| OCR Text |
Show 108 From the condition of symmetry, are no shearing m n m(l) n(l), bounded by surfaces. the stresses Fig. A.l. on The it follows the element Let s(t) m m(l) m n m(l) and n n(l) of the element, This radius r and changes by an amount the distance dr. m(l)n(l) an element n(l) is denote the hoop stress acting normal radial stress normal to the side m n. the of there two axial planes and two concentric cylindrical sides with side that The normal radial and s(r) stress to the varies (ds(r)/dr)dr in stress on the side is consequently s(r) + ds(r) dr. (A.l) dr These forces on the element in the direction of the bisector of the angle equilibrium s(r) dphi give us the following equation [2]: r dphi + s(t) -(s(r) + ds(r) dr) dr dphi (r + dr) dphi = O, (A.2) dr or, neglecting small quantities of higher order, s(t) - s(r) - r ds(r) = O. (A.3) dr The inertia force acting on the element must be adde d: of |
