Approximate Tension Buckling Capacity of Thin Edge-Cracked Web Plate Subjected to Pure Bending
The presence of a vertical edge-crack within a web
plate subjected to pure bending induces local compressive stresses
about the crack which may cause tension buckling. Approximate
theoretical expressions were derived for the critical far-field tensile
stress and bending moment capacity of an edge-cracked web plate
associated with tension buckling. These expressions were validated
with finite element analyses and used to investigate the possibility of
tension buckling in web-cracked trial girders. It was found that
tension buckling is an unlikely occurrence unless the web is relatively
thin or the crack is very long.
[1] Kouba, N.G., and Stallmeyer, J.E., "The behavior of stiffened beams
under repeated loads," University of Illinois, Urbana, IL, Struct.
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] 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.
[8] 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.
[9] 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.
[10] 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.
[11] Meguid, S.A., Engineering Fracture Mechanics. New York, NY:
Elsevier Science Publishing Co., Inc., 1989, secs. 1.17, 4.3, 5.4, 6.1.
[12] Lawn, B., Fracture of Brittle Solids, 2nd ed. E.A. Davis, and I.M. Ward,
Eds. Cambridge, UK: Cambridge University Press, ch. 9.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] Narayanan, R., and Der-Avanessian, N., " Design of slender webs
having rectangular holes," J. Struct. Eng., vol. 111, no. 4, pp. 777-787,
1985.
[18] 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.
[19] 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.
[20] Zaarour, W., and Redwood, R., "Web buckling in thin webbed
castellated beams," J. Struct. Eng., vol. 122, no. 8, pp. 860-866, 1996.
[21] 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.
[22] 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.
[23] 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.
[24] 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.
[25] Brighenti, R., "Buckling of cracked thin-plates under tension or
compression," Thin-Walled Struct., vol. 43, no. 2, pp. 209-224, 2005.
[26] Brighenti, R., "Numerical buckling analysis of compressed or tension
cracked thin plates," Eng. Struct., vol. 27, no. 2, pp. 265-276, 2005.
[27] Shimizu, S., "Tension buckling of plate having a hole," Thin-Walled
Struct., vol. 45, nos. 10-11, pp. 827-833, 2007.
[28] 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.
[29] 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.
[30] Sun, C.T., and Jin, Z.-H., Fracture Mechanics. Waltham, MA: Academic
Press, 2012, sec. 3.5.
[31] Sadd, M.H., Elasticity: Theory, Applications, and Numerics, 2nd ed.
Burlington, MA: Academic Press, 2009, secs. 5.5, 7.5.
[32] Westergaard, H.M., "Bearing pressures and cracks," J. Applied Mech.,
vol. 6, no. 61, pp. 49-53, 1939.
[33] Sedov, L.I., A Course In Continuum Mechanics. J.R.M. Radok, Trans.
Groningen, Netherlands: Wolters-Noordhoff Publishing, 1972, sec.
13.2.8.
[34] Fett, T. Stress Intensity Factors, T-Stresses, Weight Functions.
Karlsruhe, Germany: Universitätsverlag Karlsruhe, 2008.
[35] 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, Struct.
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] 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.
[8] 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.
[9] 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.
[10] 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.
[11] Meguid, S.A., Engineering Fracture Mechanics. New York, NY:
Elsevier Science Publishing Co., Inc., 1989, secs. 1.17, 4.3, 5.4, 6.1.
[12] Lawn, B., Fracture of Brittle Solids, 2nd ed. E.A. Davis, and I.M. Ward,
Eds. Cambridge, UK: Cambridge University Press, ch. 9.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] Narayanan, R., and Der-Avanessian, N., " Design of slender webs
having rectangular holes," J. Struct. Eng., vol. 111, no. 4, pp. 777-787,
1985.
[18] 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.
[19] 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.
[20] Zaarour, W., and Redwood, R., "Web buckling in thin webbed
castellated beams," J. Struct. Eng., vol. 122, no. 8, pp. 860-866, 1996.
[21] 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.
[22] 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.
[23] 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.
[24] 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.
[25] Brighenti, R., "Buckling of cracked thin-plates under tension or
compression," Thin-Walled Struct., vol. 43, no. 2, pp. 209-224, 2005.
[26] Brighenti, R., "Numerical buckling analysis of compressed or tension
cracked thin plates," Eng. Struct., vol. 27, no. 2, pp. 265-276, 2005.
[27] Shimizu, S., "Tension buckling of plate having a hole," Thin-Walled
Struct., vol. 45, nos. 10-11, pp. 827-833, 2007.
[28] 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.
[29] 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.
[30] Sun, C.T., and Jin, Z.-H., Fracture Mechanics. Waltham, MA: Academic
Press, 2012, sec. 3.5.
[31] Sadd, M.H., Elasticity: Theory, Applications, and Numerics, 2nd ed.
Burlington, MA: Academic Press, 2009, secs. 5.5, 7.5.
[32] Westergaard, H.M., "Bearing pressures and cracks," J. Applied Mech.,
vol. 6, no. 61, pp. 49-53, 1939.
[33] Sedov, L.I., A Course In Continuum Mechanics. J.R.M. Radok, Trans.
Groningen, Netherlands: Wolters-Noordhoff Publishing, 1972, sec.
13.2.8.
[34] Fett, T. Stress Intensity Factors, T-Stresses, Weight Functions.
Karlsruhe, Germany: Universitätsverlag Karlsruhe, 2008.
[35] 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:64684", author = "Sebastian B. Mendes", title = "Approximate Tension Buckling Capacity of Thin Edge-Cracked Web Plate Subjected to Pure Bending", abstract = "The presence of a vertical edge-crack within a web
plate subjected to pure bending induces local compressive stresses
about the crack which may cause tension buckling. Approximate
theoretical expressions were derived for the critical far-field tensile
stress and bending moment capacity of an edge-cracked web plate
associated with tension buckling. These expressions were validated
with finite element analyses and used to investigate the possibility of
tension buckling in web-cracked trial girders. It was found that
tension buckling is an unlikely occurrence unless the web is relatively
thin or the crack is very long.", keywords = "Fatigue crack, tension buckling, Rayleigh-Ritz,
structural stability.", volume = "7", number = "2", pages = "201-7", }
