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.
[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.
[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.
@article{"International Journal of Architectural, Civil and Construction Sciences:55454", author = "Sebastian B. Mendes", title = "Elastic Failure of Web-Cracked Plate Girder", 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.", volume = "7", number = "6", pages = "455-9", }
