Advanced Steel Construction

Vol. 8, No. 1, pp. 17-37 (2012)



S.T. Lie 1,*, T. Li 2 and Y.B. Shao 3

1 School of Civil and Environmental Engineering, Nanyang Technological University,

50 Nanyang Avenue, Singapore 639798

2 Maritime Research Centre, Nanyang Technological University,

50 Nanyang Avenue, Singapore 639798

3 School of Civil Engineering, Yantai University, Yantai City 264005, P. R. China

*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. )


Received: 9 February 2011; Revised: 15 June 2011; Accepted: 29 June 2011



The stress intensity factors at the deepest point and at the crack ends of a surface crack in a tubular K-joint are calculated by direct and indirect methods. In the direct method, the surface crack is modelled explicitly. An automatic mesh generator is developed to produce a well-graded mesh around the crack region. This is achieved by using five types of elements. Thereafter, the stress intensity factors of a surface crack located anywhere along the weld toe at the joint intersection are calculated using the J-integral method. The computed values had been verified by experimental test results. In the indirect method, the stress intensity factors are estimated by the T-butt solutions used in conjunction with the stress concentration factors (SCFs) and degree of bending (DOB) of the uncracked tubular K-joint. In this study, a total of 1024 models, covering a wide range of geometrical parameters and crack shapes, have been selected and analyzed. Both approaches are able to produce a safe estimation of stress intensity factors at the deepest point of the surface crack. However, the indirect method is found to be extremely conservative; it overestimates the stress intensity factor values by as much as 190.4% (β=0.5, γ=30, τ=0.5, a/T=0.1, c/a=5) at the deepest point, and 390.7% (β=0.4, γ=30, τ=0.5, a/T=0.5, c/a=8) at the crack ends of the surface crack respectively.



Direct method, Indirect method, J-integral method, Mesh generator, Stress intensity factor, Surface crack, Tubular K-joint


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