Indirectly Supported Bridges – Large-Scale Experiment

Christoph BUEELER Dipl. Bau-Ing. FH Lucerne University HSLU Switzerland christoph.bueeler@hslu.ch Christoph Bueeler, born 1981, received his civil engineering degree in 2007. He worked as a project engineer for 2 years before becoming a scientific associate at HSLU.

Karel THOMA Prof. Dr. dipl. Bau-Ing. ETH Lucerne University HSLU Switzerland karel.thoma@hslu.ch Karel Thoma, born 1968, received his civil engineering and PhD. degrees from the Swiss Federal Institute of Technology, Zurich. He works as a structural engineer and as a researcher at HSLU.

Summary For concrete bridge structures, the currently valid Swiss code, SIA 262:2003 [1], stipulates that in case of indirect support conditions, force transfers need to be checked utilizing stress fields. This is necessary to guarantee that sufficient hanger reinforcement is provided in load application areas. If the total shear force is supported by hanger reinforcement, it is possible to investigate static actions in the longitudinal and transverse beams independently of each other; otherwise, the load bearing capacity depends on the interaction between the longitudinal and transverse beam [2]. In order to investigate the influence of insufficient hanger reinforcement on the strength of indirectly supported beams, a large-scale experiment was conducted at the University of Applied Sciences and Arts, Lucerne [3]. The prestressed test specimen reflected a continuous, single celled box girder in the region of continuous support. The experiment clearly illustrated that the ultimate load and the failure mechanism of an indirectly supported concrete structure strongly depend on the reinforcement arrangement and the detailing. Furthermore, the deformation capacity of the plastic hinge also largely depends on the reinforcement arrangement. Keywords: Bridge, Indirect support, Brittle failure, Strength reserve, Plasticity theory, Stress field models.

1. Research Significance For concrete bridge structures, current structural codes, like the SIA 262 [1], require that in cases of indirect support conditions, force transfers need to be checked utilizing stress field models. This is necessary to guarantee that sufficient hanger reinforcement is provided at cross-section discontinuities. If the total shear force is supported by hanger reinforcement, it is possible to investigate the load path in the longitudinal and transverse girders independently of each other. Many existing, older, indirectly supported reinforced concrete bridge structures were designed with insufficient hanger reinforcement. Thus, for these older bridges, it is necessary that the interactions between the longitudinal and the transverse force flows be considered. The strength of the entire system is largely dependent on the arrangement of the reinforcement in the transverse beam and the resulting stress fields in the longitudinal and transverse beams. To avoid or minimize expensive strengthening a better understanding of the statics taking into account the reinforcement arrangement is necessary.

2. Literature review In 1965, Leonhardt and Walther [4] tested four large-scale shear walls, of which two of them were indirectly supported. These two experiments illustrated the static actions at the cross-section discontinuities; and, based on the crack pattern, Leonhardt and Walther developed an analytical model. The first large-scale experiments of indirectly supported prestressed concrete beams were conducted at the University of Stuttgart in the 1970s [5], [6]. The static actions and the influence of the shear force at cross-section discontinuities were investigated for different reinforcement layouts. In order to investigate the load path in the longitudinal and transverse beams independently of each other, the researchers discovered that the total shear force must be supported by hanger reinforcement. Based on the experimental result, Leonhardt [6] introduced a model to calculate the reinforcement requirements for indirect support conditions, which allows distributing the required hanger reinforcement around the cross-section discontinuity. In the late 1990s, one of the largest bridges in Zurich, known as the “Europabruecke”, was evaluated in terms of strength. At this time, the indirect support of the bridge was found to be inadequate. As a result of this finding, Marti and Stoffel [7] tested four large-scale beams to investigate the force flow and the influence of the hanger reinforcement on the ultimate strength of indirectly supported bridges. Based on these experiments, Stoffel [8] later introduced discontinuous stress field models describing the static actions for indirect support conditions

3. Large-scale experiment

3.1 Test Setup and Procedure Based on the experiments of Leonhardt, Koch and Rostásy [6], a large-scale experiment was carried out at the University of Applied Sciences and Arts, Lucerne. (For a detailed discussion refer to Bueeler and Thoma [3].) The test specimen reflected a continuous, single-celled box girder in the region of a continuous support. In the experimental phase 1 (cyclic loading) and phase 2 (failure longitudinal girder 1), the test specimen was set up according to Fig. 2 (a). After the failure of the longitudinal girder 1 (LG 1), the experimental setup was changed according to Fig. 2 (b).

applied load

LG 1

LG 2transverse girder

longitudinal girder 7.20 m

3.60

3.60

support 2

support 4

support 3

support 1

A2

A1

2.40 m

applied load

LG 2support 4

support 3

A2

A1support

(a) (b)

Fig. 2: Test setup; (a) test phase 1 and 2; (b) test phase 3.

During the first experimental phase, the test specimen was subjected to cyclic loading between 500 kN and 1000 kN, which resulted in the decompression of the girder cross-section in the vicinity of the continuous support and the indirect support. A total of 60 load cycles were applied. During the second experimental phase, the applied load was increased causing a ductile failure of LG 1. Afterwards, the experimental setup was changed and the applied load was increased until the longitudinal girder LG 2 failed.

3.2 Geometry, reinforcement layout and post-tensioning The structural element dimension and the post-tensioning were chosen according to Fig. 3 (a) and (b). The reinforcement layout of the two longitudinal girders was identical with the exception of the flexural tension reinforcement in the bottom chord (LG 1: 8 ø 8 mm; LG 2: 10 ø 14 mm). The shear reinforcement of the longitudinal and transverse girders was constant over the entire length, as depicted in Fig. 3 (c). No additional hanger reinforcement was provided at the cross-section discontinuities – only two stirrups of the longitudinal girder shear reinforcement were placed in the cross section area of the longitudinal and transverse girder. Furthermore, the grouted multi-wire tendon was provided by type 810 tendons (18 wires ø 7 mm) with a flat cladding tube. A parabolic duct centerline was chosen for the tendons in the longitudinal and transverse girders. The tendons were stressed up to Pk, 75% = 868 kN and afterward released to Pk, 70% = 810 kN. There was no additional force variation after anchor set, because the post-tensioning system (BBRV-System) provided a threaded anchor head. (a)

1.5090

60 90

1515

30 30

prestress tendon

applied load

LG 2LG 1

7.80 m

3.30 3.6030 30 30

prestress tendon

support 2/4 support 1/3

stirrup ø 8, s = 20

stirrup ø 8, s = 20

stirrup ø 8, s = 20

stirrup ø 8, s = 20

8 ø 8

2x2 ø 8, s = 22

stirrup ø 10, s = 10

2x4 ø 10, s = 15

stirrup ø 10, s = 10

4 ø 14, s = 10

2219

19

2 ø 14, s = 15

8 ø 8, LG 110 ø 14, LG 2

60 90

1515

A1,2

(b) (c)

Fig. 3: (a) geometry of prestressed longitudinal girders; (b) geometry of prestressed transverse girder; (c) cross-section of longitudinal and transverse girders including reinforcement arrangements.

3.3 Material Properties The stress-strain responses of the reinforcement and steel wire are shown in Fig. 4 and the material properties are shown in Table 1.

The 30-day mean value of the concrete density was 2320 kg/m³, the cylinder compressive strength was 34 N/mm², the cube compressive strength was 43 N/mm², and the initial tangent modulus (Young’s modulus) , was 25’300 N/mm². 10 days after cast, the pre-stressing was applied. At this time, the cylinder compressive strength was 30 N/mm². (a)

ø 7 mm

ø 8 mm ø 10 mm

ø 14 mm

σ[N

/mm

]p

2

σ[N

/mm

]s

2

(b)

(c) (d)

σ[N

/mm

]s

2

00

ε [%]s

5 10

800

400

00

ε [%]s

5 10

800

400

00

ε [%]p

5 10

2000

1000

00

ε [%]s

5 10

800

400

Fig. 4 Stress-strain responses; (a), (b), (c) steel bars; (d) BBRV steel wire.

Table 1: Mean values of the material properties of reinforcement and steel wire.

Material properties Bar ø 8 mm Bar ø 10 mm Bar ø 14 mm Wire ø 7 mm

Yield strength fy,dyn / fy,stat [N/mm2] 566 / 524 549 / 513 513 / 475 1621 / 1549

Ultimate strength fu,dyn / fu,stat [N/mm2] 610 / 553 595 / 542 585 / 529 1765 / 1642

Ultimate strain εu [%] 3.9 4.4 5.0 4.6

Young’s modulus E [N/mm2] 205’000 205’000 205’000 201’000

3.4 Measurement During the experiment, the deformations in various points of the test specimen were recorded with LVDT. At static loading, the deformation state was measured with extensometers. The triangular mesh grid, with a lateral length of 200 mm, was layed out as illustrated in Fig. 5 (a, b). By measuring the mesh grid deformations, using extensometers, it is possible to calculate the node deformations u and v with a linear finite element software, see Fig. 5 (c). Subsequently, an eigenvalue problem can be solved resulting in the eigenvalues (principle strains) and eigenvectors (principle directions), as depicted in Fig. 5 (d) and Fig. 5 (e) [9].

0

y

x

S

(x ,y )i i

(x ,y )j j

(x ,y )k k

u

v

i

iu

v

j

j

u

v

k

k

0

γ

εεx

εy

γxy

γxy2

2

ε1ε2 α2

(c)

(d)

(a)

(b)

a =

ui

vi

B =β1uj

vj

uk

vk

0 β2 0 β3 00 γ 1 0 γ 2 0 γ 3

γ 1 β1 γ 2 β2 γ 3 β3

Δ 1 xj yj= det1 xk yk

1 xi yi β1

β2

β3

= yj yk-= yk yi-= yi yj-

γ 1

γ 2

γ 3

= xj xk-= xk xi-= xi xj-

ε = a B = εγ

ε x

y

xy

. E =ε x

ε yγ xy2

γ xy2

(e)

1Δ

(1,2)

(3-5)

(6,7)

;

; ;

;

Fig. 5: (a) extensometer mesh grid on longitudinal girders; (b) extensometer mesh grid at transverse girder; (c) triangular grid element with its state of strain; (d) Mohr’s circle of strain; (e) equations 1 to 7.

3.5 Test Results Fig 6 shows the total shear force versus the mid-span deformation of the test specimen. The total shear force is equivalent to the sum of the support reactions of the longitudinal girder LG 1 and LG 2. The longitudinal girder LG 1 failed at 589 kN which corresponded to a mid-span deformation of 135 mm. However, the maximal total shear force was at 635 kN which corresponded to a mid-span deformation of 47 mm. The detected failure mechanism was a ductile bending failure. In contrast, the failure mechanism of longitudinal girder LG 2 was a shear failure. LG 2 failed at 831 kN corresponding to a mid-span deformation of 88 mm. However, the maximal total shear force was 863 kN corresponding to a mid-span deformation of 77 mm.

mid-span deformation [mm]0

0

1000

entir

e sh

ear

forc

e at

100

[kN

]

00

1000

100

60 c

ycle

60 c

ycle

bending failure

shear failure

failure LG 1

decompressiondecompression

(a) (b)

A1

entir

e sh

ear

forc

e at

[k

N]

A2

mid-span deformation [mm]

LL 13

LL 5

test phase 3

test phase 2

test phase 2

LL 13

Fig. 6: Entire shear force versus mid-span deformation diagram; (a) LG 1; (b) LG 2.

3.5.1 Longitudinal girder LG 1 Fig. 7 (a) shows the average strains at load level 13 of the longitudinal girder LG 1 at the top and bottom chord. Due to decompression, the tensile strains at the bottom chord of LG 1 are significant in the vicinity of the cross-section discontinuity. On the other hand, around the support, the longitudinal girder LG 1 is uncracked and (due to the prestress) the strains are small. The strains in the top and bottom chord of the transverse girder are also small, as shown in Fig. 6 (b). Similarly, the average compressive strains in the longitudinal girder LG 1 and the transverse girder are small.

top chord

bottom chord

1.0

distance [mm]

ε[%

]x

1000

0

top chord

0.5

20003000 10000 2000 3000

LL 13: 577 kN

bottom chord

-1.0

-0.5 -0.335

0.852

1.0

distance [mm]

ε[%

]x

1000

-1.0

0

top chord

0.5

-0.5

10000

LL 13: 1206 kN

bottom chord

LG 1 LG 2top chord

bottom chord

-0.205

0.139

(a) (b)

Fig. 7: Tensile and compressive strain of top and lower chord at load level 13 in test phase 2; (a) longitudinal girder 1; (b) transverse girder.

3.5.2 Longitudinal girder LG 2 Due to the higher percentage of reinforcement in the bottom chord of longitudinal girder LG 2, the average strains at the top chord were lower and the average strains at the bottom chord were higher compared to the strains of longitudinal girder LG 1 at the same load level. However, the total shear force at the cross section discontinuity of LG 2 was slightly higher than the applied total shear force in LG 1 (see Fig. 10 (a) and Fig. 6). At load level 5 (test phase 3), the average strains at the top and bottom chord were almost the same as at load level 13 (test phase 1) of LG 1. In contrast, the longitudinal girders stresses and strains of the transverse girder increased with the applied load, as depicted in Fig. 10 (b). The failure of longitudinal girder LG 2 was a shear failure mechanism. Fig. 11 (a) shows the principle strains at load level 5 (test phase 3) and the principle directions indicate the shear failure. As in LG 1, the principle strains are in good agreement with the crack pattern; therefore, there is no indication of aggregate interlock. The crack pattern, the principle strains and the principle directions (shown in Fig. 11 (b)), constitute the load path of the indirect support of longitudinal girder LG 2. The static actions and the ultimate load level of indirectly supported structures can be described and calculated with stress field models [2].

top chord

bottom chord

1.0

ε[%

]x

1000

0

0.5

20003000 10000 2000 3000

LL 13: 629 kN

-1.0

-0.5-0.183

0.270

1.0

ε[%

]x

1000

0

0.5

20003000 10000 2000 3000

LL 5: 752 kN

-1.0

-0.5 -0.361

0.544

1.0

distance [mm]

ε[%

]x

1000

-1.0

0

top chord

0.5

-0.5

10000

LL 13: 1206 kN

bottom chord

LG 1 LG 2top chord

bottom chord

1.0

ε[%

]x

1000

-1.0

0

top chord

0.5

-0.5

10000

LL 5: 1609 kN

bottom chord

-0.205

-0.313

0.139

0.306

top chord

bottom chord

top chord

bottom chord

distance [mm]

distance [mm] distance [mm]

(a) (b)

Fig. 10: Tensile and compressive strains of top and bottom chord at load level 13 in test phase 2 and load level 5 in test phase 3; (a) longitudinal girder LG 2; (b) transverse girder.

At failure, the stirrups around the cross-section discontinuity fractured with the crack pattern depicted in Fig. 12 (a) and Fig. 12 (b). Although the principle compressive strains were higher than 3 ‰, no concrete crushing occurred.

Fig. 11: Crack pattern including principle compressive strains at load level 5 in experimental phase 3; (a) longitudinal girder LG 2; (b) transverse girder.

After the experiment, the reinforcement was uncovered in the area around the controlling shear crack. It could be ascertained that other than the stirrups, no other reinforcement fractured, as displayed in Fig. 12 (c).

Fig. 12: Failure mechanism and crack pattern; (a) longitudinal girder LG 2; (b) transverse girder; (c) fractured reinforcement (circled).

4. Conclusion To investigate the static action of indirectly supported concrete structures, namely bridges, a large-scale experiment was conducted at the University of Applied Sciences and Arts, Lucerne. As a result of the missing hanger reinforcement, the static actions of the longitudinal girders and the transverse girders are not independent. It was shown that the failure mechanism, the ultimate load level and therefore the static actions are dependent on the reinforcement arrangements. The crack pattern and the principle strains at the ultimate load level indicate that the static actions, the load path and the ultimate load can be described and calculated by stress field models.

5. References [1] SIA, „Norm 262:2003, Betonbau“, Schweizerischer Ingenieur und Architektenverein,

Zuerich, Norm Ausgabe 2003, pp. 90. [2] THOMA K., BUEELER Ch., “Indirectly supported bridges – Risk of brittle failure?”,

Proceedings, 3. fib International Congress, Washington, 2010, in press. [3] BUEELER Ch., THOMA K., “Indirekt gelagerter Spannbetontraeger –

Versuchsbericht”, CC Konstruktiver Ingenieurbau, Hochschule Luzern – Technik & Architektur, Bericht, 2010, pp. 61.

[4] LEONHARDT F., WALTHER R., “Versuche an Plattenbalken mit hoher Schubbeanspruchung“, Universitaet Stuttgart, Deutscher Ausschuss fuer Stahlbeton, Heft 152, Berlin 1962

[5] LEONHARDT F., KOCH R., ROSTASY F.S, “Aufhaengebewehrung bei indirekter Lasteintragung von Spannbetontraegern, Versuchsbericht und Empfehlungen, ” Universitaet Stuttgart, Beton- und Stahlbetonbau, Heft 10, Jg. 66, Berlin Oktober 1971, pp. 233-241.

[6] LEONHARDT F., KOCH R., ROSTASY F.S., “Schubversuche an Spannbetontraegern“, Universitaet Stuttgart, Deutscher Ausschuss fuer Stahlbeton, Heft 227, Berlin 1973, pp. 179.

[7] STOFFEL Ph., MARTI P., “Europabruecke: Modellversuche“, Schweizer Ingenieur und Architekt, Heft Nr. 19, 9. Mai 1997, pp. 369-373.

[8] STOFFEL Ph.., MARTI, P., “Europabruecke: Modellversuche”, Schweizer Ingenieur und Architekt, Heft Nr. 19, 9. Mai 1997, pp. 369-373.

[9] MOJSILOVIĆ N., MARTI P., “Versuche an kombiniert beanspruchten Mauerwerkswaenden”, Institut fuer Baustatik und Konstruktion, ETH Zuerich, Bericht Nr. 203, April 1994, pp.91.