Elastic Failure of Web-Cracked Plate Girder

Authors: Sebastian B. Mendes

Abstract:

The presence of a vertical fatigue crack in the web of a plate girder subjected to pure bending influences the bending moment capacity of the girder. The growth of the crack may lead to premature elastic failure due to flange local yielding, flange local buckling, or web local buckling. Approximate expressions for the bending moment capacities corresponding to these failure modes were formulated. Finite element analyses were then used to validate the expressions. The expressions were employed to assess the effects of crack length on the capacity. Neglecting brittle fracture, tension buckling, and ductile failure modes, it was found that typical girders are governed by the capacity associated with flange local yielding as influenced by the crack. Concluding, a possible use of the capacity expressions in girder design was demonstrated.

Keywords: Fatigue crack, flange yielding, flange buckling, web buckling.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062788

References:

[1] Kouba, N.G., and Stallmeyer, J.E., "The behavior of stiffened beams under repeated loads," University of Illinois, Urbana, IL, Structural Research Series No. 173, 1959.
[2] Yen, B.T., "On the fatigue strength of welded plate girders," Lehigh University, Bethlehem, PA, Fritz Eng. Lab. Rep. No. 303-1, 1963.
[3] Hall, L.R., and Stallmeyer, J.E., "Thin web girder fatigue behavior as influenced by boundary rigidity," University of Illinois, Urbana, IL, Structural Research Series No. 278, 1964.
[4] Goodpasture, D.W., and Stallmeyer, J.E., "Fatigue behavior of welded thin web girders as influenced by web distortion and boundary rigidity," University of Illinois, Urbana, IL, Structural Research Series No. 328, 1967.
[5] Yen, B.T., and Mueller, J.A., "Fatigue tests of large-size welded plate girders," Lehigh University, Bethlehem, PA, Fritz Eng. Lab. Rep. No. 303-10, 1966.
[6] Mueller, J.A., and Yen, B.T., "Girder web boundary stresses and fatigue," Lehigh University, Bethlehem, PA, Fritz Eng. Lab. Rep. No. 327-2, 1967.
[7] Davies, A.W., Roberts, T.M., Evans, H.R., and Bennett, R.J.H., "Fatigue of slender web plates subjected to combined membrane and secondary bending stresses," J. Construct. Steel Research, vol. 30, no. 1, pp. 85- 101, 1994.
[8] Roberts, T.M., Davies, A.W., and Bennett, R.J.H., "Fatigue shear strength of slender web plates," J. Struct. Eng., vol. 121, no. 10, pp. 1396-1401, 1995.
[9] Crocetti, R., "Web breathing of full-scale slender I-girders subjected to combined action of bending and shear," J. Construct. Steel Research, vol. 59, no. 3, pp. 271-290, 2003.
[10] Marek, P., Perlman, M., Pense, A.W., and Tall, L., "Fatigue tests on a welded beam with pre-existing cracks," Lehigh University, Bethlehem, PA, Fritz Eng. Lab. Rep. No. 358-4A, 1970.
[11] Lawn, B., Fracture of Brittle Solids, 2nd ed. E.A. Davis, and I.M. Ward, Eds. Cambridge, UK: Cambridge University Press, 1993, ch. 9.
[12] Rolfe, S.T., and Barsom, J.M., Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics. Englewood Cliffs, NJ: Prentice-Hall, 1977, ch. 7.
[13] Osman, M.H., and Roberts, T.M., "Prediction of the fatigue life of slender web plates using fracture mechanics concepts," Thin-Walled Struct., vol. 35, no. 2, pp. 81-100, 1999.
[14] Kirke, B., and Al-Jamel, I.H., Steel Structures Design Manual to AS 4100. Author, 2004, sec. 2.3.3.
[15] Lichtenstein, Special Inspections of Selected Portions of The Providence Viaduct, Route I-95 from West Exchange Street to Promenade Street, Bridge No. 578 (Supplemental Report for Project No. 1213). Framingham, MA: A.G. Lichtenstein and Associates, Inc, 1990.
[16] Minor, J., and Woodward, C., "Web buckle at I-40 bridge test," J. Bridge Eng., vol. 1, no. 1, pp. 34-36, 1996.
[17] Chajes, M., Mertz, D., Quiel, S., Roecker, H., and Milius, J., "Steel girder fracture on Delaware-s I-95 bridge over the Brandywine River," in Proc. Structures Congress 2005.
[18] Bowman, M.D., "Brittle fracture of the Blue River Bridge," in Proc. Structures Congress 2004.
[19] Zhou, Y.E., and Biegalski, A.E., "Investigation of large web fractures of welded steel plate girder bridge," J. Bridge Eng., vol. 15, no. 4, pp. 373- 383, 2010.
[20] Wardhana, K., and Hadipriono, F.C., "Analysis of recent bridge failures in the United States," J. Performance of Constructed Facilities, vol. 17, no. 3, pp. 144-150, 2003.
[21] Vafai, A., and Estekanchi, H.E., "A parametric finite element study of cracked plates and shells," Thin-Walled Struct., vol. 33, no. 3, pp. 211- 229, 1999.
[22] Kumar, Y.V.S., and Paik, J.K., "Buckling analysis of cracked plates using hierarchical trigonometric functions," Thin-Walled Struct., vol. 42, no. 5, pp. 687-700, 2004.
[23] Paik, J.K., Kumar, Y.V.S., and Lee, J.M., "Ultimate strength of cracked plate elements under axial compression or tension," Thin-Walled Struct., vol. 43, no. 2, pp. 237-272, 2005.
[24] Brighenti, R., "Buckling of cracked thin-plates under tension or compression," Thin-Walled Struct., vol. 43, no. 2, pp. 209-224, 2005.
[25] Brighenti, R., "Numerical buckling analysis of compressed or tension cracked thin plates," Eng. Struct., vol. 27, no. 2, pp. 265-276, 2005.
[26] Brighenti, R., "Buckling sensitivity analysis of cracked thin plates under membrane tension or compression loading," Nuclear Eng. and Design, vol. 239, no. 6, pp. 965-980, 2009.
[27] Khedmati, M.R., Edalat, P., and Javidruzi, M., "Sensitivity analysis of the elastic buckling of cracked plate elements under axial compression," Thin-Walled Struct., vol. 47, no. 5, pp. 522-536, 2009.
[28] Seifi, R., and Khoda-yari, N., "Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading," Thin-Walled Struct., vol. 49, no. 12, pp. 1504-1516, 2011.
[29] Alinia, M.M., Hosseinzadeh, S.A.A., and Habashi, H.R., "Buckling and post-buckling strength of shear panels degraded by near border cracks," J. Construct. Steel Research, vol. 64, no. 12, pp. 1483-1494, 2007.
[30] Alinia, M.M., Hosseinzadeh, S.A.A., and Habashi, H.R., "Influence of central cracks on buckling and post-buckling behaviour of shear panels," Thin-Walled Struct., vol. 45, no. 4, pp. 422-431, 2007.
[31] Alinia, M.M., Hosseinzadeh, S.A.A., and Habashi, H.R., "Numerical modelling for buckling analysis of cracked shear panels," Thin-Walled Struct., vol. 45, no. 12, pp. 1058-1067, 2007.
[32] Brighenti, R., and Carpinteri, A., "Buckling and fracture behaviour of cracked thin plates under shear loading," Materials and Design, vol. 32, no. 3, pp. 1347-1355, 2011.
[33] Guz, A.N., and Dyshel, M.Sh., "Fracture and buckling of thin panels with edge crack in tension," Theo. and Appl. Fract. Mech., vol. 36, no. 1, pp. 57-60, 2001.
[34] Guz, A.N., and Dyshel, M.Sh., "Stability and residual strength of panels with straight and curved cracks. Theo. and Appl. Fract. Mech., vol. 31, nos. 1-3, pp. 95-101, 2004.
[35] Cooper, P.B., and Roychowdhury, J., "Shear strength of plate girders with web openings," J. Struct. Eng., vol. 116, no. 7, pp. 2042-2048, 1990.
[36] Narayanan, R., and Der-Avanessian, N., "Design of slender webs having rectangular holes," J. Struct. Eng., vol. 111, no. 4, pp. 777-787, 1985.
[37] Cheng, J., and Yura, J., "Local web buckling of coped beams," J. Struct. Eng., vol. 112, no. 10, pp. 2314-2331, 1986.
[38] Ito, M., Fujiwara, K., and Okazaki, K., " Ultimate strength of beams with U-shaped holes in top of web," J. Struct. Eng., vol. 117, no. 7, pp. 1929- 1945, 1991.
[39] Zaarour, W., and Redwood, R., "Web buckling in thin webbed castellated beams," J. Struct. Eng., vol. 122, no. 8, pp. 860-866, 1996.
[40] Redwood, R., and Demirdjian, S., "Castellated beam web buckling in shear," J. Struct. Eng., vol. 124, no. 10, pp. 1202-1207, 1998.
[41] Shanmugam, N.E., Lian, V.T., and Thevendran, V., "Finite element modelling of plate girders with web openings," Thin-Walled Struct., vol. 40, no. 5, pp. 443-464, 2002.
[42] Hagen, N.C., Larsen, P.K., and Aalberg, A., "Shear capacity of steel plate girders with large web openings, part I: Modeling and simulations," J. Construct. Steel Research, vol. 65, no. 1, pp. 142-150, 2009.
[43] Hagen, N.C., and Larsen, P.K., "Shear capacity of steel plate girders with large web openings part II: Design guidelines," J. Construct. Steel Research, vol. 65, no. 1, pp. 151-158, 2009.
[44] Bedair, O., "Stress analyses of deep plate girders used at oil and gas facilities with rectangular web penetrations," Practice Periodical on Struct. Design and Construct., vol. 16, no. 3, pp. 112-120, 2011.
[45] Roberts, R., Fisher, J.W., Irwin, G.R., Boyer, K.D., Hausammann, G.V., Krishna, V., Morf, R., and Slockbower, R.E., "Determination of tolerable flaw sizes in full size welded bridge details," Lehigh University, Bethlehem, PA, Fritz Eng. Lab. Rep. No. 399-3, 1977.
[46] Roberts, T.M., Osman, M.H., Skaloud, M., and Zornerova, M., "Residual shear strength of fatigue cracked slender web panels," Thin- Walled Struct., vol. 24, no. 2, pp. 157-172, 1996.
[47] Sadd, M.H., Elasticity: Theory, Applications, and Numerics, 2nd ed. Burlington, MA: Academic Press, 2009, sec. 7.5.
[48] Westergaard, H.M., "Bearing pressures and cracks," J. Applied Mech., vol. 6, no. 61, pp. 49-53, 1939.
[49] Sun, C.T., and Jin, Z.-H., Fracture Mechanics. Waltham, MA: Academic Press, 2012, sec. 3.5.
[50] Sedov, L.I., A Course in Continuum Mechanics. J.R.M. Radok, Trans. Groningen, Netherlands: Wolters-Noordhoff Publishing, 1972, sec. 13.2.8.
[51] Fett, T., Stress Intensity Factors, T-Stresses, Weight Functions. Karlsruhe, Germany: Universitätsverlag Karlsruhe, 2008.
[52] Salmon, C.G., Johnson, J.E., and Malhas, F.A., Steel Structures: Design and Behavior, 5th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2009, secs. 6.14, 6.15.
[53] Vinson, J.R., Structural Mechanics: The Behavior of Plates and Shells. New York, NY: John Wiley & Sons, Inc., 1974, sec. 6.1.