q Q1 TS UDL Bridge Axis 5m 5m SV / SOV α Q ψ 2 1, Q Q2 TS Remaining Area UDL 3.0m 3.0m

12 Load Model 1 Tandem System (1 per lane) + UDL 0,5m 3m lane 2m 1,2m 0,4 m square Tandem system normally positioned as shown. For local effects can be closer to adjacent one. (wheels 0,5m c to c)

13 Load Model 1 (with UK NA) 3m 3m 3m 3m Lane 1 1 Lane 2 1 Lane 3 1 Lane 4 1 (+) UDL = 0,61 X 9,0 = 5,5kN/m 2 TS Axle = 1,0 X 300 = 300kN UDL = 2,2 X 2,5 = 5,5kN/m 2 TS Axle = 1,0 X 200 = 200kN UDL = 2,2 X 2,5 = 5,5kN/m 2 TS Axle = 1,0 X 100 = 100kN UDL = 2,2 X 2,5 = 5,5kN/m 2 No TS Remaining Area 2 UDL = 2,2 X 2,5 = 5,5kN/m 2 No TS 1 Interchangeable for worst effect 2 Can be other side

14 Load Model 1 (with UK NA) 3m 3m 1.3m Lane 1 1 Lane 2 1 Remaining Area 2 UDL = 0,61 X 9,0 = 5,5kN/m 2 TS Axle = 1,0 X 300 = 300kN UDL = 2,2 X 2,5 = 5,5kN/m 2 TS Axle = 1,0 X 200 = 200kN UDL = 2,2 X 2,5 = 5,5kN/m 2 No TS 1 Interchangeable for worst effect 2 Can be other side Much simpler than BS 5400/BD37 which has many historical anomalies

15 Load Model 1 (LM1) Only one TS is applied to each lane, symmetrically around the centreline of the lane and in the position that causes the most severe effect on the element under consideration. The UDL should only be applied in the unfavourable parts of the influence surface, both longitudinally and transversely. The nationally determined adjustment factors for the UDL have been set so that a UDL of 5.5kN/m 2 is applied to all lanes and the remaining area, irrespective of the number of nominal lanes simplifying the input of loading into the analysis model. In contrast to BS 5400, the magnitude of this load pressure does not vary with loaded length.

16 Load Model 2 (LM2) Single axle load = β Q * Q ak = 400 kn 2m Where: Q ak = 400 kn β Q = α Q1 = m (NA) 0.4m (NA) LM2 is not combined with other traffic models. Consider one wheel on its own if it is more critical than the whole axle. Needs to be considered for local effects

17 Load Model 3 (LM3) LM3 represents Abnormal Vehicles. The NA defines a series of load models to be used for the design of UK road bridges, and these will be familiar to those who have used BD 86/07. The vehicles are applied in the worst position and are combined with LM1 loads at their frequent values. They can be positioned within a notional lane OR partially within a notional lane and the remaining width of the lane.

18 SV kn 165 kn 165 kn 165 kn 165 kn 165 kn 165 kn 165 kn 165 kn 180 kn 180 kn 100 kn 1.2m 1.2m 1.2m 1.2m 1.2m 1.2m 1.2m 4.0m 1.6m 4.4m 0.35m Direction of Travel Overall Vehicle Width 3.0m 3.0m 0.35m Critical of 1.2m or 5.0m or 9.0m

19 Load Model 3 (LM3) Model SV196 Basic Axle Load (kn) Dynamic Amplification Factor Design Axle Weight (kn)

20 Table 7.101N 7.101N) Recommended values of w max (mm) and relevant combination rules Exposure Class Reinforced members and prestressed members without bonded tendons Prestressed members with bonded tendons Quasipermanent load combination c Frequent load combination c X0, XC1 0,3a 0,2 XC2, XC3, XC4 XD1, XD2, XD3 XS1, XS2, XS3 0,3 0,2 (+decompression under quasi perm.) 0,2 d and Decompression Means cracked section analysis needed for prestressed! But rarely critical for XD case (except reversed moments!)

21 Cracking criteria Criteria more onerous for prestressed Does not actually say you can treat an element (e.g. deck slab) as prestressed in one direction and RC in another Neither does BS 5400! Can still do it Is not actually very logical (Said to be for durability but cracks parallel to tendons more significant) But: not clear using more severe criteria for prestressed is logical!

22 Notes From (UK NA version) a For X0, XC1 exposure classes, crack width has no influence on durability and this limit is set to guarantee acceptable appearance. In the absence of appearance conditions this limit may be relaxed. b For these exposure classes, in addition, decompression should be checked under the quasipermanent combination of loads. c For the crack width checks under combinations which include temperature distribution, the resulting member forces should be calculated using gross section concrete properties and selfequilibrating stresses may be ignored. d 0,2 applies to the parts of the member that do not have to be checked for decompression

23 Plus The decompression limit requires that all concrete within a certain distance of bonded tendons or their ducts should remain in compression under the specified loading. The distance within which all concrete should remain in compression shall be taken as the value of c min,dur (NA) determined for the relevant surface.

24 Decompression vs BS 5400 Class 1 ε ε Tendons Cracked OK to either OK for decompression, not class 1

25 Combinations of Actions 3 combinations of actions to be considered at SLS: 1) Characteristic combination (for stress checks) 2) Frequent combination (for cracking in prestrtessed) 3) Quasipermanent combination (for cracking in RC) 1 combination of action to be considered at ULS E d = E { γ G,j * G k,j + γ Q,1 * Q k,1 + γ Q,i * ψ 0,i * Q k,i } j 1; i > 1

26 Design values of actions ( 6.3.1) F d = γ f F rep = γ f yf k γ f equiv. to γ f.1 in BS 5400 y= psi factor equiv. to γ f.2 in BS 5400 = 1,0 for permanent loads y 0, y 1, y 2 in the case of variable/accidental actions Choice of psi factor depends on limit state and design situation Unlike BS 5400, y given separately

27 y y 0 = combination value (most directly equivalent to γ f2 in BS 5400) y 1 = frequent value, used for some SLS checks (prestressed cracking) + with accidental y 2 = quasi permanent value, mainly used for some other SLS checks (RC cracking) + with accidental

28 Characteristic Combination G k, j + P + Q + ψ k,1 i> 1 0,i Q k,i Permanent + full leading variable action + y o times others (combination) At SLS we have yfactors but all g factors are 1.0

29 Frequent Combination G k,j ψ + P+ Q + ψ 1,1 k,1 i> 1 2,i Q k,i Permanent + y 1 times leading variable action + y 2 times others (frequent) (quasi perm) At SLS we have y factors but all g factors are 1.0

30 Quasi Permanent Combination G k, j + P + ψ i> 1 2,i Q Permanent + y 2 times variable (quasi perm) k,i At SLS we have y factors but all g factors are 1.0

31 Combination of actions road bridges Action Traffic loads on bridges (EN 19912) gr1a (LM1 + TS pedestrian or UDL cycle) Pedestrian and cycle gr1b (Single axle) gr2 (Horizontal forces) gr3 (Pedestrian loads) gr4 (LM4 Crowd loading) gr5 (LM3 Special vehicles) Snow loads (EN ) Q sn,k (during erection) Wind loads (EN ) F Wk (persistent design situations) F Wk (during erection) F* W (with traffic actions wind speed limited) Thermal actions (EN ) T k Construction loads Q c ψ ψ (1.0) ψ

32 Creep and Shrinkage BS EN Clause and Annex B gives prediction models (also applies to high strength concrete) Shrinkage calculation: ε cs = ε cd + ε ca Total shrinkage strain Drying shrinkage strain Autogeneous shrinkage strain A notable difference from past practice! (based on more recent CEB than BS 5400 appendix)

33 EC211 CREEP AND SHRINKAGE MODEL PARAMETERS FOR PRECAST BEAM & Annex B Mean compressive cylinder strength f cm = f ck MPa Crosssection area of concrete member A = mm 2 Perimeter in contact with the atmosphere u = 3128 mm Equ. B.6 Notional size of member h 0 = 2A c / u = 262 mm Relative humidity of ambient environment RH = 75 % Equivalent concrete age at release of prestress t 0,eq = 1 days Concrete age at construction t 1 = 30 days Concrete age when bridge is opened for traffic t 2 = 180 days

34 CREEP MODEL α 1 = (35 / 58) 0.7 = 0.70 Equ. B.8c Coefficients allowing for concrete strength α 2 α 3 = = (35 / 58) 0.2 (35 / 58) 0.5 = = Equ. B.3 Factor allowing for relative humidity ϕ RH = 1.15 Equ. B.4 Factor allowing for concrete strength β(f cm ) = 2.21 Equ. B.9 Modification to t 0 to allow for type of cement t 0 = 4.0 days Equ. B.5 Factor allowing for concrete age at loading β(t 0 ) = 0.70 Equ. B.8 Coefficient dependent on Relative humidity β H = 647 Equ. B.2 Notional creep coefficient ϑ 0 = ϕ RH.β(f cm ).β(t 0 ) = 1.15 x 2.21 x 0.7 = 1.78

35 SHRINKAGE MODEL Age of concrete at beginning of drying shrinkage t s = 6 Equ Final value of the autogenous shrinkage strain ε ca ( ) = 100 Equ. B.12 Factor allowing for relative humidity β RH = 0.90 Table 3.3 Coefficient depending on notional size k h = 0.79 Equ. B.11 Basic drying shrinkage strain ε cd,0 = 354 Equ. 3.9 Final value of the drying shrinkage strain ε cd, = 279

36 Time development of Creep and Shrinkage At stress transfer At construction At opening for traffic Long term t day tt s day tt 0 day Equ. B.7 β c (t,t 0 ) Equ β as (t) Equ β ds (t,t s ) Equ. B.1 Creep coefficient, ϕ(t, t 0 ) Equ Autogenous shrinkage strain, ε ca (t) µs Equ. 3.9 Drying shrinkage strain, ε cd (t) µs Total shrinkage strain, ε cs (t) = ε cs (t) + ε cd (t) µs

37 Global Design at SLS SLS criteria governs for most prestressed structures 3 checks are required: Decompression (near tendons) Crack widths (elsewhere + in RC) Stress limits

38 Global Design at SLS For XD (chloride) exposure, decompression limit is checked for the frequent load combination (without LM3) & requires that all concrete within a certain distance of the tendons remain in compression (Table NA.1 to EN specifies the distance to be the minimum cover required for durability). Parts of the prestressed beam outside this limit may go into tension, but should be checked against a crack width limit of 0.2mm. Stress limits both in concrete and tendons, must be checked under the characteristic load combination Can treat sections as uncracked if stress less than f ct,eff

39 Summary of critical sections & checks, in service Section Midspan Over pier Likely to be critical for: ULS Decompression Stress Limit ULS Crack width Location Bottom of beam Top of beam Slab Tendons Slab (RC crack limit) Stress limit Slab reinforcement Note: This is an example, hence incomplete Load Combination Characteristic Frequent Characteristic Characteristic Quasipermanent Characteristic

40 Decompression at mid span BEAM SLAB 30mm below lowest tendon Top Bottom E C35 / E C60 = Top 0.92 MIDSPAN FREQUENT LOAD COMBINATION, LONG TERM, COOLING Normal force (kn) on SSLBM Moment (knm) on SSLBM Moment (knm) on CGM Nonlinear temp. diff. component Diff. shrinkage local component Total Normal Stress (MPa)

41 Stress Limits Concrete compressive stress limit = 0,6f ck Reinforcement stress limit = 0,8f yk Prestressing tendon stress limit = 0,75f pk (Note: only critical for cracked section analysis, otherwise governed by jacking limits as BS 5400) These stress limits are checked for the Characteristic Combination of Actions

42 Stress Checks BEAM Normal stress (MPa) SLAB TENDON BOTTOM TOP TOP BOTTOM E C35 / E C50 = E p / E C50 = Cross section area (beam only) (mm 2 ) 4.10E E E+05 Limiting stress (4.1) CHARACTERISTIC LOAD COMBINATION, AT OPENING, HEATING Initial prestress 1163 Normal force on SSLBM Prestressing moment on SSLBM Dead load moment on SSLBM Moment on CGM Nonlinear temp. diff. component Diff. shrinkage local component Total

43 Stress Checks CHARACTERISTIC LOAD COMBINATION, AT OPENING, COOLING Initial prestress 1163 Normal force on SSLBM Prestressing moment on SSLBM Dead load moment on SSLBM Moment on CGM Nonlinear temp. diff. component Diff. shrinkage local component Total

44 Pretensioned Beam: Transfer Tension (critical for top at ends) No specific rule: Decompression checked if tendons close, (assuming chloride) otherwise crack width? Gives a paradox: top strand provided to control tension but checks not needed if no top strand. Precast Manual proposes using a tensile stress

45 Pretensioned Beam: Transfer Compression (critical for soffit) BS f ci not greater than 0.4f cu EN1992 0,6 f ck(t) 0,7 f ck(t) (subject to NDP) for pretensioned elements if it can be justified by tests or experience that longitudinal cracking is prevented.

46 Transfer Stress: Comparison 0,7 f ck(t) = 0.56f ci?? But f ci = cube strength at transfer f ck(t) = Characteristic Gives c16,8 cf 20 for BS 5400 if f ck(t) from f cm(t) and Table 3.1 But: with good concrete quality control, and records to prove it, f ck(t) would be greater and result similar to BS 5400

47 Summary of critical sections & checks, at transfer Mid span End of transmission length (+ debond positions) All Section * Depends on strand layout Likely to be critical for: Nothing! (strictly strand after jacking) Compression Decompression?* Crack width (or f ct ) Strand tension at jacking Bottom of Beam C min,dur above top strand?* Top* All Location

48 Check for top of Section Decompression Check required here!

49 Strand Pattern Came out identical to BS 5400 design If you had no XD/XS (Chloride) Exposure could save c 25% prestress Similar conclusions for rail bridge

50 Critical Condition for Prestress Design in service EN 1992 BS 5400 (+BD24) Decompression under frequent LM1 + Quasi perm temperature 0.75 TS udl pedestrian temperature Class1 under full HA 1.2 HA + pedestrian Class 2 under full HA + HB for other combinations

51 With reduced prestress (no chloride) ULS might govern Increase in tendon force under live loading is much greater so fatigue or limit on tendon service stress could govern

52 In our examples ULS did not govern Upper limit on in service tendon stress did affect rail example (i.e. jacking stress had to be reduced) Fatigue limit check did not govern Since less prestress is needed and transfer is the critical condition for concrete compression, you could reduce section.

53 For Rail Loading Design code and exposure class Initial prestress force (kn) Number of Strands Tendon stress during tensioning (N/mm 2 ) BS EN 1992, XD exposure EN 1992, XC exposure

54 ULS Flexure: Similar: γ applied to prestress but no equiv to BS % rule Shear: RC and Prestressed treated the same Addition principle not used: use concrete contribution or links based on varying angle truss In our case interface governs Upper limit is significantly greater

55 Designed Links Variable Angle Truss Analogy Concrete Struts θ Steel Ties

56 Link Design Comparison (Prestressed) 3000 Strength (kn) EN 1992 BS 5400 (uncracked in flexure) For 250X1100 beam 50/60 concrete 14N/mm 2 prestress Links

57 Fatigue For reinforcement making bridge continuous Stress range under frequent load = 128 Allowable to EN = 70 Allowable to PD for this case = 85 Not OK But Using Annex NN Range under fatigue load model 4 = 96 Damage equivalent range gives allowable = 141 OK For this case PD value is very conservative but: When it works it saves significant calcs.

58 Integral Bridge Design to EN ge Integral Bridge Design to EN Will Be Published Soon!