On the Buckling of Circular Cylindrical Shells Under Pure Bending

Abstract

The stability of circular cylindrical shells under pure bending is investigated by means of Batdorf’s modified Donnell’s equation and the Galerkin method. The results of this investigation have shown that, contrary to the commonly accepted value, the maximum critical bending stress is for all practical purposes equal to the critical compressive stress.

Ultimate strength of cylindrical shells with cutouts

“…Reissner (1961) further developed a more general formulation for thinwalled cylindrical shells of arbitrary cross-sections. Seide and Weingarten (1961) used a modified Donnell equation and the Galerkin method and found that the maximum elastic buckling stress under bending is equal to the critical compressive stress under axial compression. Sherman (1976) experimentally identified that shells with a column slenderness ratio where λ was greater than about 50 did not have sufficient plastic hinge rotation capacity to develop the classical ultimate strength.…”

“…For a couple of decades, a number of studies were conducted to provide buckling analyses of circular cylindrical shells (Brazier 1927;Reissner 1961;Seide & Weingarten 1961;Fabian 1977;Gellin 1980) with cutouts under axial compression (Schenk & Schuёller 2007;Shariati &Rokhi 2010;Ghazijahani et al 2015) and pure bending (Yeh et al 1999;Dimopoulos & Gantes 2012, 2015Guo et al 2013;.…”

The continuous strength method for the design of circular hollow sections

“…Gerard and Becker [17] proposed a factor of 1.3 based upon the findings of Flügge [18]. However more recent analytical work [19][20][21] has showed that the maximum critical stress in bending is equal to the critical compressive stress for practical cylinder lengths. equivalent to applying a factor to the local buckling stress.…”

“…equivalent to applying a factor to the local buckling stress. Given the findings of the more recent research [19][20][21] and the conservative nature of the choice, the elastic critical buckling stress in bending will be taken to be the same as that in compression (see Eq. 2) in the present study and within the CSM.…”

Structural behaviour of stainless steel elements subjected to combined loading

“…This may be determined from the CSM 'base curve', which defines the relationship between the maximum strain that a cross-section can endure and its local slenderness, as shown in where ε csm is the maximum attainable strain of the cross-section under the applied loading, ε y =σ 0.2 /E is the yield strain, C 1 is a parameter related to the CSM material model (Figure 3.25) to prevent over-predictions of strength, with a value of 0.1 for austenitic and duplex stainless steels and 0.4 for ferritic stainless steel, ε u =C 3 (1-σ 0.2 /σ u )+C 4 is the predicted strain corresponding to the material ultimate strength, where the values of C 3 are equal to 1 and 0.6 for austenitic and duplex stainless steels (Afshan and Gardner, 2013b) and for ferritic stainless steel (Bock et al, 2015b), respectively, and C 4 is equal to zero for all the stainless steel grades, and c  is the local cross-section slenderness, calculated as 0.2 / cr  , in which cr  is the elastic local buckling stress of the cross-section, and is calculated from Equation (4.11) for a CHS under pure compression or pure bending (Seide and Weingarten, 1961;Reddy and Calladine, 1978;Silvestre, 2007), and thus also combined loading, in which υ is the Poisson's ratio. Note that the CSM base curve for CHS is different to that for RHS described in Chapter 3.…”