In recent papers an analysis was given of the distribution of stress in a thick elastic plate of infinite length on the smooth rigid boundary, loaded with the external pressure on a part of the plane boudary, the remainder of the plane being free. This paper is to find an approximate solution for the plane stress problem caused by a normal load on free surface of a large thick plate in tight contact with rigid foundation. This problem is complicated too much, but a solution can be obtained by properly using an approximate calculation with the aid of the Fourier integral transformation. The significance of the stress distribution that is across the contact area and interior part of the plate is discussed. As an example, the contours of the maximum shearing stress τ max are shown.

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Flat bar specimens of Epoxy Resin with two U notches of identical shape on one edge were subjected to pure bending. The effects of the pitch of two notches, the notch depth and also the root radius on the stress concentration factors were investigated. As to the effect of the pitch, the stress concentration factor of two notches decreased first owing to the overlapping effect, and then showed an increase up to the value of a single notch. With respect to the effects of the notch depth and the root radius, the stress concentration factor of two notches showed a similar change to that of a single notch. In all cases examined, the stress concentration factors of two notches obtained were smaller than those of a single notch. This fact offers a possibility of reducing the stress concentration due to a single notch by a supplementary notch formed in its neighbourhood.

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No definite analysis has not been undertaken yet regarding the strength of an elliptical plate, provided with a circular hole and subjected to uniformly-distributed load. For the purpose of clarifying this problem, the authors picked up an elliptical plate rigidly fixed in its periphery and having a circular hole, the center of which is positioned on the major axis of ellipse, but eccentrically with respect to the minor one. As a result of the experimental analysis on the above specimen, the following were clarified and moreover the calculating formulae in simple and practical form were deduced. (1) The maximum stress is observed at the inner fixing end of the maximum span along the major axis of ellipse. (2) The maximum deflection is observed at the portion slightly closer to the inner fixing end from the center of the above mentioned span. (3) The calculated values closely coincide with the theoretical values.

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This paper deals with the summary of the results of rotating-bending fatigue tests on shafts 10 to 100 mm in diameter of medium carbon steel of 0.39% carbon content. Shafts were tested under a concentrated stress, as represented by both shrink-fitted member and fillet. Shrink-fitted specimen hardened by induction-hardening exhibited large size effect as well as untreated shrink-fitted specimen ; the reudction ratio 1.8 was obtained by comparing the endurance limit for shrink-fitted specimen 10 mm in diameter with that of the 100 mm in diameter and the value 1.6 was obtained for induction-hardened shrink-fitted specimens. The enduramce limit of large shrink-fitted specimen as well as small one was increased by 1.8∼2.1 times by induction-hardening. The stress distribution of shrink-fitted specimens with fillet was studied by the photo-elastic method and was investigated the critical ratio between the diameters of fillet specimen, in which the stress at the end of shrink-fitted part is equal to that of fillet part. By using this critical ratio between the diameters was given a practical expedience for increasing the fatigue strength of shrink-fitted specimen with fillet.

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The causes of type A, C' and D deflections in five basic deflections which are observed in the heat indication test of steam turbine shafts were clarified experimentally, using a model apparatus of heat indication test shown in the 1st reports. These types of deflection have their origin in the asymmetric thermal emissivity of rotor surface, which includes the following items : (1) Dust or contamination due to cutting oil, mud, paint and others in manufacturing processes of rotors. (2) Conditions of scale before the test, of growth of scale and de-scaling during the test. (3) Roughness along the rotor surface (considering the vibration mark of cutting tool). There two kinds of asymmetry of surface thermal blackness, one is improved and the other one is hardly improved by short-time tempering or by heating during the test. It is found that type A, C' and D deflections have no difference in the cause of occurrence only excepting their stage of appearence during the test.

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In the heat indication tests, high pressure and medium pressure steam turbine rotor forgings have shown more frequently type A, C' and D deflections compared with low pressure ones. This phenomenon has hitherto been ascribable to the metallurgical properties as these forgings contain some special and carbide-forming alloy elements. In the present experiment, however, it has been clarified by using the heat indication model test apparatus that the one of the causes of the aforesaid phenomenon is the diversity of geometrical shape among the forgings. Additional experiments have shown the effect of : 1. The rates of heating and cooling at the test thermal cycles, 2. Some characteristics of furnace for heat indication test. Thus type A, C' and D deflections can disappear in a certain manner without re-heat-treatment. This is an important fact which suggests that these three deflections do not occure due to the metallurgical properties of forgings.

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There are several formulas for assuming the ultimate strength of thick walled cylinders abjected to internal pressure. To verify these formulas, pressure tests for thick walled cylinders made of mild steel, semi-hardened steel, 13 per cent Cr steel and 18Cr-8Ni stainless steel respectively were conducted. The experimental results were shown to be in approximate agreement with the ultimate pressure of the cylinders computed by Manning's theory. Manning's method is, however, so complicated and cumbersome that we used our particular method, which is simpler than Manning's method. Experimental formulas : P_B/σ_B=0.970 log_s K for cylinders made of mild steel, semi-hardened steel and 13 per cent Cr steel, respectively. P_B/σ_B=0.796 log_s K for cylinders made of 18Cr-8Ni stainless steel. Additional tests : we tested cylinders which had eccentric bores, and compared these results with those of normal cylinders.

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The vibrations in the plane and in the direction perpendicularly to the plane of rectangular frame work are discussed, of which both opposite bars are of same dimensions and of same materials, respectively. There is used such method that, from variation calculus to Lagrangian represented with displacements and unknown boundary values of each bar, the displacements are represented by unknown boundary values, and again, from the condition to make Lagrangian minimum, the unknown boundary values are determined and the frequency equations and the modes of vibrations are obtained. In the case of the vibrations of rectangular frame work, there are 24 boundary values in which 12 are represented by other 12 using the conditions of continuity at each vertex of rectangular frame work that the joints are rigid, for both vibrations in the plane and in the direction perpendicularly to the plane of rectangle, where in the former case the longitudinal and lateral vibrations and in the latter, the twisting and lateral ones are considered. There are three modes of vibrations in both cases, that is, symmetric and antisymmetric vibrations of all four bars, and symmetric vibration of a pair of bars and antisymmetric of other pair. It is, also, shown that the centre of gravity does not move in the vibrations which satisfy the frequency equations and modes obtained in this paper. Numerical calculations are carried out and the comparison are made among the results of calculations, experimental data and results by Rayleigh method.

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In order to investigate the effect of speed of stress reversal on the endurance limit, and to reduce the time needed for fatigue test, a high speed pneumatic fatigue testing machine has been developed. High-frequency siren (air-interrupter) type exciter is used as a reversed plane bending type testing machine for the frequency range of 3 to 20 kc/s. Specimen is a uniform bar of the rectangular cross section, vibrating in the first free-free mode, and is supported by steel wires at the nodal points. Tests were made on normalised 0.36 % carbon steel at frequencies up to 18 kc/s. In order to compare the endurance limit at high speed with that at ordinary speed, the same material was tested by ordinary plane bending machine and rotary bending machine. The endurance limit has a tendency of increase with the increase of reversal speed, and the one at 18 kc/s was about 68% higher than that at the ordinary speed.

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In a theoretical consideration of the Rockwell hardness, the value of elastic recovery of indentation depth which occurs on removal of major load, becomes an important problem. The effects of shape of anvil, and elastic deformation of a frame and an indentor of a testing machine were examined. The true value of elastic recovery of indentation depth could be derived experimentally from the apparent readings of elastic recovery of the testing machine. Experimental results of elastic recovery of indentation depth agreed with the theoretical value calculated by the Hertz's equation. Therefore it may be considered that the elastic recovery of indentation in the case of Rockwell hardness testing is an identical phenomenon of elastic contact expressed by the Hertz's equation. The elastic recovery of indentation depth becomes larger when the major loads is larger, the diameter of the steel ball indentor is smaller, the testing specimen is harder and the Young's modulus of the specimen is smaller. The proportion of the elastic recovery to the total depth of indentation under major load becomes larger when the major load is smaller, the diameter of the steel ball indentor is larger, the testing specimen is harder and the Young's modulus of specimen is smaller.

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The present problem is to construct the operation of controller generating the control signal which will switch the on-off relay in such a way that the mean square error becomes minimum. First, when the input to the system is a random with Gaussian amplitude probability distribution and the control signal is of some non-linear function of the error and its derivative, the general procedure of analysis for the evaluation of statistical behaviors of error signal is described. Second, the improvement of the control performance by introducing a predictor is proposed. Principal purpose of this paper is to evaluate how the optimum prediction time depends upon such important variables as (a) the value of system time constant and (b) the variance of random input signal. Finally, statistical evaluations of the response of such predictor-relay servo system are carried out and the improvement of the control performance is quantitatively shown.

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In this paper, the discrepancy from the normal distribution of the response of nonlinear control systems excited by a stationary Gaussian signal is quantitatively discussed by evaluating the skewness, β₁, and the kurtosis, β₂, for the probability distribution of response. The approach is carried out by introducing the theory of a Markov process and solving the Fokker-Planck equation. Nonlinear characteristic considered here is a symmetric one. The discussion is, therefore, directed to the evaluation of the kurtosis, β₂, as function of the various values of nonlinearity. The remainder of this paper is devoted to justify the previous consideration as already presented by the authors that the response has the same amplitude distribution function as the system input. For this purpose, a new quantity, the confidence, is defined. As a result, the dependency of nonlin-earity in the system on the probability distribution of response is obtained and the confidence that the probability distribution function can be regarded as the normal one is also evaluated by numerical computations.

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The principal purpose of this paper is to evaluate how the probability distribution of the response of a nonlinear control system subjected to a Gaussian random signal depends on such nonlinear characteristics in the system as clipping level, gradient and continuity in derivatives of the characteristic. For this purpose, three types of nonlinear characteristics, definite peak clipper (saturated characteristic) relay and smooth limiter, are treated. As we already presented in the earlier paper, the probability distribution of the response becomes non-Gaussian. The same procedure can also be used here in order to evaluate the response probability distribution. The results are shown by the curves, giving the relation between magnitude of response and probability density function or cumulative distribution function. By using these results, the variance of response in the system is calculated and the justification of appling the classical equivalent linearization technique is quantitatively checked.

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