MT-1620 Fall 2002 The resultant shear stress toe, is always tangent to the boundaries of the cross-section So, we can"cut outa circular piece(around same origin)without violating the boundary conditions(of tres acting tangent to the boundaries) Using the solution for a solid section, we subtract the torsional stiffness of the removed piece"(radius of ri from that for the solid section(radius of Ro πRxR Exact solution for thick. walled circular tube let us now consider Paul A Lagace @2001 Unit 12MIT - 16.20 Fall, 2002 The resultant shear stress, τres, is always tangent to the boundaries of the cross-section So, we can “cut out” a circular piece (around same origin) without violating the boundary conditions (of τres acting tangent to the boundaries) Using the solution for a solid section, we subtract the torsional stiffness of the “removed piece” (radius of Ri) from that for the solid section (radius of Ro) π R4 π R4 J = o − i 2 2 Exact solution for thick￾walled circular tube let us now consider: Paul A. Lagace © 2001 Unit 12 - 11