Es_09_design Examples - Incremental Launching
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Incremental launching
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SECONDINO VENTURA BRIDGE (ASTI) Incremental launching continuous beam
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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SECONDINO VENTURA BRIDGE Geographical positioning
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
SECONDINO VENTURA BRIDGE What could it have been the typical solution?
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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The typical Th t i l solution l ti f a railway for il deck is the use of simply supported beams
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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This common solution has the following g features •
Widely tested solution in term of rail traffic safety and passengers comfort
Necessity of accessibility from the bottom to the construction site (or utilization of high dimensions and expensive launching girders)
•
Practicallyy no p problem of interaction between track and structure
High number of bearings and joints (with consequent problems of durability and substitution)
•
Large width piles and capitals to accommodate d t ttwo rows off b bearings i (3.0 m, 4.1 m)
•
Non optimal distribution of the stresses and low slenderness L/h≤15 /
•
Good speed of construction
•
Computation simplicity
•
•
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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SECONDINO VENTURA BRIDGE A little history
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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A LITTLE HISTORY … •
Flooding in Piedmont in 1994 concerned principally Tanaro basin with a flow measured in Alessandria of about 3800 m3/s
•
Old Corso Savona bridge in Asti was made of a upper way road deck, realized with 4 prestressed precast concrete beams with cast in situ slab of about 20 m span, and a lower railway deck made of steel
•
Both the decks were supported by huge masonry piers that left very little free span between them them.
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
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During the flooding the bridge presented: ¾ Insufficient hydraulic clearance: water reached the intrados of th prestressed the t d concrete t d deck. k ¾ Violent impacts of transported material against the upstream beam (and consequent damage) ¾ Drifting of material against the piles with consequent dam effect During post-flooding repair works of river Tanaro, the river bed in correspondence of the bridge has been enlarged. The two decks, road and railway, had then to be replaced
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
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DESIGN RESTRAINTS •
Larger spans, to interfere as little as possible with the river and with ith th the water t fl flow (200 years return t period) i d)
•
No significant variation of the railway level (railway station is nearby)
•
Possibility of future reutilization of the rail deck as road deck, as a consequence of modification of railway line and transfer of the railway station in another zone
•
Similar transverse section for deck radicallyy different ((road deck and railway deck)
•
Construction method able to guarantee the safety of the structure and working force during construction phases
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
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SOLUTION Both road and railway decks made of prestressed concrete. Two continuous beams with 5 spans each (end spans 29.70 m and central spans 33.20 m), Incremental launching. Total depth of the beams = 165 cm (l/h≈20). Diaphragm piers with a transverse thickness of 150 cm.
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
BEARINGS Free Fixed
Long Free / Transv. Long. Transv fixed Long. fixed / Transv. free
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Cross section of the two independent decks
Railway
Road + cycle track
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
Cross section of the railway deck
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Comparison between construction techniques
•
Construction of one span (33 m) in ten days
•
Lauching time: 3 hours Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
SECONDINO VENTURA BRIDGE Launching technique
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
a)) Uplift p
c) Down lift
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
b)) Trust
d) Repositioning
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Geometrical limitations: In vertical plane
In horizontal plane
horizontal circular li linear iinclination li ti circular
straight or circular straight circular i l circular
In the last two cases the projections on the horizontal plane are ellipse circles
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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NOSE DESIGN We can assume Ln ≅ 0,65 0 65 L
Ln= nose length L = typical span of the bridge (temporary or final) qn = k Ln² qn = dead weight of nose , ÷ 0,020 , for road bridges g k = 0,012 0,018 ÷ 0,030 for rail bridges The ratio between dead weight of nose and deck can be assumed, assumed at a first approximation, as: qn/q = 0,10 The effect of relative flexural rigidity EnIn/EI on the limitation of stress variation during the launching should be evaluated. Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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For simplification, F i lifi ti as a first fi t approach, h we can analyze l a continuous ti b beam with ith an infinite number of spans and axial baricentric prestressing, to avoid the hyperstatic bending moments due to prestressing, which can assume different values for each bridge position. position
B B The launching internal actions as a function of parameter α = x/L, x/L are analyzed with: • nose cantilevering 0 ≤ α ≤ 1-Ln/L • nose on the pier pie 1 Ln/L ≤ α ≤ 1 1-L
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Variation of MB during the launching for Ln/L = 0,80 and qn/q = 0,10 with the relative rigidity ratio EnIn/EI
Variation of MB during the launching g for Ln/L = 0,50 and qn/q = 0,10 with the relative rigidity ratio EnIn/EI
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
Incremental launching 8-8 25/66 Incremental launching
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With qn/q = 0,10 the bending moment at maximum cantilevering is equal to EOL for Ln/L = 0,65 ,
Variation of MB for Ln/L = 0,65 and EnIn/EI = 0,200 as a function of the ratio qn/q. q
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
SECONDINO VENTURA BRIDGE Launching nose
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Launching nose anchoring system Longitudinal section
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Section S1 φ20/20 L70cm welded to the plate
Concrete bed for the plate Rck >45 MPa
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
(interface with the nose)
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Section S3 (2m from the nose)
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Section S5 (4m from the nose)
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Section S7 (5m from the nose)
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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SECONDINO VENTURA BRIDGE Evaluation of the internal actions during launching and launching prestressing
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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INTERNAL ACTIONS DURING THE LAUNCHING: BENDING MOMENT •
Static scheme :
Definitive restraint Temporary restraint •
Actions: ¾ Self weight ¾ Temperature variation between intrados and extrados of ± 5° ¾ Maximum differential settlement between two consecutive bearings of 5 mm Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Bending g moment at end of launching g (values in kN*10*m)
Step 95 Fase 95
Mg
M sett. Mced
M temp
M+
M-
Mtot+
Mtot-
-1200.0 -1100.0 -1000.0 -900.0 -800.0 -700.0 -600.0 -500.0 -400.0 -300.0 -200.0 -100.0 0.0
20.0
40.0
60.0
80.0
100.0
0.0 100 0 100.0 200.0 300.0 400.0 500.0 600.0 700.0
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
120.0
140.0
160.0
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Bending g moment during g launching g Fase 20 Step
Mg
Msett. Mced
M temp
M+
M-
Mtot+
Mtot-
Fase30 30 Step
-1200.0
-1200.0
-1100.0
-1100.0
-1000.0
-1000.0
-900.0
-900.0
-800.0
-800.0
-700.0
-700.0
-600.0
-600.0
-500.0
-500.0
-400.0
-400.0
-300.0
Mg
Msett. Mced
M temp
M+
M-
Mtot+
Mtot-
-300.0
-200.0
-200.0
-100.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
-100.0 0.0
0.0
0.0
100.0
100.0
200.0
200.0
300.0
300.0
400.0
400.0
500.0
500.0
600.0
600.0
700.0
700.0
Fase 40 Step
Mg
Msett. Mced
M temp
M+
M-
Mtot+
Mtot-
Fase50 50 Step
-1200.0
-1200.0
-1100.0
-1100.0
-1000.0
-1000.0
-900.0
20.0
40.0
Mg
60.0
Mced Msett.
80.0
M temp
100.0
M+
120.0
M-
140.0
160.0
Mtot+
Mtot-
-900.0
-800.0
-800.0
-700.0 700 0
-700.0 700 0
-600.0
-600.0
-500.0
-500.0
-400.0
-400.0
-300.0
-300.0
-200.0
-200.0
-100.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
-100.0 0.0
0.0
0.0
100.0
100.0
200.0
200.0
300.0
300.0
400.0
400.0
500.0
500.0
600.0
600.0
700.0
700.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Bending g moment during g launching g Fase60 60 Step
Mg
Msett. Mced M temp
M+
M-
Mtot+
Mtot-
Step Fase70 70
-1200.0
-1200.0
-1100.0
-1100.0
-1000.0
-1000.0
-900.0
-900.0
-800.0
-800.0
-700.0
-700.0
-600.0
-600.0
-500.0
-500.0
-400.0
-400.0
-300.0
Msett. Mced
M temp
M+
M-
Mtot+
Mtot-
-300.0
-200.0
-200.0
-100.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
-100.0 0.0
00 0.0
00 0.0
100.0
100.0
200.0
200.0
300.0
300.0
400.0
400.0
500.0
500.0
600.0
600.0
700.0
700.0
Fase80 80 Step
Mg
Msett. Mced
M temp
M+
M-
Mtot+
Mtot-
-1200.0
-1100.0
-1100.0
-1000.0
-1000.0
-900.0
-900.0
-800.0
-800.0
-700.0
-700.0
-600.0
-600.0
-500.0
-500.0
-400.0
-400.0
-300.0
20.0
Fase90 90 Step
-1200.0
40.0
Mg
60.0
Msett. Mced
80.0
M temp
100.0
M+
120.0
M-
140.0
Mtot+
160.0
Mtot-
-300.0
-200.0 -100.0 0.0
Mg
-200.0 20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
-100.0 0.0
0.0
0.0
100.0
100.0
200.0
200.0
300.0
300.0
400.0
400.0
500.0
500.0
600.0
600.0
700.0
700.0
20.0
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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60.0
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As the bending g moments are almost constant in all the sections and the positive values are only half of the negative ones baricentric prestressing is introduced for the launching phases.
A [m2] 7.897
Enlarged section Wsx,sup Wdx,sup Wsx,inf [m3] [m3] [m3] ‐2.828 ‐2.631 2.171
Wdx,inf [m3] 2.237
A [m2] 6.458
Current section Wsx,sup Wdx,sup Wsx,inf [m3] [m3] [m3] ‐2.498 ‐2.290 1.590
Wdx,inf [m3] 1.629
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Longitudinal g stresses during g launching g σsup M+ [MPa]
σinf M+ [MPa]
σsup M‐ [MPa]
σinf M‐ [MPa]
(σsup M+) +σprec
(σinf M+) +σprec
(σsup M‐) +σprec
(σinf M‐) +σprec
6.00 4.00 2.00
σ [MPa]
0.00 ‐2.00 ‐4.00 ‐6.00 ‐8.00 8.00 ‐10.00 ‐12.00 ‐14.00 0.00
20.00
40.00
60.00
80.00
100.00
x [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
120.00
140.00
160.00
180.00
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Shear at end of launching g (values in kN*10*m)
Fase95 95 Step
V sett. Vced
Vg
V temp
V+
V-
Vtot+
Vtot-
-300.0
-250.0
-200.0
-150.0
-100.0 100 0
-50.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0
50.0
100.0
150.0
200.0
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Shear during g launching g Fase20 20 Step
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
Fase30 30 Step
-300.0
-300.0
-250.0
-250.0
-200.0
-200.0
-150.0
-150.0
-100.0
-100.0
-50.0
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
-50.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0
50.0
50.0
100.0
100.0
150.0
150.0
200.0
200.0
Fase 40 40 Step
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
Fase50 50 Step
-300.0
-300.0
-250.0
-250.0
-200.0
-200.0
-150.0
-150.0
-100.0
-100.0
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
-50.0
-50.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0
160.0
0.0
0.0
50.0
50.0
100.0
100.0
150.0
150.0
200.0
200.0
20.0
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
40.0
60.0
80.0
100.0
120.0
140.0
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Shear during g launching g Fase Step60 60
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
Fase70 70 Step
-300.0
-300.0
-250.0
-250.0
-200.0
-200.0
-150.0
-150.0
-100.0
-100.0
-50.0
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
-50.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0
50.0
50.0
100.0
100.0
150.0
150.0
200.0
200.0
Fase Step 80 80
Vg
Vsett. Vced
V temp
V+
V-
Vtot+
Vtot-
Fase90 90 Step
-300.0
-300.0
-250.0
-250.0
-200.0
-200.0
-150.0
-150.0
-100.0
-100.0
-50.0
Vg
Vced Vsett.
V temp
V+
V-
Vtot+
Vtot-
-50.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0
160.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0
50 0 50.0
50 0 50.0
100.0
100.0
150.0
150.0
200.0
200.0
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
SECONDINO VENTURA BRIDGE SLS Verifications
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
•
Static scheme:
•
Actions:
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¾ Self weight ¾ Prestressing (considering anchorage draw in and friction) ¾ Prestressing losses ¾ Permanent loads ¾ Termic variation between intrados and extrados of ± 5° ¾ Traffic loads
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Prestressing layout – 1st span
19 T15 strands tendons
19 T15 strands tendons
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
Couplers for 19T15
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Prestressing layout – section AA S f Surface inclined 88° Live anchorage for 19 T15
Deck axis
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
4
Incremental launching Live anchorage for 19 T15
section 11
Bearings axis Live anchorage for 19 T15
Live anchorage for 19 T15
19 T15 strands tendons
section ti 22
Bearings axis
19 T15 strands tendons
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
section 33
Bearings axis
19 T15 strands tendons
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Incremental launching Live g for anchorage 19 T15
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section 55
Deck axis
19 T15 strands tendons Bearings axis
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
Prestressing layout – section BB
D k axis Deck i
19 T15 strands tendons
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Prestressing layout – section CC
19 T15 strands tendons
Deck axis
Couplers for 19T15
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
4
Incremental launching
section 44
Couplers for 19T15
19 T15 strands tendons
Live anchorage for 19 T15
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
Pier axis
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Prestressing layout – 2nd span
Couplers for 19T15
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Incremental launching
Prestressing layout – section DD
Deck axis
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
19 T15 strands tendons
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Prestressing layout – 3rd span
Couplers for 19T15
Live anchorage for 19 T15
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
4
Incremental launching
Prestressing layout – section GG
Deck axis
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
19 T15 strands t d tendons
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Incremental launching Live anchorage for 19 T15
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section 66 19 T15 strands tendons
Live anchorage for 19 T15
Bearings axis
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Bending moment Self weight Peso proprio Permanent loads Permanenti portati
Prestressing Precompressione Temperature Gradiente gradient
Prestressing losses Cadute precompressione
‐25000 ‐20000 ‐15000 ‐10000
M[kN m m]
‐5000 0 5000 10000 15000 20000 25000 30000 35000 0.0
20.0
40.0
60.0
80.0
100.0
x [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Internal actions (M,N) and relative stresses DEFINITIVE PRESTRESSING PRECOMPRESSIONE DEFINITIVA N [kN]
σ sup [MPa]
σ inf [MPa] 00 0.0
‐70000
‐2.0
‐60000
‐4.0
‐50000
‐6.0
‐40000
‐8.0
‐30000
‐10.0
‐20000
‐12.0
10000 ‐10000
‐14.0 14.0
0
‐16.0
10000
‐18.0
20000
Stresses Tensioni [MPa]
M [kNm], N [kN]
M [kN m] ‐80000
‐20.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
x [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Internal actions (M,N) and relative stresses S.L.E. IN ASSENZA PERMANENTI PORTATI (t=∞) S.L.S. WITHOUTDI PERMANENT LOADS ( t = ∞) N
σ sup [MPa]
σ inf [MPa] 0.0
‐50000
‐2.0
‐40000 40000
40 ‐4.0
‐30000
‐6.0
‐20000
‐8.0
‐10000
‐10.0
0
‐12.0
10000
‐14.0
20000
‐16.0 0.0
20.0
40.0
60.0
80.0
100.0
x [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
120.0
140.0
160.0
Stresses Tensioni [MPa]
M [kNm],, N [kN]
M ‐60000 60000
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Internal actions (M,N) and relative stresses S.L.S. QUASI-PERMANENT COMBINATION ( t = (t=∞) ∞) S.L.E. - COMBINAZIONE QUASI PERMANENTE N σ sup M‐ [MPa] σ sup M
M‐ σ inf M‐ [MPa] σ inf M
σ sup M+ [MPa]
‐60000
0.0
‐50000
‐2.0
‐40000
‐4.0
‐30000
‐6 0 ‐6.0
‐20000
‐8.0
‐10000
‐10.0
0
‐12.0
10000
‐14.0 0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
Stresses S Tensioni [M MPa]
M [kNm], N M N [kN]
M+ σ inf M+ [MPa] σ inf M [MPa]
160.0
x [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Internal actions (M,N) and relative stresses S.L.S. CHARACTERISTIC COMBINATION ( t = ∞) S.L.E. - COMBINAZIONE RARA (t=∞) N σ sup M‐ [MPa] σ sup M
M‐ σ inf M‐ [MPa] σ inf M
σ sup M+ [MPa]
‐60000
0.0
‐50000
‐2.0
‐40000
‐4.0
‐30000
‐6.0
‐20000
‐8.0
‐10000
‐10.0
0
‐12.0
10000
‐14.0
20000
‐16.0 0.0
20.0
40.0
60.0
80.0
100.0
x [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
120.0
140.0
160.0
Stresses S TTensioni [M MPa]
M [kNm], N M N [kN]
M+ σ inf M+ [MPa] σ inf M+ [MPa]
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SECONDINO VENTURA BRIDGE ULS Verifications
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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Bending g moment diagram g (excluded isostatic internal actions due to prestressing) S.L.U. - COMBINAZIONE UII((t=∞) (t=∞) U.L.S. COMBINATION ) Msd [kN m]
Mrd [kN m]
‐80000 ‐60000
M M [kNm], N [ kN]
‐40000 ‐20000 0 20000 40000 60000 80000 100000 0.0
20.0
40.0
60.0
80.0
100.0
x [m]
Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
120.0
140.0
160.0
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Ultimate limit state for shear and torsion Ultimate verification for shear of prestressed elements can be very complicated because of the necessity to take into account the interaction between compression fields due shear and prestressing. The EN1992 simplify the approach, using a formulation that, in general case, is on the safe side. Practically shear coming from prestressing (in an statically determined structure it is coincident to the vertical component of prestressing force) is subtracted to the shear due to the external actions. The limit resistance of the elements that don’t require q shear reinforcements ((VRd,c Rd c) is increased to take into account the arch-tie resisting system. Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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VRd,c = [CRd,ck(100 ρl fck)1/3 + k1 σcp] bwd Where:
CRd ,c =
k = 1+
ρl =
0.18
γc 200 ≤2 d
With d in millimeters
As ,l bw ⋅ d
k1 = 0.15 With a minimum of: Where: Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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R i t Resistance off web b compression i fi fields ld (VRd,max) iis modified difi d tto ttake k iinto t account the interaction between longitudinal and inclined compression: VRd,max = αcw bw z ν1 fcd/(cotθ + tanθ ) ν1 = 0,6 ν1 = 0,9 – fck /200 > 0,5 αcw =1 αcw = (1 + σcp/fcd) αcw = 1,25 αcw =2,5 =2 5 (1 - σcp/fcd)
for fck ≤ 60 MPa for fck ≥ 60 MPa for non prestressed structure for 0 < σcp ≤ 0,25 fcd for 0,25 fcd < σcp ≤ 0,5 fcd for 0 0,5 5 fcd < σcp < 1,0 1 0 fcd
Prestressing g reinforcement can also be used to carry y the increment of the tensile force in the tensed chord due to shear. Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”
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References • • •
CEB FIP Model Code 1990 CEB-FIP 1990, Thomas Telford – 1990 Eurocode 2 Design of concrete structures, Part 1-1: general rules and rules for buildings - 2003 E Eurocode d 2D Design i off concrete t structures t t – Part P t 2: 2 concrete t bridges - 2004
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