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For this purpose, stress-strain relationships are to be established for all the elements, namely, tensile elements, corner elements and compressive elements. In the way of progress collapse mechanism through incremented curvature, strain in some elements exceed their critical values. The strain of tensile and corner elements are assumed to observe the Deformation (Total) Theory once they have exceeded the yield strain. So the following Ramberg-Osgood model are be applied: nbaE+ =σ σε (12) Compressed elements which exceed a critical value continue bearing loads gradually lower than the ultimate loads with increasing strains. Therefore, after a certain value of applied curvature, a significant number of panels carry loads which are lower than the ultimate loads and hence the total moment of the section starts decreasing with increasing curvature, showing the maximum possible moment which the section can sustain. Therefore, definition of critical strains and stress-strain relationships above the critical strains is also a prerequisite for this procedure. The stress-strain relationships which have been used in the current algorithm throughout the loading region for all the elements are given below. Tensile and corner elements Based on the above description, the relationship of the stress-strain of tensile and corner elements can be written as: ⋅ ∆ +=) (' 'i t iiiEEσ ε σεσ crt icrt iε εε ε>≤ (13) where crtε is the critical strain. ( ) 'i tE σ is the tangent modulus in given stress, . They can be expressed as following respectively. 'iσ+ ==−1'') (1/ 1 ) (, /n ii ts crtb nbaEEEσσσ ε, (14) In this paper the parameters are taken as: n=60，b=1.005σs, a=20。 Stiffener associated with panel under compression Following the approach of Rahman et al(1996), three distinct zones in the whole range of element load-shortening behavior are considered, as can be seen in Fig. 2. The first zone is below the ultimate strength, which is called “stable zone”. The second zone starts when a panel reaches its critical load, over which the strain continues to increase with constant load at ultimate strength until plastic mechanism is formed. This second zone is called “no-load-shedding” zone as the element does not require any load-shedding to maintain equilibrium. The third and final zone is characterized by a drop-off in the element’s load-carrying capability as strain increase and is called the “load-shedding” zone. While the ultimate strength of element is obtained the mathematical formulations in these areas can be written as following: σ ε Fig. 2: -- relationship of element Ultimate strength of stiffener associated with panel A stiffener and its associated panel can be considered as a special beam-column, where the stiffener flange is free to deflect vertically and sideways, but the plating is restricted from deflecting sideways. The strain displacement used herein for axial compression, vertical bending and flange sideways bending are shown in Fig.3. The deformation of the stiffener cross-section can be described approximately by a displacement field having five degrees of freedom ) , , , , ( B T T w v u φ φ . The variable u is the uniform axial displacement along the x direction, and the cross-section deformations vT , w, T φ and B φ , are shown in Fig.3, where w is the flexural displacement of the element with respect to the neutral axis z, vT is the lateral displacement of the flange with respect to the y axis, B φ is the rotation at the web baseline and T φ is the rotation at the rotation at the tip of the web. The ultimate strength of stiffener associated with panel under compression can be determined by the method presented by Fang et al.( 1998a, 1998b). Fig. 3: The parameters and deformation of stiffener cross-section ( angle bar) The analysis of ultimate strength of damaged fb z T v ftw tp t hbB φ T φw y x ship hull To analysis of ultimate strength of damaged ship hull girder, a 34000 ton bulk carrier with large deck open is chosen for calculation. The principal dimensions of the ship are listed in the Table 1. The midship cross section is given in Fig.4. The dimensions of the longitudinals are listed in Table 2. The high strength steel (HST) is used for structures at deck and at upper part of the topside tank.