PSI - Issue 48

Petro Gomon et al. / Procedia Structural Integrity 48 (2023) 195–200 Homon Sviatoslav et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 4 Diagram of bending moments, curvature and deflections of a beam with a zone of pure bending

By substituting the same maximum load value, which can be perceived by the cross-section of the bending element, and the limit deflection, one can plot the simultaneous achievement of ultimate limit conditions - the bearing capacity for normal sections and deflections, depending on the ratio of the width and length of the beam to the height of the calculated section (Fig. 5a, Fig. 5b). The first graph is made for a bending element on two supports with an applied uniformly distributed load, and the second - with an applied point load. The graph of simultaneous achievement of limit states divides the limit state of the element into two zones. With geometric characteristics that fall below the curve shown on the graph, the bending element will reach the limit state for the first group at a normal cross-section design, and with a ratio above the graph, it will reach the limit state earlier to ensure rigidity. It is also clear from the graph that a wooden beam will be most effective if the section is within the ratio of the width to the height of the section w w w h h b 0,2 ...0,4  and its length w w w h h l 10 ...20  .

Fig. 5 Optimization (coincidence) graph of the beams destruction for two groups of limit states depending on the geometric dimensions: a) a beam on two supports with a uniformly distributed load; b) a cantilever beam with a uniformly distributed load

Bending wooden elements made of solid and glued wood are in most cases designed with a limited section height. In such elements, the limit state of the second group of limit states occurs earlier that of the first one. This method of calculation, under certain conditions, is applicable to bending elements based on other materials. 3. Conclusions 1. New method for calculating deflections, taking into account the nonlinearity of wood deformation, is developed. 2. Diagrams of deflections for wooden beams with different loading and fixing are proposed. 3. It has been established that the shape of the curvature and deflection diagrams differs significantly from the diagrams that are currently used to calculate deflections. 4. The dependences of the simultaneous achievement of the limit states for the first (in terms of bearing capacity) and the second (in terms of deflections) limit states groups depending on the ratio of the geometric dimensions of wooden beams are given.