Paul JacksonIntegral Bridge Design to EN 1992-2

Integral Bridge Design to EN 1992-2

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Integral Bridge Design to EN 1992-2

gePreacst 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!

Detail of Bridge

Image option 1

• 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 in-situ rc deck slab; in-situ diaphragms at abutments and pier

• Substructure – precast concrete piles with pile caps

Materials

Concrete• EN 1992 uses cylinder strengths• C50/60 used for precast beams• C35/45 used for deck slab, diaphragms, pier, pile-cap & precast piles

Prestressing steel• BS 5896 (EN10138 was voted down so BS has been brought into line with ENV 10138 and current practice!)

Reinforcement• Uses BS EN 10080 & BS 4449:2005. Latter specifies required properties for standardised grades

Structural Model & Analysis

Image option 1

Grillage model of bridge deck

• Global analysis – deck (grillage model)• Piers & abutment stiffness (rotational springs)• 8 longitudinal members @ 1.5m c/c (precast beam + slab)• Transverse members @ 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)

Analysis: Not much changed from BS 5400

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 8500-1:2006)

• Nominal cover = Min. cover + allowance for deviation

Cover

Dcdev currently given in IAN 95: final HA position not yet fixed.

651550XD3C35/45Stringcourse

651550XD3C35/45Pier wall

551540XD1C35/45Soffit / Side

451035XC3C35/45DeckDiaphragm

35530XD1C50/60Beam

501040XD1C35/45Soffit

451035XC3C35/45DeckSlab

mmmmmm

cnom∆cdevcminExposure class

Concrete Grade

SurfaceElement

Actions

1) Permanent Actions2) Variable Actions3) Accidental Actions

Permanent Actions

• Self-weight – 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

Variable Actions

• Wind• Thermal• Construction loads

• Traffic loads

EN 1991-2 Traffic Actions

5m

5m

5m

5m

3.0m3.0m3.0m3.0m

Brid

ge A

xis

1 2

Rem

aini

ng A

rea

TS

TSUDL

UDL

1,11 QQQ ψα

2,12 QQQ ψα

1,11 qqq ψα 2,12 qqq ψα rqqr q,1ψα

SV /SOVSV /SOV

Load Model 1Tandem System (1 per lane) + UDL

3m lane 2m

1,2m

0,5m

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)

Load Model 1 (with UK NA)

Lane 11

Lane 21

Lane 31

Lane 41 (+)

Remaining Area2

3m

3m

3m

3m

1 Interchangeable for worst effect2 Can be other side

UDL = 0,61 X 9,0 = 5,5kN/m2

TS Axle = 1,0 X 300 = 300kN

UDL = 2,2 X 2,5 = 5,5kN/m2

TS Axle = 1,0 X 200 = 200kN

UDL = 2,2 X 2,5 = 5,5kN/m2

TS Axle = 1,0 X 100 = 100kN

UDL = 2,2 X 2,5 = 5,5kN/m2

No TS

UDL = 2,2 X 2,5 = 5,5kN/m2 No TS

Load Model 1 (with UK NA)

Lane 11

Lane 21

Remaining Area2

3m

3m

1 Interchangeable for worst effect2 Can be other side

UDL = 0,61 X 9,0 = 5,5kN/m2

TS Axle = 1,0 X 300 = 300kN

UDL = 2,2 X 2,5 = 5,5kN/m2

TS Axle = 1,0 X 200 = 200kN

UDL = 2,2 X 2,5 = 5,5kN/m2 No TS 1.3m

Much simpler than BS 5400/BD37 which has many historical anomalies

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/m2 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.

Load Model 2 (LM2)

0.4m (NA)

0.4m(NA)

Single axle load = βQ * Qak = 400 kN

Where: Qak = 400 kN

βQ = αQ1 = 1.002m

• 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

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.

SV 196

4.0m

180kN

180kN

100kN

1.6m 4.4m

Direction of Travel Direction of Travel

165kN

165kN

165kN

165kN

165kN

1.2m 1.2m 1.2m 1.2m

Ove

rall

Vehi

cle

Wid

th

0.35m

0.35

m

3.0m

3.0m

165kN

165kN

165kN

165kN

165kN

1.2m 1.2m 1.2m 1.2m

Ove

rall

Vehi

cle

Wid

th

0.35m

0.35

m

3.0m

3.0m

Ove

rall

Vehi

cle

Wid

th

0.35m

0.35

m

3.0m

3.0m

165kN

165kN

165kN

165kN

1.2m 1.2m 1.2m

Critical of1.2m

or5.0m

or9.0m

Critical of1.2m

or5.0m

or9.0m

Load Model 3 (LM3) – Model SV196

Basic Axle Load (kN)

Dynamic Amplification

Factor

Design Axle Weight (kN)

100 1.20 120

165 1.12 185

180 1.10 198

Table 7.101N 7.101N) Recommended values of wmax (mm) and relevant combination rules

Exposure ClassReinforced members and

prestressed members without bonded tendons

Prestressed members with

bonded tendons

Quasi-permanent load combinationc

Frequent load combinationc

X0, XC1 0,3a 0,2

XC2, XC3, XC40,3

0,2(+decompression

under quasi perm.)XD1, XD2, XD3 XS1, XS2, XS3

0,2d and Decompression

Means cracked section analysis needed for prestressed!But rarely critical for XD case (except reversed moments!)

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!

Notes From 7.101 (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 quasi-permanent 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 self-equilibrating stresses may be ignored.

d 0,2 applies to the parts of the member that do not have to bechecked for decompression

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 cmin,dur (NA) determined for the relevant surface.

“Decompression” vs BS 5400 Class 1

Cracked

ε ε

Tendons

OK to either OK for decompression, not class 1

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) Quasi-permanent combination (for cracking in RC)

• 1 combination of action to be considered at ULS

Ed = E { ∑γG,j * Gk,j + γQ,1 * Qk,1 + ∑γQ,i * ψ0,i * Qk,i } j ≥ 1; i > 1

Design values of actions (§ 6.3.1)

γf equiv. to γf.1 in BS 5400

y= “psi factor” equiv. to γf.2 in BS 5400 =– 1,0 for permanent loads– y0, y1, y2 in the case of variable/accidental actions– Choice of “psi factor” depends on limit state and

design situationUnlike BS 5400, y given separately

Fd = γf Frep = γfyFk

yy0 = combination value

(most directly equivalent to γf2 in BS 5400)

y1 = frequent value, used for some SLS checks (prestressed cracking) + with accidental

y2 = quasi permanent value, mainly used for some other SLS checks (RC cracking) + with accidental

Characteristic Combination

QQPG1i

i,ki,01,kj,k∑ ∑>

+++ ψ

Permanent + full leading variable action + yo times others

(combination)

At SLS we have yfactors but all g factors are 1.0

Frequent Combination

QQPG1i

i,ki,21,k1,1j,k∑ ∑>

+++ ψψPermanent + y1 times leading variable action + y2 times others

(frequent) (quasi perm)

At SLS we have y factors but all g factors are 1.0

Quasi Permanent Combination

QPG1i

i,ki,2j,k∑ ∑>

++ ψ

Permanent + y2 times variable(quasi perm)

At SLS we have y factors but all g factors are 1.0

1.0-1.0Qc

Construction loads0.50.60.6Tk

Thermal actions (EN 1991-1-5)

--1.0F*W (with traffic actions – wind speed limited)

--0.8FWk (during erection)00.20.6FWk (persistent design situations)

Wind loads (EN 1991-1-4)--0.8Qsn,k (during erection)

Snow loads (EN 1991-1-3)0(1.0)0gr5 (LM3 – Special vehicles)00.750gr4 (LM4 – Crowd loading)000gr3 (Pedestrian loads)000gr2 (Horizontal forces)00.750gr1b (Single axle)00.400.40Pedestrian and cycle 00.400.40UDL00.750.75TSgr1a (LM1 +

pedestrian or cycle)

Traffic loads on bridges (EN 1991-2)ψ2ψ1ψ0Action

Combination of actions – road bridges

Creep and Shrinkage

• BS EN 1992-1-1 Clause 3.1.4 and Annex B gives prediction models (also applies to high strength concrete)

• Shrinkage calculation:

εcs = εcd + εca

Total shrinkage

strain Drying shrinkage

strain

Autogeneous shrinkage

strain

A notable difference from past practice! (based on more recent CEB than BS 5400 appendix)

days180=t2Concrete age when bridge is opened for traffic

days30=t1Concrete age at construction

days1=t0,eqEquivalent concrete age at release of prestress

%75=RHRelative humidity of ambient environment

mm262=2Ac / u=h0Notional size of memberEqu. B.6

mm3128=uPerimeter in contact with the atmosphere

mm2410191=ACross-section area of concrete member

MPa58

fck + 8=fcmMean compressive cylinder strength3.1.4 & Annex B

CREEP AND SHRINKAGE MODEL PARAMETERS FOR PRECAST BEAMEC2-1-1

-1.78=

1.15 x 2.21 x 0.7== ϕRH.β(fcm).β(t0)

ϑ0 Notional creep coefficientEqu. B.2

-647=βHCoefficient dependent on Relative humidityEqu. B.8

-0.70=β(t0)Factor allowing for concrete age at loadingEqu. B.5

days4.0=t0Modification to t0 to allow for type of cementEqu. B.9

-2.21=β(fcm)Factor allowing for concrete strengthEqu. B.4

-1.15=ϕRHFactor allowing for relative humidityEqu. B.3

-0.78=(35 / 58)0.5=α3

-0.90=(35 / 58)0.2=α2Coefficients allowing for

concrete strength

Equ. B.8c

-0.70=(35 / 58)0.7=α1

CREEP MODEL

SHRINKAGE MODEL

Age of concrete at beginning of drying shrinkage ts = 6

Equ. 3.12 Final value of the autogenous shrinkage strain εca(∞) = 100

Equ. B.12 Factor allowing for relative humidity βRH = 0.90

Table 3.3 Coefficient depending on notional size kh = 0.79

Equ. B.11 Basic drying shrinkage strain εcd,0 = 354

Equ. 3.9 Final value of the drying shrinkage strain εcd,∞ = 279

37923710918µsTotal shrinkage strain, εcs(t) = εcs(t) + εcd(t)

279143420µsDrying shrinkage strain, εcd(t) Equ. 3.9

100936718µsAutogenous shrinkage strain, εca(t) Equ. 3.11

1.791.130.700.00-Creep coefficient, ϕ(t, t0)Equ. B.1

1.000.510.150.00-βds(t,ts)Equ. 3.10

1.000.930.670.18-βas(t)Equ. 3.13

1.000.630.390.00-βc(t,t0)Equ. B.7

∞180300dayt-t0

∞180300dayt-ts

∞181311dayt

Long term

At opening

for traffic

At con-struction

At stress transfer

Time development of Creep and Shrinkage

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

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 1992-2 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 fct,eff

Summary of critical sections & checks, in service

Quasi-permanentSlab (RC crack limit)

Crack width

CharacteristicSlab reinforcement

Stress limit

Characteristic-ULSOver pier

CharacteristicTop of beamSlab

Tendons

Stress LimitFrequentBottom of beamDecompression

Characteristic-ULSMidspan

Load Combination

LocationLikely to be critical for:

Section

Note: This is an example, hence incomplete

Decompression at mid span

5.44.111.90.6Total Normal Stress (MPa)-0.2-0.20.10.1Diff. shrinkage local component

-0.50.10.1-0.7Non-linear temp. diff. component

6.14.24.6-7.81327Moment (kNm) on CGM

-1.20.7-75Moment (kNm) on SSLBM

8.28.23379Normal force (kN) on SSLBM

MIDSPAN - FREQUENT LOAD COMBINATION, LONG TERM, COOLING

0.92EC35 / EC60=

TopBottomTop30mm below lowest tendon

SLABBEAM

Stress Limits

• Concrete compressive stress limit = 0,6fck

• Reinforcement stress limit = 0,8fyk

• Prestressing tendon stress limit = 0,75fpk(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

Stress Checks

-12569.412.20.6Total

--0.20.10.1Diff. shrinkage local component 3-0.9-0.40.5Non-linear temp. diff. component 2

-558.76.6-11.61904Moment on CGM

-380.012.6-8.4803Dead load moment on SSLBM

-0.0-16.010.6-1016Prestressing moment on SSLBM

-0.09.39.33801Normal force on SSLBM

-1163---Initial prestress

CHARACTERISTIC LOAD COMBINATION, AT OPENING, HEATING

-13952130(-4.1)Limiting stress

4.10E+05-4.10E+054.10E+05(mm2)Cross section area (beam only)

5.270.92

Ep / EC50 =EC35 / EC50 =

BOTTOMTOPTOPBOTTOM

TENDONSLABBEAM

Normal stress (MPa)

Stress Checks

-12547.612.5-0.4Total

--0.20.10.1Diff. shrinkage local component

--0.60.1-0.8Non-linear temp. diff. component

-538.46.4-11.21844Moment on CGM

-380.012.6-8.4803Dead load moment on SSLBM

-0.0-16.010.6-1016Prestressing moment on SSLBM

-0.09.39.33801Normal force on SSLBM

-1163---Initial prestress

CHARACTERISTIC LOAD COMBINATION, AT OPENING, COOLING

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

Pretensioned Beam: Transfer

• Compression (critical for soffit)BS 5400 0.5fci not greater than 0.4fcu

EN1992 0,6 fck(t) 0,7 fck(t) (subject to NDP) for pretensioned elements “if it can be justified by tests or experience that longitudinal cracking is prevented.”

Transfer Stress: Comparison

• 0,7 fck(t) = 0.56fci ??• But fci = “cube strength at transfer”• fck(t) = “Characteristic…”• Gives c16,8 cf 20 for BS 5400 if fck(t) from fcm(t) and

Table 3.1• But: with good concrete quality control, and

records to prove it, fck(t) would be greater and result similar to BS 5400

Summary of critical sections & checks, at transfer

Bottom of BeamCmin,dur above top strand?*Top*

CompressionDecompression?*

Crack width (or fct)

End of transmission length(+ debond positions)

AllStrand tension at jacking

All

Nothing!(strictly strand after jacking)

Mid span

LocationLikely to be critical for:

Section

* Depends on strand layout

Check for top of Section

Decompression Check required here!

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

Critical Condition for Prestress Design in service

BS 5400 (+BD24)

Class1 under full HA

1.2 HA + pedestrian

Class 2 under full HA + HB for other combinations

EN 1992

Decompression under frequent LM1 + Quasi perm temperature0.75 TS + 0.4 udl + 0.4 pedestrian + 0.5 temperature

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

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.

For Rail Loading

Design code and exposure

class

Initial prestress

force (kN)

Number of

Strands

Tendon stress during

tensioning (N/mm2)

BS 5400 4599 21 1460EN 1992, XD

exposure4637 22 1405

EN 1992, XC exposure

2976 16 1240

ULS

Flexure:

Similar: γ applied to prestress but no equiv to BS 5400 15% rule

Shear:

RC and Prestressed treated the sameAddition principle not used: use concrete contribution orlinks based on varying angle truss In our case interface governsUpper limit is significantly greater

Designed LinksVariable Angle Truss Analogy

θ

Steel Ties

Concrete Struts

Link Design Comparison (Prestressed)

For

250X1100 beam

50/60 concrete

14N/mm2 prestress

EN 1992

BS 5400(uncracked in flexure)

0

500

1000

1500

2000

2500

3000

0 2 4 6 8 10

Links

Stre

ngth

(kN

)

FatigueFor reinforcement making bridge continuousStress range under frequent load = 128Allowable to EN 1992-1-1 = 70Allowable to PD for this case = 85Not OK

But Using Annex NNRange under fatigue load model 4 = 96Damage equivalent range gives allowable = 141 OKFor this case PD value is very conservative but:When it works it saves significant calcs.

Will Be Published Soon!Integral Bridge Design to EN 1992-2

Integral Bridge Design to EN 1992-2

ge