In this study, the stress distributions in a rectangular plate of elastic material are obtained, in the case where two opposite edges are compressed by rough rigid planes in such a way that there are uniform normal displacements and no trangential displacements while the other two opposite edges are left free. Using a stress function in the form of trigonometric series, the boundary conditions are satisfied. Numerical calculations are carried out for a square plate.

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In 1947 C.B. Ling published a research on the strip with semicircular notches under tension, but his numerical values were shown to be unreliable by several investigators. In this paper the same problem is treated by the method of perturbation, and convenient formulas available when the notches are not large, are introduced. The numerical values of the stress- concentration factor are fully examined with other data, theoretical and experimental, and they are shown to be more reliable than Ling's values. An approximate curve of α for large notches is also proposed as a result of the consideration.

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In this paper, as a paticular case of the present writer's general solution for a problem of generalized plane stress distributions in an infinite plate containing circular holes of varing sizes in any positions under the action of bending moment, a solution for the same problem but containing three circular holes in a row is obtained and discussed in detail using the method of Green's general bi-harmonic analysis and some numerical results respectively. Comparing these results with those obtained for the similar problems for an infinite plate containing (1) a singular hole treated by Dr. Tsuzi and (2) an infinite row of holes reported by the present writer, somewhat clear knowledge with respect to the influence of the presence of holes upon the stresses in a stressed plate etc. are obtained.

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Expressing the distribution of load, on a circular plate with a hole at the center under a concentrated load, by means of δ-function, and performing the integral of particular solution by the property of δ-function, we reduced the differential equation for the bending of the plate to a plane biharmonic equation. Expressing the solution of this biharmonic equation and boundary conditions by Fourier series and comparing the coefficients of both sides of the equations, we derived the exact solution of the deflection for the following cases ; (i) Both boundaries are clamped, (ii) One boundary is clamped and the other is free supported, (iii) Both boundaries are free supported, (iv) One boundary is clamped and the other is a free edge, (v) One boundary is free supported and the other is a free edge.

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[in Japanese]

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Some examples of the center of twist are reconsidered, and the exact solutions are settled by the new expressions. For the sector of circular tube with outer radius a [numerical formula] Where is ε is the distance of the center of twist from the center of circle, 2β is the angle of sector and x is the ratio of the inner radius to the outer radius. For the angle with equal legs [numerical formula] where t is the distance of the center of twist from the top point of the angle, √(2)a is the length of the leg and b/√(2) is the thickness of the leg. The usual expression for channel section is found to be applicable when the thickness of the web and flange is less than ten percent of the outer width of the channel.

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The equations of equilibrium, expressed in terms of stresses, with those of compatibility are reduced to two-dimensional forms for the present problem. For torsion, they are simplified in two extreme cases where (i) the angle between the helix and the axis of helix is small, and (ii) the angle between the helix and the plane perpendicular to the axis of helix is small. Integrating them, the expressions for stresses are derived in the forms, which contain two arbitrary functions. These arbitrary functions can be determined if the shape of the rod be specified. As an illustration of the procedure, a detailed solution for a coiled helical spring with a circular section is obtained by means of successive approximations, and the stresses on the section are discussed.

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We obtained the general expressions of displacement and stress components on the thermal stress, in terms of stress function, of cylindrical bodies in case of axial symmetry, which are expressed in different forms according to the steadiness and non-steadiness of the temperature. Several problems have been solved in terms of examples and the conclusions found are as follows : an usual solution in case of circular disc has been proved to be incorrect (Udoguchi's solution is correct as long as the temperature is steady) and, moreover, the exact solution in case of heating up gives an instantaneous maximum stress which is greater than the stress at steady state and sometimes amounts to several times as large a stress as that at steady state. This explains the danger of failure of a disc at sudden heating up.

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In the present paper, as a two dimensional problem of elasticity, the problem of the stress distribution in a thick cylinder having a regular-polygonal hole the corners of which are rounded is solved under the condition of internal pressure. As an example of the present analysis, the value of stresses at any point in a thick cylinder having a square hole the corners of which are slightly rounded were numerically obtained and the state of stress distribution in it was clarified. And these values of stresses were compared with the results obtained for the case of an infinite plate having a similar hole in it and discussed somewhat in detail.

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The Love-Meissner Theory is applied to the circular ring shells, which are submitted to the action of uniform normal pressure. The solutions of the bacic equations are worked out in a form of power series. The deformation represented by the solution of the first kind is symmetrical with respect to the circumferential line of the utmost parallel circle and the one by the solution of the second kind is symmetrical with respect to the plane involving the above circle. Some numerical calculations have been performed.

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This paper is concerned with the stress calculation of pressure vessels, which are made up by connecting spherical-, toroidal-and cylindrical shells. Love-Meissner's theory is applied to these shells. The equations of connection of such shells may be obtained by assuming the continuity of the angular displacement 〓, radial displacement κ, meridional stress resultant N_ψand meridional stress couple M_ψat the junction. Some numerical calculations are given.

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In the case of the above theme, several special cases are only solved by difference equation. In the case that the plate is compressed by equal pressure, the differential equation (1) (or (5)) of the deflection surface of the plate is solved exactly by using the deflection form of Eq.(9). For the general case as shown in Fig.1, differential equation (1) (or (4)) is solved by Galerkin's method (cf. Eq. (13)) using the deflection form as Eq. (12). The results are shown in Table 1, 2 ; Fig 4, 6, 7 ; and Eq. (23). The full lines in Fig.4, 6 and 7 are curves calculated by four terms w₂₁, w₃₁, w₄₁ and w₄₂ in Eq. (12) ; and broken lines are correction curves expected when more terms than w₂₁, w₃₁, w₃₂ and w₄₁ are used.

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In this report, the buckling problem of rectangular plates under loads distributed uniformly over a certain range of the two opposite edges is solved by using Timoshenko's method. For the Boundary conditions of the plate, four different cases are considered, namely, (1) all four edges are simply supported, (2) the loaded edges are simply supported and the others are clamped, (3) the loaded edges are clamped and the others are simply supported, (4) all four edges are clamped. Numerical calculations concerning the buckling load are carried out for various values of the breadth of the load and the ratio of the two sides of the plate. The results thus obtained are graphed and discussed in detail.

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In this report, the buckling problem of rectangular plates under loads distributed uniformly along a certain range of the two opposite edges is solved by using the so-called integration method. For the boundary conditions of the plate, the following three cases are considered, namely, the loaded edges are simply supported and the others are simply supported, clamped or free. Of these, the former two cases have been treated in the previous report, and it is ascertained that the results in each case are in good coincidence. Numerical calculations for the buckling load are carried out and results thus obtained are graphed and discussed.

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The strength of a shaft with keyways decreases considerably owing to the stress concentration at the bottoms of the grooves, when the shaft is subjected to reversal of stresses. While the endurance limit of a metal increases perceptively by suitable cold working. Accordingly, the decrease of the endurance limit due to stress concentration may be diminished, when the material at the bottoms of grooves is improved by cold working. Torsional fatigue tests have been done with this idea. The specimens used are somwhat different from serrated shafts of practical use and are those of diameter 16mm with two longitudinal grooves of 3mm depth, situated at symmetrical position. The bottoms of grooves were compressed by two rollers with the contours of the groove at their peripheries. Tests were done for two carbon steels of 0.29%C and 0.89%C, respectively. The results show that the torsional endurance limits for specimens of these metals increase in every case by about 30% due to suitable rolling at the bottoms of grooves.

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As the outer parts of a hot roll for sheat iron are subjected to repeated heating and cooling by the intermittent passages of hot materials, there arise numerous small cracks on its surface. In this research, we considered theoretically the mechanism of occurrence of these cracks and studied the necessary characters of the material of this roll in order to prevent these cracking. From the data of rolling operations we calculated the temperature variations of the outer parts of the roll, and by the method of graphical solution we analysed the stresses on the roll surface, and examined the influences of roll material upon the stresses.

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This paper presents an idea concerning the mechanism of the development of fatigue crack in bending fatigue tests. Basing on this idea the effect of the forms and dimenions of the cross section of specimens on the number of repetitions of stress in the interval between initiation of crack and fracture is calculated. Also the aspect of the development of fatigue crack with the stress repetitions is cleared. Comparing the calculated results in this paper with the experimental results made by the other investigators, good agreement has been obtained.

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The mechanism of annealing for residual stress-relieving was studied from the view point of theory of weld stresses and creep. H-type specimens as shown in fig.1 were annealed after welding and the residual stress before and after annealing were compared. Theory of annealing for stress-relieving was developed with the results of tesile creep tests and theoretical values of stress relieved were compared with experimental ones.

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This paper presents some test data on the fatigue strength of 12mm test specimens made of various materials to find how fatigue strength in rotating bending is reduced by the presence of shrink-fitted member, and how such a shrink-fitted shaft may be made stronger by induction hardening. From the test results following facts were revealed. (1) The fatigue limit of shrink-fitted shaft does not increase in proportion to the tensile strength, and the fatigue limit of the materials of high tensile strength such as Ni-Cr steel largeness of lowering ratio of the fatigue limit in the former case. So not a remarkable effect can be expected. (2) By induction hardening, the fatigue limit of shrink-fitted shaft made of middle carbon steel (C 0.4%) increases up to about 2, 3 times, and becomes stronger than the shaft made of Ni-Cr steel or of 0.5% carbon steel induction hardened. (3) From these investigations, it is preferable to use the medium carbon steel (C 0.4%) for the shrink-fitted shaft in actual machine parts, since the weakening effect on fatigue strength caused by shrink-fitted member is comparably small, and the increasing effect due to induction hardening is considerably large, and moreover the cost becomes cheaper. Additional data are presented to show how fatigue stength of pre-fatigued shaft is increased by induction hardening, and how hardness of shrink-fitted member influences on the fatigue stength of the shaft.

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The study of the forced vibration of non-linear characteristic has so far been restricted to the system of one degree of freedom It is indeed typical of the non-linear vibration that the computation becomes very complicated as the degrees of freedom is increased. In the present paper, the graphical method is obtained to find the periodic solution of the forced vibration of a system of two degrees of freedom with a symmetrical or non-symmetrical non-linear restoring force, and the satisfactory coincidence between the results of experiment and the calculation is reported.

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As to the vibrometer utilizing inductance change for displacement-measuring, about which report was made previously by one of the present authors, the greatest disadvantage is the instability of oscillation in the oscillator-circuit. In order to overcome the difficulty, researches were made from various angles and it was found out that by placing all the parts of the vacuum tube oscillator in the vibrometer, the oscillation was made quite stable and also the remote measuring was made possible.

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In this paper, the apparatus for measuring Young's modulus, the effect of holding, and results under various states of specimens are discribed. To obtain Young's modulus by vibration method is one of the best ways in many cases, for its accuracy and simple operation. But by lateral viblation of cantilever, the holding of the specimen is a important subject. The specimen has a small round section, and its one end is held by the holder. The vibration is generated electrically by a low frency oscillator, and transformed into mechanical vibration, therefore, the frequency and the amplitude of the forced vibration are varied easily. Using the apparatus, the author studied the effects of holding pressure and the dimension of the specimen etc, and obtained the error caused by holding is less than the error caused by the other effects. The relation between the maximum amplitude and the natural frequency when the specimen resonates, and the stress caused by vibration are theorically annalysed or experimentally studied.

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There is no method of conversion or comparison between Brinell hardness numbers which are obtained by different steel ball and different load respectively but they satisfying a special condition. In this report, using relations obtained in the former report, the relation to convert between Brinell hardness numbers obtained in all conditions was introduced, which was testified by previous experimental results. To convert the hardness number H₁ (the depth of indentation is h₁) or H₁' (the depth of indentation h₁') obtained by a steel ball of radius R₁ and load P₁ and P₁' respectively, to the hardness number H₂ which will be obtained with a steel ball of radius R₂ and load P₂, the conversion equation was given as following : where, [numerical formula]

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