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The Impact of Using Concrete of Various Density on the State of Stresses in Prestressed Concrete Flyovers Over Highways
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 193 (2017) 258 – 265
International Conference on Analytical Models and New Concepts in Concrete and Masonry Structures AMCM’2017
The impact of using concrete of various density on the state of stresses in prestressed concrete flyovers over highways Przemysáaw Mossakowskia, Wojciech Trochymiaka, Wojciech Radomskia,* a
Warsaw University of Technology, Institute of Roads and Bridges, ul. Armii Ludowej 16, Warsaw 00-637, Poland
Abstract A significant part of flyovers over highways and express roads in Poland is developed as two-span beam and frame structures. Due to the span length and economic conditions their superstructure are most often constructed as prestressed concrete ones. This paper presents the impact of some of the construction defects and imperfections not considered during the design stage on the stress state in the post-tensioned flyovers structures over highways. The results of the analyses concern three structures that were inspected in detail by the authors. © by Elsevier Ltd. This is an openLtd. access article under the CC BY-NC-ND license ©2017 2017Published The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Concepts in Conceptsand in Masonry ConcreteStructures and Masonry Structures. Concrete Keywords: post-tensioned bridges; prestressed concrete; concrete density;
1. Introduction In many of the existing or currently being under construction prestressed concrete bridge structures in Poland, the designers most often assume the density of concrete equal to 27 kN/m3 (crushed stone basalt aggregate concrete [1]). However, it is presently more frequent to use in practice granite or granodiorite crushed stone aggregate in concrete to construct bridge structures. Such concrete is characterized by a lower density and lower modulus of elasticity then those made using basalt aggregate.
* Corresponding author. Tel.: +48-22-825-59-37; fax: +48-22-825-88-99. E-mail address: [email protected]
1877-7058 © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Concepts in Concrete and Masonry Structures
doi:10.1016/j.proeng.2017.06.212
Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265
259
According to [2] granite or granodiorite aggregate concrete is characterized by the density within 22.6 ÷ 23.2 kN/m3. In design documentation (specification) the requirements concerning the control of density of concrete and its modulus of elasticity, are often not specified during the construction stage. This may lead to unintended work defects. While maintaining the design parameters of prestressed concrete structures designed with basalt aggregate concrete but constructed with the use of granite aggregate concrete, above defects may lead to undesired damages, for instance concrete cracks of unacceptable width. The paper presents the results of the analyses concerning the impact of density of concrete on the state of normal stresses in the girders and a possibility of crack appearance in them inconsistent with the design assumptions. The analyses were carried out using the example of typical flyovers over highways [3,4], denoted below as WD-23, WD-14 and WD-28. 2. The description of construction solutions of the analyzed objects The paper presents the results of the analysis of three two-span flyovers of girder type. The cross section of their superstructure constitute two monolithic trapezoid beams (main girders) joined with the deck slab. The beams are braced with cross beams over pillars and in some cases in spans. Exemplary geometric data of one of the structures is shown in Figures 1 and 2. The superstructures were designed using prestressed (post-tensioned) concrete [1,5,6,7]. The following actions were taken into account: dead (self-weight) load, superimposed dead load, impact of prestressing, thermal effects, loads from unequal pier settlement and traffic (live) loads for load class B according to [1,7]. Basic parameters of the analyzed structures are presented in Table 1. Table 1. Technical parameters of flyovers structure. Specification / Flyover symbol
WD-23 [3]
WD-14 [3]
WD-28 [4]
Theoretical span lt [m]
36.00+34.00
30.00+30.00
34.00+34.00
Overall width [m]
13.20
10.50
12.10
Sweep angle [°]
60.00
90.00
59.00
Construction height hk [m]
1.76
1.46
1.67
Depth/span ratio hk/lt
1/20.42
1/20.62
1/20.36
Concrete class [10]
B45
B50
B50
Volume of concrete in structure [m3]
715
426
565
Weight of reinforcing steel [kg]
94267
66770
84144
Prestressing steel
Y1860
Y1860
Y1860
Type of prestressing cables
22 L15.5
19 L15.7
19 L15.7
Number of cables [pieces]
2x7
2x6
2x6
Weight of prestressing steel [kg]
23950
16395
18480
Tensile strength of a single cable P0 [kN]
4200.0
3684.2
4134.,8
The use of bearing capacity, ı0/Rvk [%]
68.4
69.5
78.0
Load class [8]
B
B
B
Legend: * - non-usable width, i.e. barrier or balustrade fixing, distance between the barrier rail and the edge of the road
The superstructures of flyovers were designed using concrete B45 (~C35/45) or B50 (~C40/50), reinforcing steel A-IIIN (BSt500S) [5,8,9,10] and prestressing steel of the class Y1860 [5,11]. The prestressing system was composed by the prestressing tendons, system of anchorages, steel corrugated tendons sleeves and air vent injection pipes. Before concreting the superstructure, a precambering was introduced, reinforcement and prestressed elements were placed as well as filters and the elements of drainage system were installed [6,12]. The girders were supported on pot bearings, fixed bearings were placed on the intermediate pier.
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After concreting prestressing steel tendons (cables) were inserted into the tendon ducts and after the concrete reached the required strength it was prestressed according to the prepared prestressing program. All analyzed structures had typical bridge details such as reinforced concrete monolithic parapets, granite bridge curbs, steel safety barriers, balustrades, etc. The bridge pavement consisted of two layers: 40mm of wearing course and 45 mm of binder course. Waterproofing membrane with 5 mm depth was placed on the bridge deck. A thin layered asphalt surface was applied on the parapets.
Fig. 1. Elevation and longitudinal section of flyover structure WD-14 [3].
Fig. 2. Cross section of flyover WD-14 [3].
3. The scope of the analyses, adopted assumptions and calculations models The static analysis and structural design of the flyovers were carried out in order to determine the levels of stress adopted in the design documentation and in particular according to [5, pkt. 9.1], which concerns the possibility of the appearance of limit state of cracking (partial prestressing) and in order to determine the state of normal stress in main girders. The calculations were made using the standard [1] and requirements concerning prestressed structures (according to the design assumptions): during the construction state (SB), non-serviceability state (SBZ) and serviceability state (SUZ) according to [5, p. 9.2]. Superstructures were analyzed accepting the material of flyovers as linear-elastic. The impact of prestressing was modeled using a load balanced method taking into account all types of the prestressing losses [13,14]. In order to determine rheological losses it was assumed that the concrete was loaded minimum 12 days after prestressing process. The lay-out of tendons are along the curves determined by the function (1).
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f ( x ) = a 0 + a1 ⋅ x + a 2 ⋅ e px + a3 ⋅ e − px
(1)
The parameters a0 ÷ a3 were determined by the algorithm program [15] on the base of the declared coordinates of the characteristic points of the prestressing tendon arrangements and the p parameter (first derivative of the tendon curve in the characteristic point) reflecting the smoothness of the tendon curve. In the analyzed examples 5 characteristic points were declared for each of the tendon curve (the coordinates of the anchorage points, the coordinates of the points situated in the lowest parts of tendon corves along the spans and the coordinates of the tendon curve over the intermediate support). Basic parameters of materials built into superstructures were presented in Tables 2 ÷ 4 [5,11]. Table 2. Properties of concrete in superstructures: B45 and B50 [5]*). Class
RbG
Rbk
Rb1
Rb2
Rbtk0,05
Rbt0,50
Eb
gb1
gb2
(fcG)
(fck)
(fcd1)
(fcd2)
(fctk 0,05)
(fctm)
(Ecm)
(gc1)
(gc2)
[MPa]
[MPa]
[MPa]
[MPa]
[MPa]
[MPa]
[GPa]
[kN/m3]
[kN/m3]
B45
45
33.7
26.00
28.8
2.3
3.20
37.8
24.0
27.0
B50
50
37.5
28.82
32.0
2.4
3.40
39.0
24.0
27.0
*)
symbols adopted according to [10] are given in brackets Table 3. Properties of reinforcing steel A-IIIN [5] *).
Class
A-IIIN
Bar diamters
Rak
Ra
ga
φ
(fyk)
(fyd)
(gy)
[mm]
[MPa]
[MPa]
[kN/m3]
8 ÷ 32
490
375
78.5
*) symbols adopted according to[10] are given in brackets Table 4. Properties of prestressing steel Y1860 [11] Class
Y1860 S7
Relaxation class
Ev
ft
fy
φ
Ap
Fpk
gy
[GPa]
[MPa]
[MPa]
[mm]
[mm2]
[kN]
[kN/m3]
2
195
1860
1600
15.7
150
279
78.5
The following loads and impacts were considered during the analyses and according to [1] the design assumptions and parameters of built in and designed concrete: • dead-weight load (a few values were considered within the range: gb1 =23.0 kN/m3 (concrete with granite aggregate) to gb2 =27.0 kN/m3 (concrete with basalt aggregate and reinforcement component of – 1.0 kN/m3) with a step every 0.5 kN/m3 – see Table 5), • impact of prestressing (tendons trajectories according to the engineering project were adopted), • load from the weight of bridge details (e.g. elements of drainage system, etc.), • live load: vehicle K, loads uniformly distributed from vehicles q on the road and crowd on the sidewalks qt; the values of loads were adopted as for the class B according to [1], the value of the load from vehicle wheels K includes the impact of the dynamic coefficient ij, • impact of changes in temperatures (even heating and cooling and differences in temperatures at the bottom and top of the structures), • loads from unequal pier settlement. Technological parameters presented in prestressing program and design requirements were considered in the calculations of the prestressing effects [3,4]. The initial prestressing force in 19 and 22 strands and 7 wire tendons was adopted according to the engineering design (Table 1). The prestressing losses were determined taking into account the friction coefficient ȝ = 0.18,
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unintended corrugating of the cable ducts ȕ = 0.3 degree/m, sliding in the anchorage v = 5 mm, eccentric laying of the strands in the cable trail e = ± 10 mm and internal diameter of the cable ducts φ = 100 mm.
Fig. 3. Calculation model of the superstructure of flyover WD-14 [3] – top view (shaded beam elements).
Fig 4. Calculation model of the superstructure of flyover WD-23 [3] – visualization (visible routes of prestressing tendons)
Internal forces and stresses were determined using calculations models FEM (SOFiSTiK [15]). Beam-shell models (e1+e2, p3) in three-dimensional space were adopted in which the plus Z-axis is directed downwards. The structure of main girders was modeled with beam elements and cross beams and the structure of the bridge deck slab was modeled with the shell elements. The mesh of nodes of the deck slab was modeled on the fixed height without taking into account the longitudinal and transversal slops of the bridge deck. The transversal slope was considered by differentiating the thickness of
Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265
elements that were used to model the deck slab and the girders. The mesh of nodes was accepted on the upper surface of the structure. The position of the girders, cross beams and the slab was differentiated using eccentrics (offsets). Girders, cross beams and the slab were placed under the mesh of nodes which was supported on the nodes situated along the axis of the structure. The nodes in the X direction were distributed regularly, making them denser near the cross beams (spacing of the nodes was most often 1.00 m, and only near the cross beams – 0.50 m). The nodes in the Y direction were distributed in a way that allowed introduction of changes in the thickness of the structure in the transversal direction. Two-node beam elements served to model main girders and cross beams on them. The deck slab was modeled with four-node plane elements of variable thickness. An example of a scheme of a calculation model of flyover WD-14 was presented on Figures 3 ÷ 5.
Fig. 5. Calculation model of the superstructure of flyover WD-14 [3] –cross section A-A marked on Fig. 3 (shaded beam elements; points were indicated in which normal stresses in beam cross sections were verified).
4. Analysis of the superstructure The analysis of the superstructure of flyovers was conducted during the states of loading of prestressed structures according to [5, p. 9.2], and in particular during the: construction state (SB), non-serviceability state (SBZ) and serviceability state (SUZ). The aim of the calculation was to determine the level of stress and verification of the standard conditions [5], meaning the extreme values characteristic for normal stresses, ıx 0,00 or ıx Rbtk 0,05. For verification, 7 characteristic cross sections in each of the girder (Fig. 3) were selected that were respectively denoted: nr 1 at the first faces of the girders, nr 2- in the axis of the supporting cross beam, nr 3 – in the center of the span 1-2, nr 4- in the axis of the cross beam over the intermediate support, nr 5- in the center of the span 2-3, nr 6 – in the axis of the supporting cross beam, nr 7 – at the last faces of the girders. In each of the cross section, the normal stresses in characteristic points of left and right beam were determined; in points BL1 ÷ BL4 – left beam and BP1÷BP4 – right beam, respectively (Fig. 5). The selection of cross sections and points was dictated by the concentration of damages in the structure (cracks perpendicular to the axis of the structural element), places of the appearance of maximal internal forces and constructional notches. Because of the occurrence of cracks in the lower area of beams over the intermediate support, a special attention was put to the bottoms of the beams in this area.
263
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Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265 Table 5. Characteristic values of normal stresses determined in extreme, bottom fibers of girders cross sections over the intermediate support. Density of concrete [kN/m3]
Normal stresses [MPa] WD-23
WD-14
WD-28
SB
SBZ
SUZ
SB
SBZ
SUZ
SB
SBZ
SUZ
23.0
6.64
4.95
2.57
7.83
6.07
3.71
5.30
3.75
1.82
23.5
6.38
4.69
2.31
7.55
5.78
3.43
5.03
3.47
1.62
24.0
6.12
4.42
2.04
7.26
5.50
3.14
4.75
3.19
1.17
24.5
5.85
4.16
1.78
6.98
5.21
2.86
4.48
2.92
1.07
25.0
5.59
3.90
1.51
6.69
4.93
2.58
4.20
2.65
0.80
25.5
5.32
3.63
1.25
6.35
4.65
2.29
3.92
2.37
0.37
26.0
5.06
3.37
0.99
6.12
4.36
2.01
3.65
2.09
0.24
26.5
4.80
3.11
0.70
5.84
4.08
1.72
3.37
1.81
0.00
27.0
4.53
2.84
0.50
5.55
3.79
1.49
3.10
1.54
-0.30
Symbols: SB – construction state (after prestressing of the structure), SBZ – non-serviceability state , SUZ – serviceability state (structure being used), cases of exceeding acceptable stresses according to [5] were distinguished. Tensile stresses - a plus sign (+), compressive stresses - minus sign (-).
9 8 7 B45/Rbt0,05 Normal stresses [MPa]
6
WD-23/SB WD-23/SBZ
5 WD-23/SUZ WD-14/SB
4
WD-14/SBZ 3
WD-14/SUZ WD-28/SB
2
WD-28/SBZ 1
WD-28/SUZ
0 23,0 -1
23,5
24,0
24,5
25,0
25,5
26,0
26,5
27,0
Density of concrete [kN/m3]
Fig. 6. Graphic representation of calculation results. Normal stresses in bottom fibers of girders in the vicinity of the intermediate support in the function of the concrete density (the area of acceptable values of stresses is shaded) according to [5]).
Table 5 presents exemplary characteristic values of normal stress in the considered stages of loading of the structure, in a selected cross section (cross section no 4) taking into account the different concrete density. Figure 6 presents a graphic representation of the results from Table 5.
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265
5. Conclusions On the basis of the analyses it can be claimed that the assumed level of stress in designing flyovers is a partial prestress according to [5, p. 9.1] – level of stress concerns the structure of the girders (main beams) in which the acceptable level of crack width is wk = 0.1 mm. The analysis of results of calculations and in particular with regards to the basalt aggregate concrete and granite aggregate concrete, confirms the necessity to include the difference in concrete density and verification of prestress parameters in prestressed structures during the construction stage. The location of cracks (data recorded during the inspections of objects [3,4]) „overlap” the places where the characteristic values of normal stresses are exceeded in comparison to the standard value of concrete tensile strength Rbtk0,05 = 2.30 / 2.40 MPa [5], and correspond to the places where significant structural notches occur. Not meeting the standard conditions occur in calculation situations that correspond to the construction state SB (the greatest value of prestressing force) and in the non-serviceability state SBZ. Maximal stresses exceed three times the values that are recognized as limit values. Such situation should not take place due to the durability of the structures since cracking occurs during the non-serviceability state (SBZ). In the analyzed structures the extreme values of normal stresses in the girders were often bigger than those recognized as acceptable in cases where the concrete density was significantly different than the one assumed during the design stage. Therefore one can conclude that density of modern structural concrete should also be verified during the construction stage. In case of prestressed structures the normal experience of the designer may fail him because, despite of decreasing self-weight load, the structure is exposed to cracking and a significant redistribution of internal forces caused by changes in stiffness and active load induced by prestressing which its primary function is compensating of the dead loads. The results of the analyses entitle the authors to claim that schemes/systems of prestressing should be optimized. This results from the fact that in none of the analyzed flyovers even when taking into account design parameters, the standard conditions that correspond to the limited prestressing, were not fulfilled in all states of construction and service. References [1] PN-S-10030:1985 Bridges. Loads [Polish Standard]. [2] J. Biliszczuk, Several remarks on design od prestressed concrete bridges, Conference ‘Bridge Durability’, DWE, Wrocáaw 2012, pp. 375-384 [in Polish]. [3] W. Radomski, W. Trochymiak, P. Mossakowski, R. HajduĞ, J. Lembke, Technical opinion on prestressed concrete flyovers over motorway A-4, Rzeszów – Korczowa section, IDiM PW, Warszawa-Rzeszów 2013 [in Polish]. [4] W. Trochymiak, R. HajduĞ, P. Mossakowki, W. Radomski, Technical opinion on flyover over motorway A-4, Kraków-Szarów section, IDiM PW, Warszawa-Kraków 2015 [in Polish]. [5] PN-S-10042:1991 Bridges. Concrete, Reinforced Concrete and Prestressed Concrete Structures. Design [Polish Standard]. [6] PN-S-10040:1999 Bridges. Concrete, Reinforced Concrete and Prestressed Concrete Structures. Requirements and Testing [Polish Standard]. [7] Order of Minister of Transport and Maritime Economy, 30th of May 2000, concerning technical conditions for bridge structures and their location, Dz. U., Nr 63, poz. 735 (in Polish). [8] PN-B-06250:1988 Ordinary Concrete [Polish Standard]. [9] PN-EN 206-1: 2003 Concrete. Requirements, Properties, production add Compatibility [Polish Standard] [10] PN-EN 1992-1-2:2008: Eurocod 2, Design of Concrete Structures., Part 2: Concrete bridges. Calculation and Structural Rules [Polish Standard]. [11] ETA-07/0003 TECPRESA Post-tensioning System. Técnicas del pretensado y servicios auxiliares S.L. [12] A. Madaj, W. Woáowicki, Design of Concrete Bridges, WKà, Warszawa 1989 [in Polish]. [13] J. Kmita, J. BieĔ, Cz. Machelski, Computer aided design of bridges, WKà, Warszawa 1989 [in Polish]. [14] T.Y. Lin, Load-Balancing Method for Design and Analysis of Presstresed Concrete Structures. ACI Structural Journal, June (1969) 719-742. [15] SOFiSTiK AG, Oberschleissheim, 2011, 2012.
ScienceDirect Procedia Engineering 193 (2017) 258 – 265
International Conference on Analytical Models and New Concepts in Concrete and Masonry Structures AMCM’2017
The impact of using concrete of various density on the state of stresses in prestressed concrete flyovers over highways Przemysáaw Mossakowskia, Wojciech Trochymiaka, Wojciech Radomskia,* a
Warsaw University of Technology, Institute of Roads and Bridges, ul. Armii Ludowej 16, Warsaw 00-637, Poland
Abstract A significant part of flyovers over highways and express roads in Poland is developed as two-span beam and frame structures. Due to the span length and economic conditions their superstructure are most often constructed as prestressed concrete ones. This paper presents the impact of some of the construction defects and imperfections not considered during the design stage on the stress state in the post-tensioned flyovers structures over highways. The results of the analyses concern three structures that were inspected in detail by the authors. © by Elsevier Ltd. This is an openLtd. access article under the CC BY-NC-ND license ©2017 2017Published The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Concepts in Conceptsand in Masonry ConcreteStructures and Masonry Structures. Concrete Keywords: post-tensioned bridges; prestressed concrete; concrete density;
1. Introduction In many of the existing or currently being under construction prestressed concrete bridge structures in Poland, the designers most often assume the density of concrete equal to 27 kN/m3 (crushed stone basalt aggregate concrete [1]). However, it is presently more frequent to use in practice granite or granodiorite crushed stone aggregate in concrete to construct bridge structures. Such concrete is characterized by a lower density and lower modulus of elasticity then those made using basalt aggregate.
* Corresponding author. Tel.: +48-22-825-59-37; fax: +48-22-825-88-99. E-mail address: [email protected]
1877-7058 © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Concepts in Concrete and Masonry Structures
doi:10.1016/j.proeng.2017.06.212
Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265
259
According to [2] granite or granodiorite aggregate concrete is characterized by the density within 22.6 ÷ 23.2 kN/m3. In design documentation (specification) the requirements concerning the control of density of concrete and its modulus of elasticity, are often not specified during the construction stage. This may lead to unintended work defects. While maintaining the design parameters of prestressed concrete structures designed with basalt aggregate concrete but constructed with the use of granite aggregate concrete, above defects may lead to undesired damages, for instance concrete cracks of unacceptable width. The paper presents the results of the analyses concerning the impact of density of concrete on the state of normal stresses in the girders and a possibility of crack appearance in them inconsistent with the design assumptions. The analyses were carried out using the example of typical flyovers over highways [3,4], denoted below as WD-23, WD-14 and WD-28. 2. The description of construction solutions of the analyzed objects The paper presents the results of the analysis of three two-span flyovers of girder type. The cross section of their superstructure constitute two monolithic trapezoid beams (main girders) joined with the deck slab. The beams are braced with cross beams over pillars and in some cases in spans. Exemplary geometric data of one of the structures is shown in Figures 1 and 2. The superstructures were designed using prestressed (post-tensioned) concrete [1,5,6,7]. The following actions were taken into account: dead (self-weight) load, superimposed dead load, impact of prestressing, thermal effects, loads from unequal pier settlement and traffic (live) loads for load class B according to [1,7]. Basic parameters of the analyzed structures are presented in Table 1. Table 1. Technical parameters of flyovers structure. Specification / Flyover symbol
WD-23 [3]
WD-14 [3]
WD-28 [4]
Theoretical span lt [m]
36.00+34.00
30.00+30.00
34.00+34.00
Overall width [m]
13.20
10.50
12.10
Sweep angle [°]
60.00
90.00
59.00
Construction height hk [m]
1.76
1.46
1.67
Depth/span ratio hk/lt
1/20.42
1/20.62
1/20.36
Concrete class [10]
B45
B50
B50
Volume of concrete in structure [m3]
715
426
565
Weight of reinforcing steel [kg]
94267
66770
84144
Prestressing steel
Y1860
Y1860
Y1860
Type of prestressing cables
22 L15.5
19 L15.7
19 L15.7
Number of cables [pieces]
2x7
2x6
2x6
Weight of prestressing steel [kg]
23950
16395
18480
Tensile strength of a single cable P0 [kN]
4200.0
3684.2
4134.,8
The use of bearing capacity, ı0/Rvk [%]
68.4
69.5
78.0
Load class [8]
B
B
B
Legend: * - non-usable width, i.e. barrier or balustrade fixing, distance between the barrier rail and the edge of the road
The superstructures of flyovers were designed using concrete B45 (~C35/45) or B50 (~C40/50), reinforcing steel A-IIIN (BSt500S) [5,8,9,10] and prestressing steel of the class Y1860 [5,11]. The prestressing system was composed by the prestressing tendons, system of anchorages, steel corrugated tendons sleeves and air vent injection pipes. Before concreting the superstructure, a precambering was introduced, reinforcement and prestressed elements were placed as well as filters and the elements of drainage system were installed [6,12]. The girders were supported on pot bearings, fixed bearings were placed on the intermediate pier.
260
Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265
After concreting prestressing steel tendons (cables) were inserted into the tendon ducts and after the concrete reached the required strength it was prestressed according to the prepared prestressing program. All analyzed structures had typical bridge details such as reinforced concrete monolithic parapets, granite bridge curbs, steel safety barriers, balustrades, etc. The bridge pavement consisted of two layers: 40mm of wearing course and 45 mm of binder course. Waterproofing membrane with 5 mm depth was placed on the bridge deck. A thin layered asphalt surface was applied on the parapets.
Fig. 1. Elevation and longitudinal section of flyover structure WD-14 [3].
Fig. 2. Cross section of flyover WD-14 [3].
3. The scope of the analyses, adopted assumptions and calculations models The static analysis and structural design of the flyovers were carried out in order to determine the levels of stress adopted in the design documentation and in particular according to [5, pkt. 9.1], which concerns the possibility of the appearance of limit state of cracking (partial prestressing) and in order to determine the state of normal stress in main girders. The calculations were made using the standard [1] and requirements concerning prestressed structures (according to the design assumptions): during the construction state (SB), non-serviceability state (SBZ) and serviceability state (SUZ) according to [5, p. 9.2]. Superstructures were analyzed accepting the material of flyovers as linear-elastic. The impact of prestressing was modeled using a load balanced method taking into account all types of the prestressing losses [13,14]. In order to determine rheological losses it was assumed that the concrete was loaded minimum 12 days after prestressing process. The lay-out of tendons are along the curves determined by the function (1).
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f ( x ) = a 0 + a1 ⋅ x + a 2 ⋅ e px + a3 ⋅ e − px
(1)
The parameters a0 ÷ a3 were determined by the algorithm program [15] on the base of the declared coordinates of the characteristic points of the prestressing tendon arrangements and the p parameter (first derivative of the tendon curve in the characteristic point) reflecting the smoothness of the tendon curve. In the analyzed examples 5 characteristic points were declared for each of the tendon curve (the coordinates of the anchorage points, the coordinates of the points situated in the lowest parts of tendon corves along the spans and the coordinates of the tendon curve over the intermediate support). Basic parameters of materials built into superstructures were presented in Tables 2 ÷ 4 [5,11]. Table 2. Properties of concrete in superstructures: B45 and B50 [5]*). Class
RbG
Rbk
Rb1
Rb2
Rbtk0,05
Rbt0,50
Eb
gb1
gb2
(fcG)
(fck)
(fcd1)
(fcd2)
(fctk 0,05)
(fctm)
(Ecm)
(gc1)
(gc2)
[MPa]
[MPa]
[MPa]
[MPa]
[MPa]
[MPa]
[GPa]
[kN/m3]
[kN/m3]
B45
45
33.7
26.00
28.8
2.3
3.20
37.8
24.0
27.0
B50
50
37.5
28.82
32.0
2.4
3.40
39.0
24.0
27.0
*)
symbols adopted according to [10] are given in brackets Table 3. Properties of reinforcing steel A-IIIN [5] *).
Class
A-IIIN
Bar diamters
Rak
Ra
ga
φ
(fyk)
(fyd)
(gy)
[mm]
[MPa]
[MPa]
[kN/m3]
8 ÷ 32
490
375
78.5
*) symbols adopted according to[10] are given in brackets Table 4. Properties of prestressing steel Y1860 [11] Class
Y1860 S7
Relaxation class
Ev
ft
fy
φ
Ap
Fpk
gy
[GPa]
[MPa]
[MPa]
[mm]
[mm2]
[kN]
[kN/m3]
2
195
1860
1600
15.7
150
279
78.5
The following loads and impacts were considered during the analyses and according to [1] the design assumptions and parameters of built in and designed concrete: • dead-weight load (a few values were considered within the range: gb1 =23.0 kN/m3 (concrete with granite aggregate) to gb2 =27.0 kN/m3 (concrete with basalt aggregate and reinforcement component of – 1.0 kN/m3) with a step every 0.5 kN/m3 – see Table 5), • impact of prestressing (tendons trajectories according to the engineering project were adopted), • load from the weight of bridge details (e.g. elements of drainage system, etc.), • live load: vehicle K, loads uniformly distributed from vehicles q on the road and crowd on the sidewalks qt; the values of loads were adopted as for the class B according to [1], the value of the load from vehicle wheels K includes the impact of the dynamic coefficient ij, • impact of changes in temperatures (even heating and cooling and differences in temperatures at the bottom and top of the structures), • loads from unequal pier settlement. Technological parameters presented in prestressing program and design requirements were considered in the calculations of the prestressing effects [3,4]. The initial prestressing force in 19 and 22 strands and 7 wire tendons was adopted according to the engineering design (Table 1). The prestressing losses were determined taking into account the friction coefficient ȝ = 0.18,
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unintended corrugating of the cable ducts ȕ = 0.3 degree/m, sliding in the anchorage v = 5 mm, eccentric laying of the strands in the cable trail e = ± 10 mm and internal diameter of the cable ducts φ = 100 mm.
Fig. 3. Calculation model of the superstructure of flyover WD-14 [3] – top view (shaded beam elements).
Fig 4. Calculation model of the superstructure of flyover WD-23 [3] – visualization (visible routes of prestressing tendons)
Internal forces and stresses were determined using calculations models FEM (SOFiSTiK [15]). Beam-shell models (e1+e2, p3) in three-dimensional space were adopted in which the plus Z-axis is directed downwards. The structure of main girders was modeled with beam elements and cross beams and the structure of the bridge deck slab was modeled with the shell elements. The mesh of nodes of the deck slab was modeled on the fixed height without taking into account the longitudinal and transversal slops of the bridge deck. The transversal slope was considered by differentiating the thickness of
Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265
elements that were used to model the deck slab and the girders. The mesh of nodes was accepted on the upper surface of the structure. The position of the girders, cross beams and the slab was differentiated using eccentrics (offsets). Girders, cross beams and the slab were placed under the mesh of nodes which was supported on the nodes situated along the axis of the structure. The nodes in the X direction were distributed regularly, making them denser near the cross beams (spacing of the nodes was most often 1.00 m, and only near the cross beams – 0.50 m). The nodes in the Y direction were distributed in a way that allowed introduction of changes in the thickness of the structure in the transversal direction. Two-node beam elements served to model main girders and cross beams on them. The deck slab was modeled with four-node plane elements of variable thickness. An example of a scheme of a calculation model of flyover WD-14 was presented on Figures 3 ÷ 5.
Fig. 5. Calculation model of the superstructure of flyover WD-14 [3] –cross section A-A marked on Fig. 3 (shaded beam elements; points were indicated in which normal stresses in beam cross sections were verified).
4. Analysis of the superstructure The analysis of the superstructure of flyovers was conducted during the states of loading of prestressed structures according to [5, p. 9.2], and in particular during the: construction state (SB), non-serviceability state (SBZ) and serviceability state (SUZ). The aim of the calculation was to determine the level of stress and verification of the standard conditions [5], meaning the extreme values characteristic for normal stresses, ıx 0,00 or ıx Rbtk 0,05. For verification, 7 characteristic cross sections in each of the girder (Fig. 3) were selected that were respectively denoted: nr 1 at the first faces of the girders, nr 2- in the axis of the supporting cross beam, nr 3 – in the center of the span 1-2, nr 4- in the axis of the cross beam over the intermediate support, nr 5- in the center of the span 2-3, nr 6 – in the axis of the supporting cross beam, nr 7 – at the last faces of the girders. In each of the cross section, the normal stresses in characteristic points of left and right beam were determined; in points BL1 ÷ BL4 – left beam and BP1÷BP4 – right beam, respectively (Fig. 5). The selection of cross sections and points was dictated by the concentration of damages in the structure (cracks perpendicular to the axis of the structural element), places of the appearance of maximal internal forces and constructional notches. Because of the occurrence of cracks in the lower area of beams over the intermediate support, a special attention was put to the bottoms of the beams in this area.
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Przemysław Mossakowski et al. / Procedia Engineering 193 (2017) 258 – 265 Table 5. Characteristic values of normal stresses determined in extreme, bottom fibers of girders cross sections over the intermediate support. Density of concrete [kN/m3]
Normal stresses [MPa] WD-23
WD-14
WD-28
SB
SBZ
SUZ
SB
SBZ
SUZ
SB
SBZ
SUZ
23.0
6.64
4.95
2.57
7.83
6.07
3.71
5.30
3.75
1.82
23.5
6.38
4.69
2.31
7.55
5.78
3.43
5.03
3.47
1.62
24.0
6.12
4.42
2.04
7.26
5.50
3.14
4.75
3.19
1.17
24.5
5.85
4.16
1.78
6.98
5.21
2.86
4.48
2.92
1.07
25.0
5.59
3.90
1.51
6.69
4.93
2.58
4.20
2.65
0.80
25.5
5.32
3.63
1.25
6.35
4.65
2.29
3.92
2.37
0.37
26.0
5.06
3.37
0.99
6.12
4.36
2.01
3.65
2.09
0.24
26.5
4.80
3.11
0.70
5.84
4.08
1.72
3.37
1.81
0.00
27.0
4.53
2.84
0.50
5.55
3.79
1.49
3.10
1.54
-0.30
Symbols: SB – construction state (after prestressing of the structure), SBZ – non-serviceability state , SUZ – serviceability state (structure being used), cases of exceeding acceptable stresses according to [5] were distinguished. Tensile stresses - a plus sign (+), compressive stresses - minus sign (-).
9 8 7 B45/Rbt0,05 Normal stresses [MPa]
6
WD-23/SB WD-23/SBZ
5 WD-23/SUZ WD-14/SB
4
WD-14/SBZ 3
WD-14/SUZ WD-28/SB
2
WD-28/SBZ 1
WD-28/SUZ
0 23,0 -1
23,5
24,0
24,5
25,0
25,5
26,0
26,5
27,0
Density of concrete [kN/m3]
Fig. 6. Graphic representation of calculation results. Normal stresses in bottom fibers of girders in the vicinity of the intermediate support in the function of the concrete density (the area of acceptable values of stresses is shaded) according to [5]).
Table 5 presents exemplary characteristic values of normal stress in the considered stages of loading of the structure, in a selected cross section (cross section no 4) taking into account the different concrete density. Figure 6 presents a graphic representation of the results from Table 5.
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5. Conclusions On the basis of the analyses it can be claimed that the assumed level of stress in designing flyovers is a partial prestress according to [5, p. 9.1] – level of stress concerns the structure of the girders (main beams) in which the acceptable level of crack width is wk = 0.1 mm. The analysis of results of calculations and in particular with regards to the basalt aggregate concrete and granite aggregate concrete, confirms the necessity to include the difference in concrete density and verification of prestress parameters in prestressed structures during the construction stage. The location of cracks (data recorded during the inspections of objects [3,4]) „overlap” the places where the characteristic values of normal stresses are exceeded in comparison to the standard value of concrete tensile strength Rbtk0,05 = 2.30 / 2.40 MPa [5], and correspond to the places where significant structural notches occur. Not meeting the standard conditions occur in calculation situations that correspond to the construction state SB (the greatest value of prestressing force) and in the non-serviceability state SBZ. Maximal stresses exceed three times the values that are recognized as limit values. Such situation should not take place due to the durability of the structures since cracking occurs during the non-serviceability state (SBZ). In the analyzed structures the extreme values of normal stresses in the girders were often bigger than those recognized as acceptable in cases where the concrete density was significantly different than the one assumed during the design stage. Therefore one can conclude that density of modern structural concrete should also be verified during the construction stage. In case of prestressed structures the normal experience of the designer may fail him because, despite of decreasing self-weight load, the structure is exposed to cracking and a significant redistribution of internal forces caused by changes in stiffness and active load induced by prestressing which its primary function is compensating of the dead loads. The results of the analyses entitle the authors to claim that schemes/systems of prestressing should be optimized. This results from the fact that in none of the analyzed flyovers even when taking into account design parameters, the standard conditions that correspond to the limited prestressing, were not fulfilled in all states of construction and service. References [1] PN-S-10030:1985 Bridges. Loads [Polish Standard]. [2] J. Biliszczuk, Several remarks on design od prestressed concrete bridges, Conference ‘Bridge Durability’, DWE, Wrocáaw 2012, pp. 375-384 [in Polish]. [3] W. Radomski, W. Trochymiak, P. Mossakowski, R. HajduĞ, J. Lembke, Technical opinion on prestressed concrete flyovers over motorway A-4, Rzeszów – Korczowa section, IDiM PW, Warszawa-Rzeszów 2013 [in Polish]. [4] W. Trochymiak, R. HajduĞ, P. Mossakowki, W. Radomski, Technical opinion on flyover over motorway A-4, Kraków-Szarów section, IDiM PW, Warszawa-Kraków 2015 [in Polish]. [5] PN-S-10042:1991 Bridges. Concrete, Reinforced Concrete and Prestressed Concrete Structures. Design [Polish Standard]. [6] PN-S-10040:1999 Bridges. Concrete, Reinforced Concrete and Prestressed Concrete Structures. Requirements and Testing [Polish Standard]. [7] Order of Minister of Transport and Maritime Economy, 30th of May 2000, concerning technical conditions for bridge structures and their location, Dz. U., Nr 63, poz. 735 (in Polish). [8] PN-B-06250:1988 Ordinary Concrete [Polish Standard]. [9] PN-EN 206-1: 2003 Concrete. Requirements, Properties, production add Compatibility [Polish Standard] [10] PN-EN 1992-1-2:2008: Eurocod 2, Design of Concrete Structures., Part 2: Concrete bridges. Calculation and Structural Rules [Polish Standard]. [11] ETA-07/0003 TECPRESA Post-tensioning System. Técnicas del pretensado y servicios auxiliares S.L. [12] A. Madaj, W. Woáowicki, Design of Concrete Bridges, WKà, Warszawa 1989 [in Polish]. [13] J. Kmita, J. BieĔ, Cz. Machelski, Computer aided design of bridges, WKà, Warszawa 1989 [in Polish]. [14] T.Y. Lin, Load-Balancing Method for Design and Analysis of Presstresed Concrete Structures. ACI Structural Journal, June (1969) 719-742. [15] SOFiSTiK AG, Oberschleissheim, 2011, 2012.