《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

Plate BendingDerivation of Equilibrium Equations16

Plate Bending Derivation of Equilibrium Equations 16

FlexuralComponentsQdx49M262X2XoXOm.For eguilibrium normal to elementaQaQdx dydy dx + q dx dy = 0axayQ0Qxi.e(1)axdy17

Flexural Components • For equilibrium normal to element i.e (1) dx dy dy dx + q dx dy = 0 y Q x Qx y        0      q y Q x Qx y 17

CNeglectingtheeffectsof rateof changeofshearandlateral load, taking moments about the x-axisaMaMXi.e.dy-O dx dy= 0draxOaMaMX(2)axoy18

• Neglecting the effects of rate of change of shear and lateral load, taking moments about the x-axis i.e.   0      dx dy Q dx dy x M dy dx M y xy y y x M y M Q y xy y       (2) 18

. Similarly, moments about the y-axisamamyx(3)Qaxaya"Ma?M.oM0Myxq=0ax?Oxdyaxdyaxdyorsince Mxv=MV20?Ma?Ma?M1=0(4)ax?axoyoy19

• Similarly, moments about the y-axis (3) • or since Mxy= Myx (4) 0 2 2 2 2 2                q x y M x y M xdy M x Mx yx y xy 0 2 2 2 2 2 2            q y M x y M x Mx xy y y M x M Q x yx x       19

InPlaneComponentsNN0JuudxaLA53Equilibrium in the x-directionaNaNVdy dx=0axayaNan(5)i.e.x:0axdySimilarly, for the equilibrium in the y-directionan,anx)(6)0dxay20

In Plane Components • Equilibrium in the x-direction i.e. (5) • Similarly, for the equilibrium in the y-direction (6) dy dx=0 y N dx dy x N yx x       0      y N x Nx yx  0     y N dx Nxy y 20