In the last two terms there appear the nonzero integrals of even functions.If one neglects the contribution of the rates of variation along the x and y direction,respectively,of these terms,the previous equation is reduced to' a0+C× My =Cu ax d0. dy Moment resultantM b/2 Oz dz b/2 dz.. 6M2 -b12 which is reduced to: -Ms=Gi2dx and in neglecting the contribution of the last two terms': a8+C2×- -Ms Cdx aθ dy 。Moment resutantM=-」2g2tk b/2 which is reduced to: Essnyzdz and in neglecting the contribution of the variations of the differences nx and ny: -M=C- The existence of such approximation does not appear if one neglects apriori the increments nx nn:in Equation 17.3. 2003 by CRC Press LLCIn the last two terms there appear the nonzero integrals of even functions. If one neglects the contribution of the rates of variation along the x and y direction, respectively, of these terms, the previous equation is reduced to7
Moment resultant : which is reduced to: and in neglecting the contribution of the last two terms7 :
Moment resultant which is reduced to: and in neglecting the contribution of the variations of the differences hx and hy 7 : 7 The existence of such approximation does not appear if one neglects a priori the increments hx, hy, hz in Equation 17.3. My C11 ∂qy ∂x -------- C12 ∂qx ∂y = + ¥ –-------- Mx sy z zd –h/2 h/2 Ú = – –Mx E12 ze ox z2 ∂qy ∂x -------- z ∂hx ∂x + + -------- Ë ¯ Ê ˆ dzº –h/2 h/2 Ú = º E22 ze oy z2 – ∂qx ∂y -------- z ∂hy ∂y + -------- Ë ¯ Ê ˆ dz –h/2 h/2 Ú + –Mx C12 ∂qy ∂x -------- C22 ∂qx ∂y ¥ –-------- ∂ ∂x ------ E12hx z z ∂ ∂y ----- E22hy z zd –h/2 h/2 Ú d + –h/2 h/2 Ú = + + –Mx C12 ∂qy ∂x -------- C22 ∂qx ∂y = + ¥ – -------- Mxy txy z zd –h/2 h/2 Ú = – –Mxy E33 zg oxy z2 ∂qy ∂y -------- ∂qx ∂x – -------- Ë ¯ Ê ˆ z ∂hx ∂y -------- z ∂hy ∂x + + + -------- Ë ¯ Ê ˆ dz –h/2 h/2 Ú = –Mxy C33 ∂qy ∂y -------- ∂qx ∂x – -------- Ë ¯ Ê ˆ ∂ ∂y ----- E33hx z z ∂ ∂x ------ E33hy z zd –h/2 h/2 Ú d + –h/2 h/2 Ú = + –Mxy C33 ∂qy ∂y -------- ∂qx ∂x – -------- Ë ¯ Ê ˆ = TX846_Frame_C17 Page 324 Monday, November 18, 2002 12:33 PM © 2003 by CRC Press LLC