Resistance of columns and beamcolumns

Transcription

1 Resistance o columns and beamcolumns TMR4195 Buckling and ultimate load analsis o marine structures Jørgen Amdahl Dept. Marine strucutures

2 Eaxmple o column buckling due to excessive jacking during installation.

3 M N CM l l e Element Idealized Beam Column STRUCTURE Idealisering av stavelementer i et rammeverk til en isolert bjelkesøle

4 Interaction equation or tubular beamcolumns subjected to axial orce and bending moment (ISO,( NORSOK) ) N N Sd c,rd 1 M Rd C mm N 1 N,Sd Sd E 2 C mzm N 1 N z,sd Sd Ez

5 Table 6-2 Eective length and moment reduction actors or member strength checking Structural element k (1) C m Superstructure legs - Braced 1.0 (a) - Portal (unbraced) k (2) (a) Jacket legs and piling - Grouted composite section 1.0 (c) - Ungrouted jacket legs () (c) - Ungrouted piling between shim points 1.0 (b) Jacket braces - Primar diagonals and horizontals 0.7 (b) or (c) - K-braces (3) 0.7 (c) - Longer segment length o X-braces (3) 0.8 (c) Secondar horizontals 0.7 (c) Notes: 1. C m values or the cases deined d in Table 6-2 are as ollows: (a) 0.85 (b) or members with no transverse loading, C m = M 1,Sd /M 2,Sd where M 1,Sd /M 2,Sd is the ratio o smaller to larger moments at the ends o that portion o the member unbraced in the plane o bending under consideration. M 1Sd 1,Sd /M 2Sd 2,Sd is positive when the number is bent in reverse curvature, negative when bent in single curvature. (c) or members with transverse loading, C m = N c,sd /N E, or 0.85, whichever is less, and N E = N E or N Ez as appropriate. 2. Use Eective Length Alignment Chart in Commentar. 3. At least one pair o members raming into the a K- or X-joint must be in tension i the joint is not braced out-o-plane. For X-braces, when all members are in compression, the k-actor should be determined using the procedures given in the Commentar. 4. The eective length and C m actors given in Table 6-2 do not appl to cantilever members and the member ends are assumed to be rotationall restrained in both planes o bending.

6 Buckling coeicient or X-braces dependeing on orce condition and rotational end support

7 ISO column buckling curve Comparison with test t data 1.2 c /F c Euler ISO ( l², 0.9/l²) Chen & Ross - abricated Smith, Somerville & Swan - abricated Smith, Somerville & Swan - seamless Steinmann & Vojta - ERW Yeomans - ERW Yeomans - seamless = (F c /F e ) 0.5 Bias COV = n = 84 Figure A Comparison o Test Data with Column Buckling Design Equation or Fabricated Clinders Subjected to Axial Compression

8 Eect o local buckling cl cl cl ce xe

9 Capacit in bending Tpical normalized moment-rotation curves or clinders or various D/tratios (M PS is plastic bending moment)

10 Capacit in bending m Z D W Et D m D Z Et W Et m D Z D Et W Et E 4 4 D ( D2 t) W = elastic section modulus 32 D ( 2 ) 6 D D t Z = plastic section modulus

11 Allowable bending stress or tubular members ISO/DIS 19902/NNORSOK N_004 Plastic thin-walled Yield

12 Stresses in circular cross-sections sections or external hdrostatic pressure p Axial stress rom capped end orces x =0.5 h q,sd h Hoop stress rom external hdrostatic pressure h =pr/2t

13 Hoop buckling he Hoop buckling strength o abricated clinders subjected to hdrostatic pressuretest data compared with design equation (rom ISO19902)

14 Interaction local buckling hdrostatic pressure 2 2 ch c x ch x x 2 x 10, λ 1.34 (1 ) cl cl cl cl cl cl cl cl 2 cl cl cl ch x 2 2 x x [ 1.12 ], λ 1.34 (1 ) 1

15 Interaction local buckling hdrostatic pressure Interaction betwen hdrostatic pressure and column buckling _ch/ cl lamda=0.5 lamda=0.7 lamda=0.9 lamda=1.1 lamda=1.3 lamda=1.5 D/t = 30 D/t = 50 D/t = 70 D/t = Water dep pth [m] Sigma_x/_cl

16 Interaction equations 1) combined tension and hdrostatic pressure 2) combined bending and hdrostatic pressure a,sd d 2 p,sd h,rd 2η 2ν p,sd h,rd a,sd d 1.0 d γ M m,sd m,rd 2 p,sd h,rd 2η 2ν p,sd h,rd m,sd m, Rd 1.0 m,rd γ m M Bending resistance with no external hdrostatic pressure Design ield stress Design hoop buckling resistance 5 4 h

17 Interaction between bending and hdrostatic pressure 2 2 mh mh h h 2 v 0 m m h h h η 54 _mh/_m _h/_ =0.2 _h/_ =0.4 _ h/_ =0.6 _h/_ = η mh h h h m h h h Sigma_p/_h

18 Interaction between bending and hdrostatic pressure Waterd depth (m) % 5% 10 % 100 % Diameter/thickness Reduction in bending strength as a unction o water depth and D/t-ratio

19 Interaction equation or beamcolumns with external hdrostatic pressure T l ti i d di Two ormulations given, depending on capped end orces included or not

20 Interaction equation or tubular beam-columns subjected to axial compression, bending moment and external hdrostatic pressure (capped end orces NOT included). d) ac,sd ch,rd 1 mh,rd C 1 m ac,sd Axial compressive strength in the presence o external hdrostatic pressure m,sd E q,sd 2 C 1 mz ac,sd mz,sd Ez q,sd Bending resistance in the presence o external hdrostatic pressure

21 1,4 ISO 1,2 1,0 h /F 0,8 0,6 0,4 Miller & Kinra - abr.+ rings Miller, Kinra & Marlow - abr.+rings Miller, Kinra & Marlow - abr. unsti. Eder et al - abr.+ rings Eder et al- ERW + rings Kiziltug et al - ERW unsti. Steinmann & Vojta - ERW unsti. 0,2 0,0 F /F he Sammenligning av kapasiteten mot tre vanntrkk i NORSOK N-004 med orsøk

22 Yield check or tubular beam-columns subjected to axial compression, bending moment and external hdrostatic pressure (capped end orces NOT included). ac,sd q,sd 2 m,sd 2 mz,sd 1.0 cl,rd mh,rd Local buckling strength not aected b external hdrostatic pressure Bending resistance in the presence o external hdrostatic pressure

23 Yield check or tubular beam-columns subjected to axial tension, bending moment and external hdrostatic pressure (capped end orces NOT included). ac,sd q,sd (net axial tension) ac,sd q,sd 2 m,sd 2 mz,sd 1.0 th,rd mh,rd Axial tensile resistance in the presence o external hdrostatic pressure Bending resistance in the presence o external hdrostatic pressure

24 Materialaktor or staver med Materialaktor or staver med rørtverrsnitt 05 λ or 115 γ 1.0 λ 0.5 or 0.60λ 0.85 γ 0.5 λ or 1.15 γ s s M s M 1.0 λ or 1.45 γ γ s M s s M p,sd c,sd 2 σ σ λ he cle j,sd s σ λ