Virtual Work Adjustment of Trilateration Nets

One imagines the measured distances as elastic members in an internally redundant framework. The redundant members are thought to have fabrication errors equal to the differences between the measured and the calculated lengths of these redundant lines. If such differences, called closing errors, are not zeros, forces must be applied to fit the redundant members in position. To find these forces, the redundant members are cut and replaced by unit virtual loads. It is shown that the forces developed in the members due to each of these unit loads are the coefficients of the corrections in the condition equations. They can be determined by statical methods either graphically or analytically. A mathematical check is given to ensure the correct calculations of these coefficients. The final force in each member causes a change in its length, which is in fact the required correction of the corresponding distance.