Using the Sinusoidal Shape Function in Analyzing the 3-Span Continuous Concrete Bridges in Lateral Direction

Document Type : Research Article


1 Department of Civil Engineering, University of Qom, Qom, Iran

2 Assistant Prof, International Institute of Earthquake Engineering and Seismology(IIEES).

3 Associate Prof, Department of Civil Engineering, University of Qom, Qom, Iran


With attention to the importance of the three-span continuous bridges and the complexity of analyzing structures with multi-degree of freedom, utilizing desirable numerical models to estimate the internal forces of this group of structures is highly effective. A new analyzing method is introduced in this study which can be used to the 3-span continuous bridges with constant section and heavy moment resistance in the transverse direction. The defined pattern is based on employing sinusoidal shape function both the bridge’s deflection shape and its corresponding applied forces. This model is developed by assuming a simple beam on the elastic constraints and thereby its results can be earned by minimizing the created potential function of the whole structure. Creating a desirable manual method in calculating the internal shear forces of columns in the three-span bridges is a good comparative idea over the complicated method proposed by Aashto needing 3-dimensional modeling in related software. By considering 5 different states of an example sample and analyzing those, the obtained results of the suggested way prove its high precision and efficiency on controlling the calculations manually because of having mostly the errors less than 3 percent related to the exact method.   


Main Subjects

1. AASHTO, 2012 AASHTO LRFD Bridge Design Specifications, Customary U.S. Units (6th Edition), American Association of State Highway and Transportation Officials, 4th Edition, Washington, D.C.
2. Barker, R. M. & Puckett, J. A. 2013 Design of Highway Bridges: A LRFD Approach, 3rd Edition, John Wiley & Sons, Inc., New York, NY.
3. Clough, R.W.  & Penzein, J. 1993 Dynamics of Structures, McGraw Hill, New York.
4. Chopra AK, Chopra AK. Dynamics of structures: theory and applications to earthquake engineering. Upper Saddle River, NJ: Pearson/Prentice Hall; 2007 May 1.
5. chen, W.F. & Lui, E.M. 1987 Structural Stability, Elsevier, New York.
6. Caltrans, 2014a California Amendments to AASHTO LRFD Bridge Design Specifications – 6th Edition, California Department of Transportation, Sacramento, CA.
7. Najm H, Vasconez R. Assessment of AASHTO LRFD guidelines for analysis of regular bridges subjected to transverse earthquake ground motions. Bridge Structures. 2015 Jan 1; 11(1, 2):3-18.
8. Calvi GM. Recent experience and innovative approaches in design and assessment of bridges. Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, Canada, 2004.
9. Tubaldi E, Barbato M, Dall’Asta A. Transverse seismic response of continuous steel-concrete composite bridges exhibiting dual load path. Earthquake and Structures 2010; 1(1):21–41. 
10. Tsai MH. Transverse earthquake response analysis of a seismically isolated regular bridge with partial restraint.Engineering Structures 2008; 30(2):393–403.
11. Makris N, Kampas G, Angelopoulou D. The eigenvalues of isolated bridges with transverse restraints at the end-abutments. Earthquake Engineering and Structural Dynamics 2010; 39(8):869–886.
12. Tubaldi E, Dall'Asta A. Transverse free vibrations of continuous bridges with abutment restraint. Earthquake Engineering & Structural Dynamics. 2012 Jul 25; 41(9):1319-40.
13. Buckle, I.G., Mayes, R.L. & Button, M.R., 1987 Seismic design and retrofit manual for highway bridge, Report No. FHWA-IP-6, Final Report, National Technical Information Service, Springfield, Verginia. 130-136.