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Abstract: Concrete precast multicell box-girder (MCB) bridges combine aesthetics with torsional stiffness perfectly. Previous analytical studies indicate that currently available specifications are unable to consider the effect of the twisting moment (torsional moment) on bridge actions. In straight bridges the effect of torsion is negligible and the transverse reinforced design is governed by other requirements. However, in the case of skewed bridges the effect of the twisting moment should be considered. Therefore, an in-depth study was performed on 90 concrete MCB bridges with skew angles ranging from 0° to 60°. For each girder the bridge actions were determined under the American Association of State Highway and Transportation Officials (AASHTO) live load conditions. The analytical results show that torsional stiffness and live load positions greatly affected the bridges’ responses. In addition, based on a statistical analysis of the obtained results, several skew correction factors are proposed to improve the precision of the simplified Henry’s method, which is widely used by bridge engineers to predict bridge actions. The relationship between the bending moment and secondary moments was also investigated and it was concluded that all secondary actions increase with an increase in skewness.

[1]AASHTO, 2002. Bridge Design Specifications. American Association of State Highway and Transportation Officials (14th Edition), Washington DC.

[2]AASHTO, 2008. AASHTO LRFD Bridge Design Specifications: Customary US Units (5th Edition). American Association of State Highway and Transportation Officials, Washington DC.

[3]Ashebo, D.B., Chan, T.H.T., Yu, L., 2007. Evaluation of dynamic loads on a skew box girder continuous bridge Part I: Field test and modal analysis. Engineering Structures, 29(6):1052-1063.

[4]Bae, H.U., Oliva, M., 2012. Moment and shear load distribution factors for multigirder bridges subjected to overloads. Journal of Bridge Engineering, 17(3):519-527.

[5]Barker, R.M., Puckett, J.A., 1997. Design of Highway Bridges Based on AASHTO LRFD Bridge Design Specifications. John Wiley & Sons, New York, USA.

[6]Begum, Z., 2010. Analysis and Behavior Investigations of Box Girder Bridges. MS Thesis, University of Maryland, USA.

[7]CHBDC, 2000. Canadian Standards Association: Canadian Highway Bridge Design Code. CAN/CSA-S6-00, CSA International, Toronto, Ontario, Canada.

[8]Chun, B.J., 2010. Skewed Bridge Behaviors: Experimental, Analytical, and Numerical Analysis. PhD Thesis, Wayne State University, USA.

[9]Dicleli, M., Erhan, S., 2009. Live load distribution formulas for single-span prestressed concrete integral abutment bridge girders. Journal of Bridge Engineering, 14(6):472-486.

[10]Ebeido, T., Kennedy, J.B., 1996. Shear and reaction distributions in continuous skew composite bridges. Journal of Bridge Engineering, 1(4):155-165.

[11]Euro-Code 2, 2005. European Standard: Design of Concrete Structures-Concrete Bridges: Design and Detailing Rules. London, UK.

[12]Fan, Z., Helwig, T.A., 2002. Distortional loads and brace forces in steel box girders. Journal of Structural Engineering, 128(6):710-718. [10.1061/(ASCE)0733-9445 (2002)128:6(710)]

[13]Foinquinos, R., Kuzmanovic, B., Vargas, L.M., 1997. Influence of Diaphragms on Live Load Distribution in Straight Multiple Steel Box Girder Bridges. Proceedings of 15th Structures Congress, ASCE, Portland. OR, USA, p.89-103.

[14]Fu, C.C., Tang, Y., 2001. Torsional analysis for prestressed concrete multiple cell box. Journal of Engineering Mechanics, 127(1):45-51.

[15]Hall, D., Grubb, M., Yoo, C., 1999. Improved Design Specifications for Horizontally Curved Steel Girder Highway Bridges. National Cooperative Highway Research Program (NCHRP), Washington DC.

[16]Hambly, E.C., 1991. Bridge Deck Behaviour (2nd Edition). Chapman & Hall, New York, NY.

[17]Heins, C., 1978. Box girder bridge design state-of-the-art. Engineering Journal of the American Institute of Steel Construction, 15(4):126-142.

[18]Huo, X., Zhang, Q., 2008. Effect of skewness on the distribution of live load reaction at piers of skewed continuous bridges. Journal of Bridge Engineering, 13(1):110-114.

[19]Huo, X., Conner, S., Iqbal, R., 2003. Re-Examination of the Simplified Method (Henry’s Method) of Distribution Factors for Live Load Moment and Shear. Final Report, Tennessee DOT Project No. TNSPR-RES, 1218, USA.

[20]Huo, X., Wasserman, E., Iqbal, R., 2005. Simplified method for calculating lateral distribution factors for live load shear. Journal of Bridge Engineering, 10(5):544-554.

[21]Jaeger, L.G., Bakht, B., 1982. The grillage analogy in bridge analysis. Canadian Journal of Civil Engineering, 9(2):224-235.

[22]Kolbrunner, C.F., Basler, K., 1969. Torsion in Structures: An Engineering Approach. Springer-Verlag, Berlin, p.1-21, 47-50.

[23]Krätzig, W., 1993. Best transverse shearing and stretching shell theory for nonlinear finite element simulations. Computer Methods in Applied Mechanics and Engineering, 103(1-2):135-160.

[24]Park, N.H., Choi, S., Kang, Y.J., 2005. Exact distortional behavior and practical distortional analysis of multicell box girders using an expanded method. Computers & Structures, 83(19-20):1607-1626.

[25]Razaqpur, A.G., Li, H., 1991. Thin-walled multicell box-girder finite element. Journal of Structural Engineering, 117(10):2953-2971.

[26]Sennah, K., Kennedy, J.B., 1999. Load distribution factors for composite multicell box girder bridges. Journal of Bridge Engineering, 4(1):71-78.

[27]Song, S., Chai, Y., Hida, S., 2003. Live-load distribution factors for concrete box-girder bridges. Journal of Bridge Engineering, 8(5):273-281.

[28]Théoret, P., Massicotte, B., Conciatori, D., 2012. Analysis and design of straight and skewed slab bridges. Journal of Bridge Engineering, 17(2):289-301.

[29]Tobias, D.H., Anderson, R.E., Khayyat, S.Y., Uzman, Z.B., Riechers, K.L., 2004. Simplified AASHTO load and resistance factor design girder live load distribution in Illinois. Journal of Bridge Engineering, 9(6):606-613.

[30]Zhang, Q., 2008. Development of Skew Correction Factors for Live Load Shear and Reaction Distribution in Highway Bridge Design. PhD Thesis, Tennessee Technological University, Tennessee, USA.

[31]Zokaie, T., Mish, K., Imbsen, R., 1993. Distribution of Wheel Loads on Highway Bridges, Phase III. NCHRP Final Report 12-26(2), Transportation Research Record, Washington DC.

[32]Appendix A: Non-Orthogonal grillage method

[33]The same procedure as recommended by Hambly (1991) was used to obtain the grillage layout and properties. The grid mesh is chosen with longitudinal members coincident with webs. Two nominal members are located along the edges of the cantilevers. The section is divided in such a way that each internal longitudinal member has half of the top and bottom slabs. The torsion constant and shear area in the longitudinal direction can be determined by the following equations, respectively:

[34]
(A1)

[35]A_s=W·h, (A2)

[36]where h and W stand for depth and width of deck, and d' and d" are the top and bottom thicknesses, respectively.

[37]The transverse member represents the top and bottom slab and is perpendicular to the longitudinal members. The maximum spacing of transverse members is taken as one-quarter of the contra-flexure point’s distance but the spacing is chosen to be shorter near the intermediate supports to give greater detail.

[38]Hambly (1991) indicated that the moment of inertia (i_s) per unit width in the transverse direction is half of the torsional constant (c_s) and their equivalent shear area can be obtained by

[39]

[40](A3)

[41]where d_w, E and G are the thickness of web, the modulus of elasticity and shear modulus of bridge, respectively.

[42]Appendix B: Simplified Henry’s EDF method

[43]Henry’s EDF method requires only the roadway width (W_roadway), number of beams (N_beam) and an intensity factor (IF) based on a linear interpolation to determine the total number of traffic lanes considered as live load on the bridge. From the AASHTO Standard, the intensity factor of live load equals 100% for a two-lane bridge, 90% for a three-lane bridge, or 75% for a four-line or more lane bridge. Henry’s EDF method for interior and exterior beams

[44]is as follows:

[45]

[46]The multicell box is considered as a group of equivalent I-beams based on the centre-to-centre distance between the webs. The number of equivalent I-beams is counted as the number of beams in the calculation.