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Designing concrete bridges to EN 1992-2
Dr Stephen Salim
Structure of Eurocodes
EN 1990
EN 1991
EN 1992 EN 1993 EN 1994
EN 1995 EN 1996 EN 1999
EN 1997 EN 1998
Design & Detailing
Actions on structures
Geotechnical & seismic design
Structural safety, serviceability & durability
Eurocodes have “National Annexes”
Gives values/approaches where National Determination is allowed
Eurocodes required for concrete bridge design
EN 1990 EN 1991
EN 1992 EN 1997
Design
Analysis and section design, partial factors
Design approach, partial factors, foundations, earth pressures etc.
Limit states, combination and partial factors
Actions, inc. load groups, application etc.
Comparisons with current practice – Concrete design
• Uses cylinder strength ( ≈ 0.8fcu )• More rooted in plasticity theory• Consistent approach for reinforced concrete and
prestressed concrete• Greater coverage of non-linear analysis and time
dependent effects
What effect will change of code have on designs?
ULS Flexure
Stress BlocksStrain Stress
αcc * fck / γc αcc * fck / γc0,0035 (for fck< 55)
0.8
or
Design Concrete Strength
fcd = αcc * fck / γc
Whereαcc = 0,85 (From UK NA)
γc = 1,5
fck = 0,8 * fcu (approx)
αcc * fck / γc = 0,453 * fcu Close to BS 5400!
Reinforcement
γ = 1.15 as BS 5400
Stress/strain relationship very similar (actually closer to 8110).
Overall effect on Flexural design at ULS
• Compression steel more advantage than in BS 5400 but otherwise Very Similar
• Some change due to loading (e.g. switching from the old “HB” abnormal loads to new loads similar to the loads already used in BD 86 assessment
ULS Shear
Case 1: No designed links
• For RC approach and results fairly similar to BS 5400 except more benefit for compression
• For Prestressed approach same as for RC with axial load. Tends to be more conservative than BS 5400, except for external prestress.
Case 2: Designed Links
• Unlike BS 5400 which uses the addition principle ( V = Vconcrete + Vlinks)
• In EN 1992 - shear is taken by the links once the shear strength without links are exceeded and the strength is calculated using the varying angle truss approach
Case 2: Designed LinksVariable Angle Truss Analogy
θ
Steel Ties
Concrete Struts
Strength limited by Links
VRd,S = (Asw / s) *z * fywd * cot θ
whereAsw / s = Link Area / Spacingz = Lever Arm (normally 0,9d for RC)fywd = Design yield strength of links
(i.e. with γ factor of 1,15)θ = Angle of struts (1< cotθ <2,5)
Strength limited by Concrete
VRd,max = αcw * b * w * z * ν1 * fcd / (cot θ + tan θ)
where αcw = Coefficient taking account of
compression stress (1.0 for R.C. can be up to 1.25)
bw = Web width (after reductions for ducts)
fcd = Design concrete strength(As in flexure but αcc can be 1.0)
Choice of θ
For minimum links cot θ = 2.5
But, for maximum shear cot θ = 1.0 (45o truss)
If shear too great for cot θ of 2.5 but within limit,
optimum is with:
VRd,s = VRd.max
for higher shear, pays to use 80% yield
Link Design Comparison
0
100
200
300
400
500
600
0 1 2 3 4 5
Links
Sten
gth(
kN)
Shear Strength of
300 wide 400 deep RC beam
with 25/30 Concrete
(1% steel)
EN 1992
BS 5400
Link Design Comparison
Shear Strength of
300 wide 400 deep RC beam
with 50/60 Concrete
(1% steel)
10 links = T16-60A lot but possible!
EN 1992
BS 5400
0
200
400
600
800
1000
1200
0 2 4 6 8 10
Links
Sten
gth(
kN)
Varying Angel Truss Analogy
• Can give significant link savingBut• Affects curtailment and EN 1992 already tends to be more
conservative for these• Design calculations more complicated (can optimise θ for
link design with simple excel spreadsheet)
Shear in Prestressed Concrete
• Same general approach as RCBut• Strength without links enhanced
VRd,max = αcw * b * w * z * ν1 * fcd / (cot θ + tan θ) + k1 * σcp
• Concrete crush strength increased for( 0 < σcp < 0.5fcd )
Effect of Compressive Stress on αcw
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
Stress/fcd
Link Design Comparison (Prestressed)
0
500
1000
1500
2000
2500
3000
0 2 4 6 8 10
Links
Stre
ngth
(kN
)
For
250 x 1100 beam50/60 concrete
7N/mm2 prestressBS 5400
(uncracked in flexure)
EN 1992
Shear in Prestressed Concrete
• Can have thinner webs• May require more links• Bigger reduction for plastic ducts
Short Shear Spans
av
Load multipliedby
β = av/2d(av ≥ 0.5d)
Short Shear Span Enhancement
• Altering loads is inconvenient and conservative for multiple loads and impractical for envelope load cases
So• EN 1992-2 NA has changed it back to an enhancement
factor to the resistance
Serviceability Limit state (SLS)
SLS Stress Limits
• Steel: 0.80fyk(0.75fy in BS 5400)
• Concrete: 0.6fck for both RC & PSC(0.50fcu for RC and 0.40fcu for PSC in BS 5400)
but calculated on cracked section
SLS Cracking
Crack Width Check(As for RC)
3
None2
“Decompression”1
EN 1992 EquivalentBS 5400 Class
Decompression VS Class 1
Cracked
ε ε
Tendons
OK to either OK for decompression, not class 1
Table 7.101N – Recommended values for wmax & relevant combination rules
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 be checked for decompression
0.20.3aX0, XC1
0,2d and Decompression0.3XD1, XD2, XD3 XS1, XS2, XS3
0.2b0.3XC2, XC3, XC4
Frequent load combinationcQuasi-permanent load combinationc
Prestressed members with bonded tendons
Reinforced members and prestressed members without bonded tendonsExposure Class
Cracking in RC
• Only checked under quasi-permanent• Unlikely to be critical• Result: despite apparently radical treating of RC and
prestressed together, still tends to give:
RC: designed at ULSPrestressed: designed at SLS
Cracking in PSC
• More sensitive to damage from corrosion than normal reinforcement due to smaller diameter and higher level of stress under which they normally operate
Therefore more onerous ruler and reflects in stricter crack control criteria for bonded tendons
• Checked under frequent OR quasi-permanent load combination depending on exposure class
Determination of crack widths
• Calculateor• Comply with max bar spacingor• Comply with max bar diameter table
Same basic approach used for PSC
Design Examples
1. Concrete composite construction with precast, pre-tensioned beams and a cast in-situ slab
2. In-situ post-tensioned box girder bridge
Precast Beam & Slab Bridge
Section
Elevation (half in Section)
Comparison of moments - BS 5400 and EN 1992
1230(Quasi-permanent LC)
2460(Frequent LC)
1160(LC 1, no LL)
Decompression / Class 1
2460(Frequent LC)
3090(Characteristic LC)
EN 1992XC exposure
3090(Characteristic LC)
3000(LC 1-5)
Compression
Design moment (kNm) for checking
3090(Characteristic LC)
EN 1992XD exposure
2900(LC 3)
BS 5400
Cracking / tensile stress
Design code & exposure
class
Precast Beam & Slab Bridge
In-Situ Post-tensioned Box Girder Bridge
Mid-span section
Spans 70m - 100m – 70m
Support section
Comparison of moments - BS 5400 and EN 1992
115-2.29
(Quasi-permanent LC)
199-346
(Frequent LC)
109-224
(LC 1, no LL)
Decompression / Class 1
199346
(Frequent LC)
235-397
(Characteristic LC)
EN 1992XC exposure
235-397
(Characteristic LC)
235-402
(LC 1-5)
Compression
Design moment (MNm) for checking
235-397
(Characteristic LC)
EN 1992XD exposure
231-386(LC 3)
BS 5400
Cracking / tensile stress
Design code & exposure
class
Post-tensioned Box Girder Bridge
First positive value represents the sagging moment at mid-span, second negative is the hogging moment at the piers
Comparison of prestress requirement
45000
66700
70800
Prestressing force (kN)
Mid-span
22.0
18.7
18.5
Peak concrete
compressive stress
(N/mm2)
50500
76400
73000
Prestressing force (kN)
Pier
26.0EN 1992XC exposure
22.7
23.3
Peak concrete
compressive stress
(N/mm2)
EN 1992XD exposure
BS 5400
Design code & exposure
class
Post-tensioned Box Girder Bridge
Challenges for UK bridge designers and clients
• To be ready for the introduction of the Eurocodes• Minimise increases in design costs due to unfamiliarity of
documents• Manage the risks associated with this magnitude of
change
