Finding displacements from measured strains in 2D frames

Sometimes it is difficult to measure the deflections of structure directly when investigating its behaviour. Thisis particularly true when the measurements are to be made on a structure in service. In such cases it may be much easier to measure the strains that develop in the structure under load and to infer the deflections of the structure from these measurements. The analytical procedures for doing this are given in the paper: they are a relatively straightforward extension of well-known structural theory, but they do not seem to have been published before. In this paper, attention is focused on two-dimensional beams and frames. Two methods for calculating the deflections are described: method 1 is a simplified, version which is effective for a particular class of beam/frame, whereas method 2 can be applied to any frame. The results obtained also serve as a check on the accuracy of the strain measurements, and on whether the structure is behaving as expected. The proposed methods are applied to problems for which the strains are known, and it is shown that both methods predict the exact deflected shape of thestructure. The effect of errors in the strain measurements is also considered. The way the procedure could be used in a real situation is considered in the final example. The extension of method 2 to three-dimensional frames is straightforward. It is believed that the proposed methods would be useful both to research workers and to engineers involved in structural assessment.