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Marine_Structural_Design Episode 7

Tham khảo tài liệu 'marine_structural_design episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 218 Part ỊỊ Ultimate Strength The pre-buckling deformations of cylinders are highly non-linear due to ovalization of the cross-section. Brazier 1927 was the first researcher who derived elastic bending moment and crosssectional ovalization as a function of curvature in elasticity. He found that the maximum moment is reached when critical stress is cfj 0.33 11.20 r However in plastic region the buckling strain for cylinders in pure bending may be substantially higher than that given by plastic buckling theory for cylinders in pure compression. Many researchers have been trying to derive mathematical solutions for inelastic cylinders in pure bending see Ades 1957 and Gellin 1980 . Unfortunately no one has been successful so far. The effect of boundary conditions may also play an important role affecting buckling strength of un-stiffened short shells under bending. The shorter the cylinder the higher the buckling strength is. This is because pre-buckling deformation which is less for shorter cylinder may reduce shell buckling strength. When the length of the cylinder is long enough the bending strength may be close to those given by Beazier 1927 Ades 1957 and Gellin 1980 . 11.2.4 External Lateral Pressure In the pre-buckling state the external pressure sets up compressive membrane stresses in the meridian direction. Retaining only the linear terms in Eq. 11.3 Ne -pr 11.21 Introducing Eq. l 1.21 into Eq. 11.8 yields the following stability equation DV M -y ri7 0 11.22 r õx r 03 The displacement function is of the same form as the axial compression. Introducing Eq. 11.22 yields _ pr E Y - Ã2 2 r 12z2 ƠOE t 12 1-V2 U 2 tt2 1 2 2 11.23 where one axial wave m 1 gives the lowest buckling load. The last term is interpreted to be the buckling coefficient kg. The smallest value of kg may be determined by trial. If n is assumed large 1 analytically minimizing Eq. 11.23 gives 4 6 r 11.24 3 r The approximate buckling coefficient valid for small and medium values ofz now reads . .