Compressive membrane action in concrete decks

Proc. of the 9th

fib International PhD Symposium in Civil Engineering

July 22 to 25, 2012, Karlsruhe Institute of Technology (KIT), Germany

Compressive Membrane Action In Concrete Decks

Sana Amir

Department of Design and Construction, Structural and Building Engineering, Technical University Delft,

Stevinweg 1, 2628 CN Delft, the Netherlands

Supervisor: Prof. Dr. ir. J. C. Walraven, Dr. ir. C. van der Veen

Abstract

One of the major challenges facing the designers today is to investigate if the old bridges are still safe for modern traffic. The current research deals with this question by taking into account compressive membrane action (CMA) in determining the capacity of reinforced and transversely prestressed con-crete decks. CMA can significantly affect the flexural and punching shear strength of deck slabs but it is usually neglected for design and assessment purposes. Therefore, a flexural theory was used and a punching shear model was modified to fully utilize the effect of strength enhancement by CMA. Several experiments done by various researchers have been analysed by using these theories. It was concluded that considering CMA in the assessment shows that bridge decks can have a considerably larger shear capacity than assumed in the initial design. This is of high significance because in The Netherlands about 70 bridges have to be investigated, with very thin decks cast between the flanges of long prestressed beams. Using the actual design codes for the verification of the bearing capacity leads to values showing that the safety standards are not met. However, theoretical analyses show that nevertheless sufficient residual capacity might be available. In order to confirm the validity of the calculations large scale laboratory tests are carried out. Variables are the geometry of the deck, the confining effect on the punching shear capacity, and the role of transverse prestressing.

1 Introduction

In the Netherlands, there are a large number of bridges that were built around 50 years ago or even earlier using the design codes and construction methods of that time. Since then, not only the traffic loads have increased drastically but codes have also evolved with additional safety requirements being incorporated into them. It has been observed that bridge deck slabs in typical beam and slab type bridges have inherent strength due to presence of in-plane forces. This is typically defined as compressive membrane action (CMA) or arching action and it occurs in slabs with laterally restrained edges. This restraint induces compressive membrane forces in the plane of the slab enhancing the flexural and punching shear capacities. Therefore, it is possible that such bridges need not to be strengthened if CMA of concrete decks is taken into account while assessing their real capacities.

2 Past research

Traditionally concrete deck slabs have been designed for bending effects only, with the assumption that shear capacity is adequate. However, it has been generally observed that typical bridge deck slabs tend to fail in punching shear rather than flexure. A lot of research has been done in past on the flex-ural and punching strengths considering compressive membrane action focusing on reinforced con-crete bridge deck slabs. CMA was first reported by Ockleston [1] during tests on a 3-storey building in South Africa. Subsequent research in the bending strength area was done by Wood [2] and Park [3]. Research conducted at Queen’s University, Canada in the late 1960’s has led to compressive membrane action been incorporated in the current Ontario Highway Bridge design Code (OHBDC) [4] and the New Zealand Code [5].

Another rational treatment of the compressive membrane action has been done in the UK Highway Agency standard BD81/02 [6] which resulted from the research done at Queen’s University Belfast [7-10]. However the UK Highway method is valid more for rigidly restrained decks and there-fore for deck slabs with low restraint, Taylor’s approach [11] is used.

The most significant contribution in punching shear considering CMA was made by Hewitt and Batchelor (H&B model) [12] who modified the Kinnunen and Nylander (K&N) punching shear mod-el [13] by including an empirical restraint factor to show the impact of boundary restraint. Some tests

9 fib International PhD Symposium in Civil Engineering

were done in Queen’s University, Kingston, Canada [14] on transversely prestressed concrete decks with steel girders and the H&B model was used to evaluate the punching shear capacity. However, the tests were done on small scale models and till today there has been insufficient research done to include CMA in current codes for prestressed decks with precast concrete girders. Therefore, this research aims to investigate transversely prestressed concrete decks after studying reinforced concrete deck slab methods in detail.

3 Load capacity of reinforced concrete decks 3.1 Flexural capacity

The method used to calculate the flexural capacity considering CMA are Rankin and Long method. It is based on deformation theory and utilizes an elastic-plastic criterion for concrete. The loads carried by bending and arching are calculated separately and then added to give the ultimate load capacity [8].

3.2 Punching shear capacity

The methods used to calculate the punching shear capacity considering CMA are the UK Highway Agency standard BD81/02 [6], Taylor’s approach [11] and the modified Hallgren model.

3.2.1 Modified Hallgren model

In 1996, Mikael Hallgren proposed a mechanical model of punching based on the model by Kinnunen and Nylander [13]. The ultimate tangential concrete strain was the failure criterion in the K&N model and was based on a set of semi-empirical expressions developed from the strains measured in punch-ing shear tests and no size effect was considered. In the Hallgren model, the main modification was the ultimate tangential concrete strain derived from a simple fracture mechanics model reflecting both the size effect as well as the brittleness of the concrete [15]. The model did not take into consideration the lateral restraint, however, it was open for further development by introducing forces from the boundary restraint and prestressing.

Therefore, a modified form of the Hallgren model has been proposed in this paper and applied to relevant set of experimental data. In Fig. 1, boundary forces have been introduced into the Hallgren

model of a slab with diameter or equivalent diameter, C and depth, h. An empirical restraint factor, η,

proposed by Hewitt and Batchelor [12] is used in the Hallgren model to estimate the boundary forces.

Fig. 1 Modified Hallgren Model for CMA

3.3 Application of CMA theories to experimental data

Several tests done by various researchers have been analysed by the CMA methods, both in flexure and shear but primarily focusing on punching shear as it is more commonly observed failure mode in rigidly restrained deck slabs.

Table 1 and Fig. 2 show comparison of test data (less than rigid restraint slabs) and the ultimate capacity calculated by various methods.

Table 1 Tests by S. E. Taylor et al [11]

Test Panel Pt PBS PBD81 Ptaylor Pmh Pt/PBD81 Pt/Ptaylor Pt/Pmh

[kN] [kN] [kN] [kN] [kN] D1 185 49.4 341.1 191.8 219.8 0.54 0.96 0.84 D2 200 49.3 317.6 181.3 206.8 0.63 1.10 0.97 D5 150 38 268 151.1 164.5 0.56 0.99 0.91 D6 182 38.1 276 173.3 184.12 0.66 1.05 0.99 D7 135 38.1 280.9 92.5 155.29 0.48 1.46 0.87 D8 157 38.7 274 148.9 167.45 0.57 1.05 0.94 Average 0.57 1.10 0.92 St. deviation 0.06 0.18 0.057

Table 1 shows that Taylor’s approach and the modified Hallgren model give good results as they incorporate deck slabs with less than rigid restraint. The UK Highway BD81/02 shows higher values confirming that it is more suitable for rigid boundaries. However, BS5400 gives very conservative estimates. Fig. 2 shows tests done on 1:3 scale model of an M-beam bridge deck. Both the modified Hallgren and BD81/02 show good estimation of failure loads with the latter being slightly conserva-tive showing presence of adequate rigidity during tests. However, the flexural capacity method of Rankin and Long over estimates the failure load.

Fig. 2 Tests by Kirkpatrick et al [9]

Table 2 shows test results of experiments done on a real bridge. Each panel was intended to be loaded to three times the UK service wheel load (337.5kN), while not exceeding a midspan deflection of 2.5mm. The BS5400 code, BD81/02 and the modified Hallgren were used to predict the capacity. It is interesting to observe that while the code methods only gave the ultimate loads, the modified Hallgren method could be used to estimate the load corresponding to a certain deflection as well.

4 Punching shear capacity of transversely prestressed concrete decks

The methods used to calculate the punching shear capacity considering CMA are the New Zealand code [5] and the modified Hallgren model. An equivalent steel ratio was used in place of the pre-stressing steel ratio to find the capacity using the code. The modified Hallgren method was further adapted to include forces by prestressing.

Table 3 shows results by modified Hallgren model and the New Zealand code applied on tests done in Queen’s University, Kingston, Canada. The method of superposition was used to calculate the punching load [14]. Both the methods show good results compared to the experimental loads and it can be observed that the punching load and hence the membrane action increases with the increasing

9 fib International PhD Symposium in Civil Engineering

transverse prestress level (TPL). It is interesting to note that the New Zealand code over estimates the capacity at lower transverse prestress levels.

Table 2 Tests by S. E. Taylor et al [16]

Test Panel Deflection [mm] Pt [kN] PBD81 [kN] Pmh [kN] PBS [kN] PBD81/PB S Pmh/PBS Pt/Pmh A1 2.5 333 570.1 401 128.3 4.44 6.75 0.83 A2 1.5 428 600.8 426.4 178.3 3.37 5.70 1.00 B1 2.15 344 563.6 381 66.5 8.48 11.07 0.90 B2 1.15 428 610.4 445.2 92.3 6.61 9.60 0.96 C1 2.6 333 588 406 66.6 8.83 11.58 0.82 C2 1.2 428 588 427.5 92.2 6.38 9.24 1.00 D1 1.85 368 553.5 365 127.9 4.33 5.51 1.01 D2 1.75 428 568.3 412 177.3 3.21 5.35 1.04 E1 1.95 392 632.8 484 202.1 3.13 3.89 0.81 E2 1.6 428 648.7 484.7 280 2.32 3.36 0.88 F1 1.9 371 566.5 415 199.5 2.84 3.56 0.89 F2 0.75 428 601.2 464.2 275.2 2.18 3.19 0.92 Average 0.92 St. deviation 0.08 5 Future tests

In the Netherlands, about 70 bridges have to be investigated with very thin decks cast between the flanges of long pre-stressed beams. Using the actual design codes for the verification of the bearing capacity leads to values showing that the safety standards are not met. However, theoretical analyses show that nevertheless sufficient residual capacity might be available. In order to confirm the validity of the calculations large scale laboratory tests are carried out. Variables are the geometry of the deck, the effect of confinement or the restraint on the punching shear capacity, and the role of transverse prestressing.

Fig. 3 shows the test setup of the 1:2 scale model of the van brienenoord bridge near Rotterdam. However, the scale model is still in the design stage and many variables are yet to be determined. To ensure adequate confining effect and the failure within the slab portion, girders have been over de-signed and a suitable overhang is provided to the external girders for the development of compressive membrane forces. It is expected that a restraint factor, η, of atleast 0.5 will be observed during the tests.

6 Conclusions and recommendation

The UK Highway Agency BD81/02 gives good results for rigidly restraint deck slabs. However, when the restraint is low, the results are unsafe. Also, this method does not allow for the effect of varying reinforcement ratio. For such situations, Taylor’s approach is a good tool especially because it incorporates both flexural punching and shear punching failures. The New Zealand code can be used for transversely prestressed decks. However, it gives better estimation when the TPL is high. Modified Hallgren model gives excellent results both for reinforced and transversely prestressed deck slabs, therefore it will be used for future tests as well.

It would be useful if the actual stiffness and restraint can be calculated as it could lead to better estimation of the compressive membrane action. Also, more tests on transversely prestressed decks could be done in future to verify results obtained from this research.

Table 3 Tests in Queen’s University, Kingston, Canada [14]

Notations

Φ Angle of sector element of slab

B Width of loaded area

Fb Boundary restraining force

Mb Boundary restraining moment

P, Pt Failure load in tests or applied test load

PBD81 Predicted ultimate capacity from BD81/02

PBS Predicted ultimate capacity from BS5400

Ptaylor Failure load according to Taylor’s approach

Pmh Predicted ultimate capacity from modified Hallgren model

PNZ Predicted ultimate capacity from the New Zealand code

PR&L Predicted ultimate capacity from Rankin and Long method

Rct Horizontal force in concrete crossing the shear crack

Rsr Horizontal force in reinforcement at right angles to the radial cracks

Rst Horizontal force in reinforcement crossing the shear crack

TPL Transverse Prestress Level

Test Panel Ap [mm2] TPL [MPa] Pt [kN] Pmh [kN] PNZ [kN] Pt/Pmh Pt/PNZ SW-1A 0.0869 1.84 53.1 59.77 67.39 0.89 0.79 SE-1B 0.0869 1.84 53.04 59.77 67.39 0.89 0.79 CW-2B 0.105 2.15 54.82 64.16 70.45 0.85 0.78 CE-2B 0.105 2.15 57.26 64.16 70.45 0.89 0.81 NW-2A 0.1198 2.5 63.85 67.57 71.68 0.94 0.89 NW-2B 0.1198 2.5 48.7 67.57 71.68 0.72 0.68 CE-1B 0.14 2.91 74.43 72.08 74.74 1.03 1.00 CW-1A 0.14 2.91 65.82 72.08 74.74 0.91 0.88 SE-2B 0.1549 3.32 66.31 75.42 76.58 0.88 0.87 SW-2A 0.1549 3.32 72.97 75.42 76.58 0.97 0.95 NE-1B 0.176 3.88 80.54 80.15 79.65 1.00 1.01 NW-1A 0.176 3.88 77.52 80.15 79.65 0.97 0.97 CE-1A 0.19 4.37 94.12 83.42 80.87 1.13 1.16 NE-2A 0.19 4.37 92.28 83.42 80.87 1.11 1.14 NW-3B 0.19 4.37 80.11 83.42 80.87 0.96 0.99 CW-4B 0.19 4.37 82.66 83.42 80.87 0.99 1.02 SE-5B 0.19 4.37 87.3 83,42 80.87 1.05 1.08 SW-6A 0.19 4.37 92.23 83.42 80.87 1.11 1.14 Average 0.96 0.94 St. deviation 0.10 0.14

9 fib International PhD Symposium in Civil Engineering

Fig. 3 The scale model test set-up (All linear dimensions are in mm)

References

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Johannes-burg,” The Structural Engineer, V. 33, Oct. 1955, pp. 304-322

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[4] Ontario Ministry of Transport and Communications: Ontario Highway Bridge Design Code

(OHBDC), Toronto, Ontario, 1979 (amended 1983 & 1992)

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Design Manual for Roads and Bridges, V. 3, Section 4, part 20, Aug. 2002

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[13] Kinnunen, S., and Nylander, H.: Trans. Royal Inst. Technology, Stockholm, No. 158, 1960

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