The yielding phenomena of steel bar under uniform bending stress has been fully explained by the authors. The yielding phenomena of a twisted steel bar has also been discussed in the same manner. The idea is supported by their experiments for specimens of various sectional shapes of steel bars. But these are the cases where the stress gradient does not exist in the axial direction. In the present paper, the authors intend to examine whether their theory is applicable even when the stress gradient exists in the axial direction, e. g., the yielding of bending steel bar under concentrated load. The problems of elastic-plastic bending are treated analytically in the same manner as in the former cases and the result is compared with the experiments. The both results agreed very well, and it is ascertained that the theory is applicale to the present case.

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In this report, the effect of thickness and weight of the specimen on Shore hardness number was investigated. Under the general requests for the testing with the Shore scleroscope being satisfied and especially attending to free from the effect of the operating handle and of pressing force with consideration of the results of the preceding reports, using many specimens which were different in hardness or in material, hardness numbers were measured with verieties of thickness from 10 to 0.1 mm. As a result, the effect of thickness and weight of the specimen on hardness number was made clear. That is ; the effect of thickness is due to (1) spring effect, (2) deformation effect, and (3) anvil effect. However, these effects may be classified to three main types according to the material, whose hardness undergoes the test, as follows : a type containing (1), (2) and (3) effects (iron and steel), a type containing (2) and (3) effects (nonferrous Ist. type). and a type containing only (3) effect (non-ferrous 2 nd. type). Critical (minimum) thicknesses immune from this effect were decided according to the above mentioned types, as about 5 mm for iron and steel, about 2 mm for non-ferrous Ist. type, and about 0.5 mm for non-ferrous 2 nd. type. Above mensioned results are also applicable to the effect of weight of the specimen. According to the results, specimen weighing 0.1 kg or even less give no effect on hardness number, if sufficient pressing force is applied.

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In this paper, using the photoelastic method, stresses in rectangular plates under compressive loads distributed uniformly along a certain range of the two opposite edges were studied. Test pieces, made of phenolite, have the same length 25 mm and 5 sorts of width, ie. 25, 20, 15, 10 and 5 mm. Systems of compresive load in each test piece are of approximately concentrated compressive load 4 sorts of local uniform compressive load on the opposite sides. As a result of this experiment, main characteristics of stress distribution in this case were explained and discussed.

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The deformation theory and the flow theory of plasticity were compared with experiments of plastic deformation, under the variable stress ratios, by means of vectors of shearing strains and stresses on the plane of octahedron. The shearing strains given by both theories do not show sufficient agreement with those given by the experiments. Then it may be supposed that anisotropy grows in the material as its deformation increases. An orthotropic relation between the plastic strain and stress was derived from generalized type of the flow theory under the condition of incompressibility of plastic deformation. The factors multiplied by the principal stress in the relation, are not only functions of the strain history, but functions of the next new stress ratio.

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Plastic deformation of metals under two or three dimensional stress, where the stress ratio is variable, was studied from the experimental results, which had been treated in the 1 st, 2 nd and 3 rd reports, and from Bridgman's experimental results. The octahedral shearing stress theory can not be applied to such general problems. The relationship between stress and strain depends upon the kinds of previous deformation, especially upon the shape of the short preceding"strain path". Considering these conditions, the new equation for plastic deformation is obtained.

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Utilizing an othogonal curviliniar co-ordinate α, β obtained from a relation [numerical formula], the following problems of torsion are studied : (1) The torsion of a round bar with a number of semi-circular notches is calculated and numerical calculations in the case 4-notches for variable radius of curvature have been carried out. (2) The torsion of a bar with a section of a circular sector and a round bar with a sharp notch reaching the center (i, e, the case of a crack) have been calculated and then compared with the former results. (3) The torsion of a bar with an angle section has been calculated. The corner-stress of the angle degreases for the larger opening even for the same radius of curvature of the corner and the same thickness of the angle. The calculation formulas for the torque and the corner-stress for the angles sold on the markets are developed and the results obtained from them are compared with the values obtained from the formulas developed by Trefftz, Timoshenko and Huth.

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In this paper, the general solution of stress of a coil spring which has an arbitrary sectional form is obtained by using the orthogonal curvilinear coordinate system to express the sectional form of coil spring. According to this result, the stress of a coil spring which has a complicated section is easily obtained by using the general solution.

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If the Schwarz's transformation is taken for the mapping function of the stress formula of the coil spring which has an arbitrary section, we can get the stress of the coil spring which has a regular polygonal section. Moreover, expanding the mapping function into infinite series, and picking up the beginning finite terms of series, we can get the mapping function of a regular polygon which has rounded corner. In this paper, taking the polynomial as a mapping function of corner removed regular polygon, we shall analyse the stress of coil spring which has a regular polygonal section.

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A method of calculating the torsional strength of the cylinders having the aerofoil sections was studied. The analysis was carried out in the rectangular co-ordinate system. As the dimentions of the aerofoils are given in rectangular co-ordinate customarily, this method is suitable for practical application. As certain examples the torsional rigidities and the shearing stress distributions of the Clark-Y series propeller section and the symmetrical section with a circular hole were oalculated.

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As far as the author's aware, the problem of the stresses in a semi-infinite strip under the forces applied at its end has scarcely been treated. Previously, however, the problem of a semi-infinite strip subjected to the normal compressive forces at its end was studied rather exhaustively by Prof. S. Higuchi. In this paper, we will treat a problem similar to the problem mentioned above taking shearing forces near the end of strip instead of the normal forces treated by Prof. Higuchi. Solution to this problem is obtained by using the stress function and from the results of numerical calculations of stresses characteristic properties with respect to the distribution of stress were pointed out and discussed.

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This paper treats the problem of the bending of a uniformly loaded circular plate with a clamped boundary which is supported by a single-beam grid formed of two beams intersecting at the center of the plate at right angles and clamped at edges. The deflection of the plate due to the reaction of the grid can be obtained by the Duhamel's method of superposition from the solution for the unit concentrated load. The reaction can be determined by solving an integral equation expressing that the deflections are equal on the grid for the plate and the grid. Hence superposing the deflections due to the reaction of the grid and the uniform load, we obtain the deflection of the plate, and hence stresses.

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In this paper a solution is given for problems of generalized plane stress distributions in a circular plate of radius α, containing k holes of same radius, the centres of which are arranged symmetrically on the circle of radius b. Using a stress function in polar coordinates, the boundary conditions are satisfled. As a particular case of this solution, the problem of the stress distributions in a rotating circular plate containing k holes (their radii bλ) is discussed under the conditions that the periphery of the plate and the edges of holes are free from external forces. Calculations have been carried out for the case b/α=3/7 and tangential stresses along holes are obtained for λ=1/5, 1/3 when two holes, λ=1/5 when 4 and 6 holes.

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In the present paper, as a two dimensional problem of elasticity, the problem of the stress distribution in a hollow ovaloid cylinder is solved under the condition of internal pressure. As an example of the present analysis, first, the values of stresses at any point in a hollow ovaloid cylinder under the condition of locally distributed internal pressure were obtained numerically and, finally, the state of stress at any point in the cylinder was clarified. Thus, the values of stresses obtained here were compared with the results of the photo-elastic investigation on an elliptical chain link due to E. G. Coker and L. N. G. Filon and discussed anew somewhat in detail. As another similar example, the values of stresses at any point in an infinite plate having an ovaloid hole under the same condition of loading mentioned above were obtained numerically and the state of stress etc. at any point in the plate was also clarified.

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The strength of a horizontal reservoir with equidistant supports filled with a liquid is discussed as an example of the strict solution of a cylindrical shell, applying the fundamental differential equation in a single displacement which has been given by the auther. The results are summarized by several approximate formulas for convenience sake of the practical design of the reservoir.

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The object of this paper is to estimate the stress distribution in a roll for a cold rolling mill. The problem of a circular disk under equal and opposite isolated forces balanced by a torque applied at the center has already been discussed by Timoshenko. In the present paper the plane stresses along a concentric circle in a roll are calculated, assuming that the vertical pressure distribution is uniform along the are of contact between a roll and materials, and that the angle of contact is very small (below 4 deg.). Though the pressure distribution upon the surface of contact has been precisely investigated, the results of the assumption of the uniform pressure are supposed not to differ considerably except portions neighbouring tractions.

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In built-up-type rubber vibration isolator, it is well known that the characteristics depend on initial compression, load and exciting force. We have studied the characteristics by varying not only the said three conditions, but also the hardness, using the same form as is now used practically for automobile. The technical points found by this research are as follows : First, the damping coefficient is decided with initial compression and load. Secondly, the larger the exciting force becoms, the larger the coefficient grows. Thirdly, the stiffness depends on initial compression and hardness.

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In order to carry out a complete discussion of forced vibrations in nonlinear systems, it is obviously important to determine stable and unstable regions. This paper is mainly concerned with establishment of the general rule of the stability criterion of forced vibrations, for nearly linear but generalized nonlinear systems. Obtained conclusion is as follows. 1) The boundary lines between a stable and an unstable region are given by the loci of the vertical tangent of the response curve. 2) The region in which -[numerical formula]<0 is stable, and -[numerical formula]>0 is unstable, where α is an amplitude of forced vibration, -ψ₂ is the positve or negative damping force.

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