《船舶与海洋工程结构风险评估》课程教学课件（讲稿）Lecture 6 Reliability of Steel Plates -I

Et3. Define flexural rigidity of plate by 12(l-y)ThenOSimilarlya=-Daxav11

• Define flexural rigidity of plate by • Then • Similarly   2 3 12 1 v Et                 2 2 2 2 y w v x w M x D                2 2 2 2 My D x w v y w 11

aTwistingcurvatureisdefinedasaxoyand gives rise to an in-plane shear xyon a fibre distant za?wfrom the neutral surface of - 2zaxoy·Shear Stress2M-2Gaxy12

• Twisting curvature is defined as and gives rise to an in-plane shear on a fibre distant z from the neutral surface of . • Shear Stress x y w     2 x y w z     2 2 xy G xy    x y w Gz      2 2 xy  12

: Twisting moment in face x = O or a isz dz dy7Mxv dyxy12Gt3a?w6axdyEt3 a?w2(1 +v) 6 axoya"w= -D(1-OxoySimilarly,, M dx=Jt zdzdxSinceT, =tr,M..=MXyxX13

• Twisting moment in face x = 0 or a is Mxy dy • Similarly, • Since z dz dy 2 2 xy t t     x y Gt w      3 2 6   x y t w v E       3 2 2 1 6   x y w D v       2 1 xy  yx Mxy  M yx   , M dx z dz dx yx yx   13

In-PlaneStressResultantsaNyt/272 0x dzOt. If , and , are the X- and y-direction in plane strains,then via Hooke's LawEt14

In-Plane Stress Resultants • If and are the x- and y-direction in plane strains, then via Hooke’s Law  x y  N dz x t x t  / 2  / 2     x x y v v Et N      2 1 t.   x 14

EtSimilarly,N.AndNH=Gt xyWhere is the in-plane shear strain15

• Similarly, • And • Where is the in-plane shear strain.   y y x v v Et N      2 1 xy  G t γ N t xy xy  xy  15