The authors have studied on the stress concentration at the reentrant corner of triangular rib under pure bending by the two dimensional photoelastic method. Further experiment has been made on the triangular rib, the apex of which was cut off, and the change or the stress concentration (s.c.f.) at the reentrant corner aue to the amount or cutting the apex off has been examined. The results obtained are as follows : 1) The s.c.f. decreases with the increasing of the rib size, but no appreciable reduction of s.c.f. can be recognized when the rib size exceeds a cirtain value. 2) The value of s.c.f. and the rate of its increase become larger with the fillet radius. 3) When the apex of the triangular rib is cut off, the s.c.f. at the reentrant corner becomes smaller than the s.c.f. for the triangular rib and increases with the increase of the amount to be cut off.

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The exact solution of the stress distributions in chain links loaded by two concentrated forces has not been presented. Stresses in chain links are always analysed approximately by means of "Theory of beams". In the present paper, the stresses in a two-dimensional chain link are analysed by using the mapping function[numerical formula] In additon, the stresses in a simple chain link with a uniform and rectangular cross-section are obtained by the formulas based on "Theory of beams". The former results are compared with the latter ones. In each case, the tangential stresses on the free boundary are measured by the photo-elastic method. When the theoretical results in the former analysis are compared with experimental ones, there is a good agreement between them, but the theoretical results in the latter analysis are slightly different from the experimental ones.

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In this paper a solution has been given for the problem of generalized plane stress in an infinite plate under the two concentrated forces in the vicinity of the separated, the intersected or the contacted two circular holes The bipolar or the crowded circular coordinates were used in the solution, and the basic stress functions were expanded in the Fourier series or integrals by means of parallel movements of the complex coordinates. A complete stress function in the plates with the holes was established in a form, in which a basic stress function was added to the auxiliary ones. The calculations have been carried out for the stress distributions and the rates of stress concentration.

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The present paper deals with the buckling problem of a clamped equilateral triangular plate under uniform compression after the method adopted by G.I. Taylor when he obtained the buckling load of a clamped square plate. The buckling loads are calculated for each case of symmetrical and antisymmetrical buckling of a clamped equilateral triangular plate and, as an application of the problem, buckling of a clamped triangular plate having inner angles of 30, 60, and 90 degrees respectively. The numerical calculation is carried out in a few orders of approximation. The critical values obtained are shown in the table together with those obtained by the Ritz method.

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In the preceding reports, we solved numerically the plane stresses when the Belt has a rectangular projection on one side. But, it is much labourious and takes fairly long time to calculate numerically such problems in large number, for the convergence of the series is not so favourable. So, in this report, to accomplish the numerical calculation, we have an experimental study how 2k, h and ρ exert the influence upon the stress concentration of the edge stress. (2k, h : the breadth and height of the rectangular projection, ρ : the radius of the curvature of the root) In consequence, we find out the stress concentration factor is proportional to √(a/ρ) and k/a, and hardly depends on h/a, when h/a is more than about 0.4.

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In the preceding reports, we solved numerically and experimentally the plane stresses when the belt has a recutangular projection on one side. In this report, we calculate numerically for the cross-shaped plate by the same method as the preceding reports and find out the magnitude of the stress concentration of the edge stress for the various radius of curvature of the root in the cross-shaped plate. In consequence ; the stress concentration factor is proportional to √(a/ρ)= (a : half breadth of the plate, ρ : radius of the curvature of the root) and the stress concentration occurs at the point of constant ratio for various radius.

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In this report, we make numerical calculation and conduct an experiment by the photoelasticitv-photograph and wire strain meter when the belt has the rectangular projections and makes the steps on both sides same as in the preceding reports. In consequence, when the height of the rectagular projections or of the steps h, the breadth of the rectangular projections is 2k and the radius of the curvature or their roots is ρ for the breadth of the belt a, we find out the stress concentration factor is proportional to √( a/ρ) and k/a, and hardly depends on h/a when h/a is more than 0.4 same as in the preceding reports.

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In order to obtain the practical design data for a pressure vessel having an elliptical shellplate, the authors examined the effects of the shellplate length on the stress and deformation distributions using several model vessels. As the results the following matters have been made clear : (1) The stresses in an elliptical shell are, far from those of cylindrical one, affected by its length to much extent.(2) The stresses in the cross section at longitudinal vessel center, being most sensitive to the effect of the length, are extremely larger than those in the shellend-part for a long-shell vessel. But in the case of a short-shell vessel the latter sometimes become larger than the former.(3) In a vessel having nearly-cylindrical shell, the supporting effect due to the end plate connection is much more influencial comparing with one having a shallow-elliptical shell.

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In the conventional method of the fatigue test, the accuracy of the endurance limit cannot be estimated. On the other hand the statistical methods represented by the probit method, the staircase method and so on require large number of test pieces. In the previous report the fatigue test by staircase method with small samples was presented. However it was assumed that the standard deviation σ of the endurance limit is known, and the accuracy of the endurance limit was not thoroughly discussed. This report treats the case in which σ is unknown. Since the size of the step in the staircase method must be approximately equal to σ, it is necessary to find σ. The fatigue test is performed in the neighborhood where the S-log N curve is represented approximately by the straight line having a negative slope. The experimental results are plotted in the S-log N diagram, and the regression analysis is applied to find σ. This method is presented and thebasic assumptions are considered. The methods of calculating the confidence limit of the mean value and the tolerane limit of the endurance limit are discussed. "The tolerance limit" corresponds to "the lower limit of the endurance limit", and it is defined from the statistical point of view. At the end of this report these methods are applied to some experimental examples.

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As a continuation of previous investigation concerned with fatigue of steel, the fatigue process in cast iron and cast steel is studied by observing the half-value breadth of intensity distribution curves taken from X-ray diffraction lines. X-ray photographs were taken at several stages of fatigued specimens subjected to rotary bending. It is found that the fatigue process of cast iron and cast steel is similar to that of steel from the stand point of the change of half-value breadth. Results conducted are as follows : (1) As pointed out in the previous papers, on a view of the half-value breadth variation during stress repetition, it is considered that the fatigue process consists of the three sequent stages, that is, (a) A stage in which the half-value breadth changes markedly with stress cycles (the first stage of fatigue)-in the process, the work hardening is considered to occur.(b) A stage in which the half-value breadth changes steadily with stress cycles (the secondary stage of fatigue)-the fatigue fine cracks are intiated and grow by the micro-stress concentration around micro-cracks due to stress cycles.(c) A stage in which the half-value breadth steeply varies until fracture occurs (the tertiary stage of fatigue)-in the process it is considered that the visible cracks, which lead to fracture, are initiated.(2) At the end of the secondary stage of fatigue the half-value breadth has a constant value irrespective of the magnitude of alternate stresses.(3) The relation between b/B and log n/N, where b and B are the current and the initial value of half-value breadth and n and N are the current and ultimate number of stress cycles respectively, is represented by a straight line irrespective of magnitude of alternate stress applied. This relation offers the possibilty of the non-destructive prediction of fatigue life.

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The deformation and thermal stress for a rectangular plate, subjected to an arbitrary symmetrical temperature distribution, are analyzed for the case where the edges of the plate are simply supported, taking the finite deformation into account. The fundamental non-linear simultaneous partial differential equations for the thermoelastic problem are derived from the variational principle and are solved, and it is shown that, if there exists a temperature gradient through the thickness of the plate as seen in the aerodynamic heating, the plate starts to deflect at the moment of heating and does not exhibit the buckling phenomenon according to the mode of temperature distribution and the boundary conditions. Some numerical examples are given i) for the case where the temperature distribution through the thickness is specified as linear, and ii) for the case of instantaneous heating where the temperature distribution through the thickness is a function of time, and then some discussions on the analytical results are given.

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The causes of deflections of turbine rotor forgings at the heat indication test were studied experimentally. Using a model apparatus of heat indication test, the deflections of type A, B, C and D as well as a deflection of type C' newly proposed by the authors were presented. It was confirmed that the tangential non-uniformity in heat treatment could be a direct cause for the origination of type B and C deflections in rotor forgings. It was found, futher, that the deflections of types A, C' and D, which were reproduced in model rotors having had no deflections when their surface uniformly treated in some ways, could be referred to the asymmetric thermal emissivity of surfaces. (It is known that there are two kinds of the tangential non-uniform thermal emissivity, i.e., one capable of improvement by a short time tempering and the other which scarcely admits the improvement.) Thus, it could be said that the heat indication test primarily intended for the inspection of metallurgical quality of rotor forgings has been utilized, for the most part, for the examination of surface condition. The authors wish to draw much attention to this point, with particular remarks to the view that the type D deflection is one of the surface phenomena and with the proposal of type C' deflection as well. The study of the origin of each deflection and the experiments with real rotor forgings demonstrated for confirming the conclusion derived from the model test results will be presented later in the coming paper.

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The behavior of the stress and strain in the thermal fatigue of 18-8 Cb stainless steel is analysed and as a result, some of its theoretical information are obtained. The experimental observations, which the auther has reported already, are compared with the theoretical results and it is known that some of them can be explained satisfactorily from the theoretical view point.

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The lengths of the cracks formed by the corrosion fatigue in saline are studied on the smooth specimens of a carbon steel, and the effect of corrosion fatigue on the low temperature brittleness is discussed. The cracks occur at early stage of the fatigue life and the cyclic rates of their propagation dl/dN depend on the actual stress σ_ck repeated at the root of the crack, where k represents the notch effect of corrosion pits increasing with time. The transition temperature T_r °C. of the specimens having the cracks caused by corrosion fatigue and the rate of its change with cycle ΔT_r/ΔN rise with increasing of cyclic ratio. It also rises according to the increase of square root of crack length l^1/2, having no relation to the nominal stress σ_c of the corrosion fatigue.

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The atmospheric effect on the frequency effect was studied in high temperature fatigue of a carbon steel by using dried town gas as an inert environment. At 550°C, the fatigue strength was higher in gas than in air for long life test under low stress levels owing to the reduction of corrosion fatigue effects by high temperature oxidation. At 400°C, the effect of gas was hardly found on fatigue strengths. Considerations were made on the frequency effect in stress τ-rupture time t curves and in plastic strain amplitude γ_p-cycles to rupture N curves. The relation of γ_pN^0.44=K was carried under various cyclic frequencies and various temperatures, covering over wide range of N. The value of K was larger for lower frequency than for higher frequency, the effect of frecquency increasing at higher temperature. The deviation was found after long time in the air, due to corrosion fatigue by high temperature oxidation.

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A special apparatus was constructed for tests of the wear on plastics, the essential part of which is a metal rod vibrating at a high frequency (18.3 kc). Certain experiments were carried out in the range from 140 to 560 g of the pressure of contact and from 25 to 75 μ of the amplitude of vibration. The amount of wear can be measured at any time of the duration of experiments. Polyethylene, Nylon-6 and Poly-vinyl-chloride were tested. Effects of load, amplitude, irradiation of γ-ray and other factors upon the wear are investigated. Speculation on the mechanism of wear for the results is done with help of the microscopic observation on sliding surfaces.

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The end effect of a coil spring is analysed from the standpoint of perturbation as that on a three dimensionally curved slender beam which forms a coil spring with a constant pitch angle. The variation of the twisting moment or shearing stresses along the axis of wire becomes large in any numbers of turn near the both ends. The maximum shearing stresses are illustrated in terms of the number of turns of coil springs so as to be convinced to designing.

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Free vibrations of coil springs are investigated as those of three dimensionally curved slender beams which form coil springs with constant pitch angle. Vibrations of coil springs, it has become clear, can be regarded as longitudinal vibrations of straight bars only in cases the pitch angle is very small, the ratio to the radius of wire and coil is small, and the spring has many numbers of turn. Morever, we introduced the exact frequency equations and modes as the vibrations of circular rings in the same manner as Waltking.

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First, in case of no damping, the forced vibrations of coil springs under periodical excitation of the lift of the cam have been analytically studied, and the amplitude and resonance frequency made clear. Secondly, the maximum amplitude and shearing stress of vibration resonant with the j th harmonics of the cam are shown by B=2δ_j/c, τ_dy=τ₀(2π/c). Where B : the amplitude in the center of the spring. δ_j : the j th harmonics of the cam. τ_dy : the shearing stress of surging at the end of the spring. τ₀ : the static stress due to δ_j. c : the logarithmic decrement. Next, we have measured the logarithmic decrement in which case c was 0.07∼0.02.

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In the previous papers the authors dealt with the axial harmonic vibrations and the subharmonic vibrations of the order one-half caused by the passing balls. In these papers the stability of the axial motion and the amplitudes of the steady state were discussed in the linear region of the axial spring characteristic. But for the large amplitudes of the axial vibrations the nonlinear phenomena appear. In the present paper, firstly, the nonlinear characteristic in the axial direction of a ball bearing is analyzed and the analytical results have been found in good agreement with the experimental ones. Secondly, the amplitudes of the steady motion at the rotational angular speeds nearly equal to the natural circular frequency of the system are ana1yzed. The various typical response curves calculated from the analysis are compared with those obtained from the experiments. As a result, the nonlinear vibratory phenomena caused by a ball bearing were clarified.

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We studied the load distribution on rivets of the joint, when the rivets line up in the direction of the load. We obtained the load distribution experimentally at first, and then represented it approximately by a difference equation. We compared the numerical calculation of this solution with the experimental result, and found out that this approximate solution gave us sufficiently accurate result. It was also found that, within the elastic limit, most of the loaded rivets in a five-rivet joints were under the load twice the mean value, contrary to the supposition that all the rivets carry equal load.

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