Evaluation of Ultimate Ship Hull Strength R

,sc., nC,$ THE SOCIETYOF NAVALARCHITECTSAND MARINE ENGINEERS . OneWorldTrade Center,Suit. 1369, NewYork, N.Y. 10048 # “+ ~ PaPer,tobe PresentedatExtremeLoad,Res$mseSymDosium 8 : Arl,mton,VA,October1>20,1981 ;$ 01! # “o, & o*H,.S,** Evaluation of Ultimate Ship Hull Strength R. S. Dow, R. C. Hugill, J, D. Clark and C. S. Smith, Admiralty Marine Technology Establishment, Glasgow, Scotland ABSTRACT plastic strength of ships’ hulls (1 to 6)* and a method of estimating hull strength has been The problem of evaluating the U1timate proposed (4) which takes account of local buck- longitudinal strength of a ship’s hull is dis- ling failure and [email protected]~f10@ cussed. In addition to behaviour under quasi- carrying capacity in elements of the hull cross- static loads, the whipping response of a section. The purpose of the present paper is ship’s hull to impulsive loads, eg bow- to examine the accuracy of this approach by slamming and underwater explosions, is con- correlation of analysis with collapse tests on sidered. A method of analysis is described, various longitudinally stiffened steel box- based on approximate characterization of the girders and to consider extension of the strength of elements of hul1 cross-sections analysis method to deal with the case of under tensile and compressive loads associated dynamic loading, in particular whipping of the with hull-girder bending togetherwith local hull girder caused by bow-slamming or under- lateral-pressureeffects. The influence of water explosions which, as shown by recent imperfections (initial deformations and theoretical studies and seakeeping trials, may residual stresses) is accounted for. The cause severe midship bending moments. analysis is illustrated with reference to a tYPiCal warship hull design. Theoretical STATIC ANALYSIS OF HULL STRENGTH results are correlated with experimental data derived from collapse tests on a number of Strength and Stiffness of Plate Elements stiffened box-girders. Between 6L12iand 80% of a typical hull INTRODUCTION cross-section is for-redby deck, shell and longitudinal bulkhead plating: hull strength is Assessment of the ultimate longitudinal therefore likely to be critically influenced by strength of a ship’s hull under loads imposed the stiffness and strength of plate elemnts, by the sea has traditionally been made by com- particularly under compressive load. Loss of paring calculated elastic stresses in the deck stiffness in the plating, which may be caused by or bottom shell with allowable stresses, buckling or premature yielding, leads directly usually corresponding to prescribed fracticms to loss of effective moment of inertia and of the material yield strength. This dppt.~~~h, section modulus in a hull cross-section and applied,in conjunction with a nominal ~stiwte also accelerates yield in the stiffeners and of vertical wave bending moment based on hence elasto-plastic buckling of stiffened static-balance analysis, has a certain empiri- panels. cal validity when applied to conventional ships closely resembling previous successful hulls In longitudinally framed deck and shell designed in the same way, but fails to provide structure containing closely spaced stringers a true estimate of hull strength and is clearly with relatively widely spaced transverse fram?s, unsatisfactory when applied to unconventional plates of aspect ratio a/b (length/breadth), desi ns. If the hull structure does not fail 1.5 will buckle into one or more half-waves of Iota?lY, the actual collapse bending rmment may length x somewhat less than the plate breadth exceed the wment which nominally causes outer- (0.7 < A/b < 1.0). Various approximate methods fibre yield; on the other hand the collapse of characterizing the strength and stiffness of moment may be substantially less than the such plates, based on large-deflection elastic nominal yield moment if local compressive fail- analysis or on interpretation of test data, have ure of plating or stiffened panels occurs in been reviewed by Faulkner (7). A much improved parts of the cross-section. understanding of plate buckling has been ob- tained in recent years from the application of A recent trend in the design of ships, nonlinear finite element and finite difference offshore platforms and civil engineering analysis representing large deflection elasto- structures is towards use of limit-state design plastic behaviour (S to 13): parametric appli- criteria, requiring explicit consideration of cation of such analysis, accounting for imper- ultimate strength in relation to statistically fections (distortions and residual stresses) as defined loads. Some effort has consequently been devoted to evaluation of ultimate, elasto- * Denotes references at end of paper, 133 from analysis of simply su ported square or nearly square plates with l’”ongltudinal edges constrained to remain straight but free to nwve bodily in the plane of the plating. Over the strain range preceding plate fai1ure these curves may be applied without modification to long rectangular plates on the assumption that buckling occurs in approximately square half- waves and that compressive strain occurs uniformly over the ful1 length of each plate: in the post-collapse range, where end-shortening strain may be confined to a single, approximately square CO1lapse zone with virtually zero increase of strain over the ramainder of the plate, a simple correction dependent on the aspect ratio a/b may be applied to the strain scale. In the case of transversely framed deck and shell structure, as commonly employed in the fore and after regions of a ship’s hull, failure of wide plate panels (a/b .< 1) under ~ 1.,O longitudinal compression is 1ikely to occur by % 0“’ .0 buckling into single lobes over the full width of each plata. Recent numerical studies (15, $0 16, 17) have provided some information about 0, 80 ,. the stiffness, strength and imperfection sensi- ,0 tivity of such plating. It has been shown that .. loss of stiffness and strength depends criti- 0.. callY on the form of initial deformation, as shown in Figure 2. Some strength curves for 0> very wide plates (b/a + -) having initial deformations of symmetric and antisynnetric form (17), together with curves derived from References 15 and 16 for wide plates of finite aspect ratio (1 6 b/a & 5) having various P’ levels of antisjnanetricdistortion, are shown in Figura 3. ,.. .. O .mwwa%rm brsfl ,.,1’.1.3S,awm 4. so T I ,6 +.,80 ,0 015 ,0 9. 0- .. F3 01 0, -_. —._._- &=05&, -&=o :7- 005- Fig. 1 Load-St?orteni ng Curves far Square PI tes 1 2 3 E/e ~ ~ under Uniaxial Compression ~= $~ [1 measured in surveys of ships and welded steel Fig. 2 Load-Shortening Curves for Transversely box-girder bridges (13, 14) has led to data Compressed Long Plates (a/b . -) with curves of the type shown in Figure 1 (13) Synmetric, Antisymetric and Inter- which have the msrit of defining not only mediate Forms of Distortion maximum load-carrying capacity but also plate stiffness at any point in the strain range. The curves shown in Figure 1 have been derived I L 134 shel1 and deck structures in ships is column- 1ike interframe f1exural buckling of 1ongi- tudinal stiffeners with attached plating under longitudinal compression induced by hull bending: this form of failure, which may be strong- ly influenced by loss of compressive stiffness of the plating, will in most practical cases precede other collapse modes including lateral- torsional buckling of girders and overall buckling involving bending of transverse frames. I !-/2 1 L/2 “’k0.2 0.4~,t *I a) Subdivision of stiffened panel into elements showing assumed ‘. --: initial deformation ----.3 - --- -- ox -----_5 _ . --- ---.--m- pm tm.ltd.35siqle librewithMfmss 1---- Wiwd by*e d agpwde s!m-sttin mrw(smfig1) v 1 H , b) Subdivision of cross section into fibres Fig. 4 Idealisation of Stiffened Panels ------------- ~ For the purpose of examining the CO1umn- O.e 1ike interframe flexural buckling of closely I spaced longitudinal stiffeners with attached P1sting under 1ongitudinal compression, -. 5- analysis may be confined to a single stiffener 0.! ---------with attached strip of plating treated as a . beam column with conditions of simple or ‘--- elastic support at positions of transverse ------- -m frames as shown in Figure 4a. In order to examine the large deflection, inelastic buck- 1--- ling behaviour of such structures, a computer (!, program has been developed (18, 19) for the nonlinear analysis of plane frames of general geometry, including straight or initially de- Fig. 3 Strength Curves for Wide P]ates Under formed beam CO1umns as a special case. The Compression in Shorter Direction main features of the analysis method are as follows: Strength and Stiffness of Stiffened Panels (i) Frames of arbitrary polygonal or It has been shown (18) that the most curved geometry are represented as 1ikely form of failure qn flat panels of assemblies of straight beam elements, orthogonallY stiffened plating forming bottom Polygonal representation of curved 135 frames wil1 give satisfactory results M - is the column vector of provided that a sufficient number of incremental nodal dis- straight 1ine elements are included placements in the idealisation. In accordance with normal beam theory the element AP - is the COIUm” vectOr Of employed has a cubic representation incremental nodal loads of flexural deformation (w) and a 1inear representation of extensional The above linearised incremental pro- deformation (u). F“]1 account is cess is coupled with a generalised taken of the coupled flexural and Newton Raphson iterative equilibrium extensional deformations of a frame. correction scheme based on the matrix Plane sections are assumed to remain equation.: plane under conditions of elastic and inelastic bending and extension. (6}j+, = (61j + Provision is made for finite separa- tion between node points at the ~nd~ of elements, account thus being taken of changes in the position of the [K~j’[{pext}- {pint}](2) element elastic neutral axes (caused by progressive yielding or local buckling of cross sections) and con- The expression in parenthesis repre- sequent eccentricity of element axial sents the unbalanced forces arising forces.

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