218 Mechanics of Materials §10.2 +do dr Fig.10.3. a,+do, Unit length de Fig10.4. For small angles: do do sin22 radian Therefore,neglecting second-order small quantities, rdo,+a,dr oHdr dor o,+dr =0H dor or GH-c,=r (10.1) Assuming now that plane sections remain plane,i.e.the longitudinal strain &L is constant across the wall of the cylinder, then 6L=E[aL-vo,-vOH] -E [GL-Y(o,+oH)]=constant It is also assumed that the longitudinal stress aL is constant across the cylinder walls at points remote from the ends. ,+H constant 2A (say) (10.2)218 Mechanics of Materials 410.2 Fig. 10.3. q +do, length Fig. 10.4. For small angles: . d9 d9 22 sin - - radian Therefore, neglecting second-order small quantities, rda, + a,dr = aHdr .. or do, a, + r- = an dr (10.1) Assuming now that plane sections remain plane, Le. the longitudinal strain .zL is constant across the wall of the cylinder, 1 E 1 E then EL = - [aL - va, - VaH] = - [aL - v(a, + OH)] = constant It is also assumed that the longitudinal stress aL is constant across the cylinder walls at points remote from the ends. .. a, + aH = constant = 2A (say) (10.2)