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Forces And Moments

For the force calculation the forces on each element at the cutting plane summed for each component jj by

fa,j=∑i=1nfi,jf_{a,j} = \sum_{i = 1}^{n}f_{i,j}

and for the moment calculation

{ma,xma,yma,z}={mx,0my,0mz,0}+[0−z/ry/r1/z00−1/y00]{fx,0fy,0fz,0}\begin{Bmatrix} m_{a,x} \\ m_{a,y} \\ m_{a,z} \\ \end{Bmatrix} = \begin{Bmatrix} m_{x,0} \\ m_{y,0} \\ m_{z,0} \\ \end{Bmatrix} + \begin{bmatrix} 0 & - z/r & y/r \\ 1/z & 0 & 0 \\ - 1/y & 0 & 0 \\ \end{bmatrix}\begin{Bmatrix} f_{x,0} \\ f_{y,0} \\ f_{z,0} \\ \end{Bmatrix}

where subscript 0 refers to the element cut position on the cutting plane, giving a resulting moment of

ma,j=∑i=1nmi,jm_{a,j} = \sum_{i = 1}^{n}m_{i,j}