Use of polar coordinates for improving the measurement of resistant cross-sections of existing timber elements combining laser scanner and drilling resistance tests

•Historic timber structures typically have elements with irregular cross-sections.•Real apparent external shape of the beam may be obtained by laser scanning.•Resistant cross-section may be obtained using drilling resistance tests data.•The use of polar coordinates improves the measurement of the resistant cross-sections.•The calculation of the resistant section becomes independent of the number of drilling teste. Historic timber structures typically have elements with irregular cross-sections often with decayed segments, making of extreme importance to have proper methods to obtain the resistant cross-section. Knowing as accurately as possible the measurements of the resistant section of these beams is fundamental for the structural safety analysis. Small changes on the size and geometry of the resistant cross-section may be fundamental in an intervention decision process. In this work an algorithm was created that allows to obtain the geometry of the resistant section of existing timber beams by use of data obtained by laser scanning of the external apparent sections combined with drilling resistance tests. The algorithm is based on polar coordinates and proved to obtain more reliable resistant cross-sections than those obtained solely by common practice using drilling resistant tests. The developed algorithm was calibrated with a laboratory beam and subsequently applied and validated in a case study.