Indirectly measuring the displacements of tension structures under dominant design loads by exerting simple testing loads

•A method is proposed to indirectly measure displacements under dominant design loads by exerting several simple testing loads.•Proper testing loads can be quickly found and have far less loading points than design loads.•Proposed indirect method is more robust to resist measurement noise than traditional direct method.•Reason why proposed indirect method has better robustness is explained. Structural stiffness of a real tension structure may degrade due to many factors, so the stiffness monitoring is very important. If the displacements under the dominant design loads are obtained, the stiffness state of the real structure can be intuitively assessed by a deformation checking process. However, exerting design loads on a real structure is neither efficient nor economical, because they usually have too many loading points. A method is hence proposed to indirectly measure the displacements under the design loads by merely exerting several simple testing loads. By utilizing the linear combination of several contributing eigenvectors to express the displacements, the problem of measuring displacements is transformed to that of measuring combinational coefficients of these contributing eigenvectors. The relationship between the combinational coefficients of the mutual contributing eigenvector of the design load and the testing load is set up firstly, with two basic conditions established. To satisfy the basic conditions, a strategy to decompose the design load and an algorithm to find proper testing loads are suggested. The numerical example of a cable net with two typical design loads is finally analyzed. Results illustrate that the proposed indirect method is effective, with three simple testing loads (no more than 3 loading points) found to replace the two design loads (181 loading points) in the on-site static testing. Besides, the proposed indirect method is more robust to resist the influence of measurement noise than the traditional direct method. The reason why the proposed indirect method has better robustness is also discussed.