Processing the results of research on the scale factor in flexure

Abstract

Authors who have dealt with the influence of the scale factor have studied it only for the cases of compression and tension. Some of them give a method of processing test results [1][2][3][4][5][6][7][8]. There are scaroely any papers on fiexural tests, and those which have been published [4,5] analyze individual probiems in the processing of test results.In this article I consider some questions concerning the method of processing, analyzing, and presenting research results on the influenceofthe seam factor in flexure, using as an example some experimental data obtained in field and laboratory tests on limestone under flexure. The field tests were performed in Pit 8 of the "leningradslanets" group. In the floor of a working we partly cut and tested four cantiiever beams and four embedded onboth sides [6]. In the laboratory we tested 21 beams of various dtmensiom made from samples taken from the in situ beams. The load was imposed in stages which were kept until rapid deformation increase stopped, and the flexure was measured and the displacement of the fixed parts monitored. The stages were 250-500 kg for the field tests and 4-8 kg in the laboratory tests. Load relaxation was performed only for the laboratory tests in four to five stages with recording of the residual flexures. The loads were measured by oil manometers with a scale division of 1 kg/cm z, which corresponded to a load of 25 kg in the field hydraulic apparatus, and 4 kg in the laboratory apparatus. The displacements were measured by clock gages with scale divisions of 0.01, 0.002, and 0.001 ram.The results of the laboratory and field tests are plotted in Figs. 1 and 2.The fiexural strengths of the beams and the moduli of elasticity were calculated from the usual formulas for strength of materials. The functional coefficients of deformation were calculated with the aid of formulas for the modulus of elasticity with elastic fiexure instead of geueral flexure.To study the influence of the scale factor, the experimental data must be divided into groups according to each dimensional parameter. For compression, tension, or shear tests, according to the statistical theory of strength [7][8][9], for this parameter we take the cross-sectional area or volume of the test bodies. Under flexure, for equally long beams, it is more convenient, in order to elucidate the influence of the scale factor on the strength, to take as the dimeusional parameter the moment of resistance of the cross section, W, and for the deformation index, the moment of inertia of the cross section, I. In particular cases, as the dimensional parameters, instead of W and I we can, for beams of circular cross section, take the diameter d and correspondingly d 2 and d ~, and for rectangular beams with constant width and height, h 2 and h a.We should note that in connection with results on the influence of the dimensions of beams on their deformation (see Fig. 2), by the term "scaie factor" we shall in future mean the influence of the dimensions of a body on its strength and deformation indic...