Direct Strut-and-Tie Model for Reinforced Concrete Bridge Pier Cap

Open access

Abstract

A simple and direct Strut-and-Tie Model (STM) is proposed here to predict the ultimate shear strength of the reinforced concrete bridge pier cap for shear span to depth ratio of 0.4 to 2.4. The model is based on the Kupfer-Gerstle Biaxial Compression-Tension failure criterion which includes the concrete softening effect produced by the presence of transverse tensile stress. The earlier models consider the stress distribution factor for the varied stress distribution across the section by assuming it as linear function which is derived by satisfying equilibrium conditions. In this study the principal stresses have been evaluated by satisfying the compatibility condition at the time of impending failure which has been accounted for the effective area of concrete resisting tension. Also the softening effect has been included by using the formula for tensile strength of cracked concrete proposed by Belarbi and Hsu. The proposed model has been validated with 43 experimental results by author and from literature which confirm the coherency and conservativeness of the predicted results. The parametric study on ultimate shear strength is done so as to infer the relation between various abstract quantities such as compressive strain, shear capacity, span depth ratio and other material properties and get a deeper insight into the behavior of the Pier cap. Thus this paper tries to extend the practical application of Strut-and-Tie Model for reinforced concrete bridge pier cap in understanding the actual behavior of the structure on various dimensional and material parameters.

[1] Schlaich, J., Schäfer, K. and Jennewein, M. (2008). Toward a Consistent Design of Structural Concrete. PCI Journal, 82(1), 74–150.

[2] Karl-Heinz-Reineck. (2002). Example for Design of Structural Concrete with Strut-and-Tie Model. ACI-SP-208.

[3] ACI Committee 318. (2008). Building Code Requirements for Structural Concrete (ACI 318-08). American Concrete Institute (Vol. 2007). http://doi.org/10.1016/0262-5075(85)90032-6.

[4] Alshegeir, A. and Ramirez, J. (1992). Computer Graphics in Detailing Strut-Tie Models. Journal of Computing in Civil Engineering, 6(2), 220–232. http://doi.org/10.1061/(ASCE)0887-3801(1992)6:2(220)

[5] Marti, P. (1985). Basic tools of reinforced concrete beam design. ACI, 82(1), 46–56.

[6] Alshegeir, A. (1992). Analysis and design of disturbed regions with strut-tie models. Ph.D. thesis, West Lafayette (IN), Purdue University.

[7] MacGregor, J. G. (1988). Reinforced concrete: Mechanics and design. Prentice Hall, 848.

[8] Foster, S. J. and Malik, A. R. (2002). Evaluation of Efficiency Factor Models used in Strut-and-Tie Modeling of Nonflexural Members. Journal of Structural Engineering, 128(5), 569. http://doi.org/10.1061/(ASCE)0733-9445(2002)128:5(569)

[9] Zhang, N. and Tan, K. H. (2007). Direct strut-and-tie model for single span and continuous deep beams. Engineering Structures, 29(11), 2987–3001. http://doi.org/10.1016/j.engstruct.2007.02.004

[10] Wang, G. L. and Meng, S. P. (2008). Modified strut-and-tie model for prestressed concrete deep beams. Engineering Structures, 30(12), 3489–3496. http://doi.org/10.1016/j.engstruct.2008.05.020

[11] Belarbi,.A., Hsu, T. T. C. (1994). Constitutive laws of concrete in tension and reinforcing bar stiffened by concrete. ACI Struct J, 91(4)(1994), 465–74.

[12] Cedolin, L. and Mulas, M. G. (1984). Biaxial Stress-Strain Relation for Concrete. Journal of Engineering Mechanics, 110(2), 187–206. http://doi.org/10.1061/(ASCE)0733-9399(1984)110:2(187)

[13] Sami. (1990). The Response of Reinforced Concrete.

[14] McLeod, G. (1997). Influence of Concrete Strength on the Behaviour of Bridge Pier Caps. McGill University, Montreal, Canada.

[15] Rogowsky, D.M., MacGregor, J.G. and Ong, S. Y. (1983). Tests of reinforced concrete deep beams. Univ. of Alberta, Canada.

[16] Cook, W.D. and Mitchell, D. (1988). Studies of disturbed regions near discontinuities in Reinforced Concrete Members. ACI Struct J, 85(2), 206–216.

[17] Rogowsky, D. M. and MacGregor, J. G. (1983). Tests of Reinforced Concrete Deep Beams.pdf.

[18] Leonhardt, F. and Walther, R. (1966). WandartigerTraiger. DeutscherAusschuss Fur Stahlebeton, Wilhelm Er, Bulletin No.178, Berlin 159.

[19] Gilbert., S. J. F. and R. lan. (1998). Experimental studies on high-strength concrete deep beams. ACI Structural Journal, 95(4)(1998), 382–390.

Mathematical Modelling in Civil Engineering

The Journal of Technical University of Civil Engineering of Bucharest

Journal Information

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 202 202 24
PDF Downloads 92 92 7