Stress distributions in a rotating spherical shell is strikingly effected by the curvature and the thickness of the shell. A membrane theory which is useful in shell analyses, is not adapted for the shells with small curvature, and in the authers problem not comparable with the general theory of rotating disk. For this reason, the author studied the problem according to the Reissner-Meissner's method, which has led to the hypergeometric equation, and carried out numerical evaluations as to the shells with the free edge and showed that the results approach to the solutions of rotating disk as the curvature decrease and to the solutions in membrane theory as increase.

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In the membrane theory of a shell in form of a surface of revolution, using a relation between the fundamental magnitudes of a surface and by the selection of some suitable variable, it is shown that in general the equ. of stress resultant, the equ. of deformation and the equ. of neutral surface will be reducible to a differential equ. of second order with an invariant R₂³/R₁. Particurally, when the invariant is equal to a constant, the form of shell is a quadrics of revolution, and by this result the general solution of stress and deformation of shell in the form of a quadrics of revtion under an arbitary distributed load is obtained. Furthermore the dispersion of stress under olua concentrated load is analyxed by the method of complex variable.

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In this paper, the torsion or the stretching problem for a spiral rod is treated theoretically. The equations of equilibrium expressed in terms of displacements are reduced to the forms which are independent of one co-ordinate. They are readily integrated for the particular case of small helix angle, and the corresponding displacements and stresses can be expressed in the forms which contain three arbitrary plane harmonic functions, determination of which is depending on the shape of the section. As an application of the general solution, the problem of an elliptic section is solved explicitly. The numerical results are also given.

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In this paper, an attempt is made to clarify the stress distribution in a regular polygon plate subjected to the action of forces in its plane on each side. To get a solution of the problem, we used the Schwarz-Christoffel's conformal transformation. This method of solution was applied to the case of a regular polygon plates under a concentrated force P on the middle of their each side and as the numerical examples, the following three cases were treated. (2) The equilateral triangular and square plates loaded by a concentrated pressure -P on the middle of each side. (2) The square plate loaded by a concentrated pressure -P and tension P on the middle of each side alternately. (3) The square plate loaded by a concentrated pressure -P on the two oppsite sides.

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The object of this paper is to find the stresses and displacements in a short circular cylinder or a disk deformed symmetrically with respect to its axis. The surface tractions are separated into eight cases, each of which is expanded in a series of trigonometric or Bessel functions and the stress system for each case is found and combining these stress systems, the general solution has been obtained. This method is applied to a short circular cylinder, strained by surface tractions, viz., (1) a uniform pressure distributed over the middle zone of the cylindrical surface, (2) a uniform pressure distributed over a circle at the centere of each end-surface.

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In the present paper, the problem on the stress distributions in a plate with a circular hole where a rivet is fittedand pulled, is solved, in the following way. First, the force acting on the rivet hole is assumed as -P (1+cosθ) distributed along the periphery of the hole, and, next, using the method of solution due to Howland, a solution of the problem in question is obtained for the case of an infinite strip, and moreover extending it, an approximate solution of a rectangular plate is finally obtained under the boundary conditions mentioned above. Comparing the results of the present numerical calculations with those of the similar problems treated by many other authors, many important and interesting characteristics about the distributions of stress in a plate are pointed out and discussed somewhat in detail.

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In this paper, the approximate stress distributions of a plate having a hole in which a rivet whose dimension is smaller than that of the hole is driven, are obtained. Using the method of solution due to Howland, and at the same time, that of Bickley in which an infinite plate under the pressure between the rivet and the hole is treated with the idea of the famous Hertz's solution of two bodies in contact, a solution of the problem of an infinite strip under the same boundary condition mentioned above is obtained. Applying the solution thus obtained under the conditions of an infinite plate, an approximate solution of the case considered for a rectangular plate is newly deduced. From the numerical calculations carried cut for the case of rectangular plate, some important and interesting properties implied in the problem are pointed out and discussed.

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The analogies existing between the mathematical formulations of the bending of elastic plates and two dimensional stress problem has been well known, and so it is quite natural that we can apply the analytical methods which have been used in the latter to the former. In this paper the complementary function of the fundamental equation of the bending of isotropic plates is represented by means of the so-called Goursat's stress function. By the use of derived formulae and relations, several fundamental solutions are obtained. As examples, bending of a clamped circular plate under a concentrated load, bending of a simply supported circular plate under a concentrated load, bending of a circular plate under several concentrated loads on the boundary and bending of an infinite plate with an elliptic hole are treated.

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The method of analysis of two dimensional stresses of orthogonally aeolotropic plates has been well formulated and treated by many authors. It seems, however, somewhat laborious. In this paper, the another's method of analysis is attempted by the use of Muschelisvili's theorem which is used in the two dimensional stress analysis of isotropic plates. As examples, (1) an infinite plate with an elliptic hole and subjected to uniform stresses at infinity, (2) an infinite plate with a circular hole and subjected to a concentrated load, and (3) an infinite plate with an elliptic hole and subjected to a pair of concentrated loads on the boundary, are treated.

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If a helical spring is fixed at one end, and subjeded to any force and moment at the other end, the deflection of the spring will be caused. The value of this deflection is necessary for the design of helical spring and calculation of any vibration problem, but its precise solutions have not been hitherto known. Now evaluating the precise expressions of lateral rigidity of helical spring by theory of elasticity, we found them quite appropriate by comparing them with experimental values, and also they are more precise than the values calculated by "Die Federn" published by V.D.I.

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There are two kinds of method to caluculate stress of leaves of the laminated springs. The one assumes that each leaf is centilever, and the other assumes that all leaves are laminated with equal curvature. And it was known by experiments that stress due to load may be calculated by the former and that stress due to nipps by the latter in good accuracy. But at the center of leaves, because the leaves are tightly bound each other by means of center bolts or bands, the curvature of the all leaves may be equal, even if there are no load. Author introduced equation to find stress due to nipps of the laminated springs by the former method, and found that this equation coincide with experimental results better than by the latter method. And besides, with this method, introduced the equation for practical design to find curvature of each leaf with simplified stress caluculation.

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To get a clear knowledge of the condition for yielding of mild steel subjected to the combined action of tension and bending, the authors treated this problem theoretically and experimentally. They carried out the eccentric tension tests of mild steel specimens and compared their results with the theoretical values which were calculated by them. They recognized that the value of yield stress in the conbined case of tension and bending lies between σ_v and 3/2σ_v according to the eccentricity of tensile load where σ_v stands for the yield stress in the simple tension and 3/2σ_v is that of the pure bending which corresponds to the case of infinite eccentricity. The linear relation σ₂=3/2σ_v-1/2σ_t where σ₃ stands for the yield stress and σ_t the mean tensile stress on the cross section, shows to be in good conformity with the condition of yielding in these cases. In the case of the large eccentricity, the first yielding occurs on the surface of tension side of the bar and extends inwards with the load increasing or the development of yielding and accordingly the neutral axis changes its position slightly. But, as soon as both sides of the test piece began to yield, the translation of the neutral axis ceases and the maximum stress in the cross section rises to the value 3/2σ_v. The bending moment keeps constant during the period of both sides yielding. On the contrary, when the eccentricity is relatively small, the compression side disappears from the cross section and though the bending moment takes the value corresponding to the above relation (1) at the begining of yielding, it decreases its value. with the development of yielding and there occurs both sides yielding near the end of yielding.

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The yielding of steel proceeds with successive appearance of flow layers. With this taken into account, the yielding phenomena of bending steel bar has been fully explained by the authors. In the present paper, as another example of the yielding of steel under uneven distribution of stress, the yielding phenomena of a twisting steel bar is discussed. In the first part are exhibited the results of measuring the stress existing in a yielding bar subjected to pure torsion. It leads to the conclusion that the twisted steel bar yields by the same mechanism as that of the yielding of a bent steel beam. Then the problems of elastoplastic torsion are generally treated analytically in the same fashion as the case of bending.

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The yield point of mild steel under the low stretching speed is unstable and shows yield phenomenon of various types. Under the same stretching speed the yield process in which the stress increases gradually from a low stress value progresses slowly, the yield process which begins with a high stress value terminates instantaneously, and the yield process which begins with medium stress value is medium. Therefore the writer considers the so-called upper and lower yield point as the super-saturated state. Thus the lowest saturated yield point is found from many low stretching tension tests, and the mechanism of yield phenomenon is given. This lowest yield value is nearly 60% of the usual lower yield point.

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It happens sometimes that mechanical engineers have to deal with the mechanical behavior of high polymeric substances. In most cases, however, they must reconcile themselves to much qualitative estimation, with all the knowledge of advanced chemistry and chemical physics, because of the different nature of the problems of mechanics from those in the laboratories of chemists and chemical physicists. One of these cases is the evaluation of the residual stress in a molded article of phenol resin, for which it may be necessary to resort to rules-of-thumb in designing molds, as the inherent stress seems to be related definitely to the spontaneous cracking in course of time as well as immediately after taking the article out of the molds. As the first foothold for dealing with more general cases of residual stress, those of bending test specimens are, at in present work, evaluated numerically in accordance with the approximate formula established for this investigation. Preliminary experiments were carried out and Young's moduli at room temperature obtained in relating to the variation of the temperature and the pressing time on molding. Then, the variation of the warping of specimens due to the relaxation of the surface stress by taking off the surface layer of small depth from the specimen was measured. The locked-in stress distribution is naturally characteristic of the cooling rate of the specimen. The results are reproduced in the accompanying diagrams for air-cooled and oil-cooled specimens. Oil cooling causes a steeper gradient of the stress in the neighborhood of the surface than in natural cooling in the air, and the greatest residual stress reaches 200 kg/cm² compression at the edges. In such a state of stress, the apparent modulus of flexure must be 10 per cent higher than that of the naturally cooled case and this the fact was ascertained experimentally.

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In a previous paper, the author reached a consideration that the endurance limit of a material should be determined by the amount of the mean stress in a certain small area around a point, instead of the stress at the point, and the extent of the area was determined for several kind of metals, by using the results of tension-compression fatigue tests. In this paper, the extent of area where the mean value of stress to be taken is determined for a mild steel in another way, viz., by a torsion fatigue test. The extent of the area for mild steel almost agrees with the one obtained in the previous tests, and the conclusion that the extent of area chiefly depends on the kind of metal and is independent of the course of the experiment was reached.

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With round-cracked specimens prepared by making a circumferential crack at the root of a round machined notch, statical bending and tension tests were carried out at room as well as low temperature (about-10°C). Rotary bending fatigue strength was also measured. It was found that, under statical load, considerable plastic deformation takes place at the root of a crack ; that a crack deepens discontinuously ; that statical crack strength increases as the depth of the crack penetration deepens ; that the low temperature annealing (about 600°C) to relieve the residual stress of a member with crack makes its fatigue strength decrease considerably. The conditions of brittle fracture and the factor of stress concentration due to a shallow crack are discussed.

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To clarify the role played by graphite flakes in notch effects of ordinary gray cast iron rotary bending tests with pipes with a radial hole were carried out. It is found that ; the notch-factors are strongly influenced by the dimensions of specimens but so long as the ratio of the radius of radial hole to that of the specimen is small the notch-factors are nearly equal to unity. To explain these phenomena a model showing the action of graphite flakes in relation to machined notch was proposed. Combining the condition that fatigue crack starts at the tips of graphite flakes with this model an expression of notch-factor was obtained which showed good agreement with experimental results. There is an optimus diameter of a hole which will be effectively be drilled at the end of a crack in oder to stop further spreading of that crack.

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The stress distribution being taken into account, the rupture strength of cast iron beams of rectangular section under bending becomes, [numerical formula] where, M_B=bending moment at rupture, b=breadth of the beam, h=height of the beam, nh=distance of the neutral axis from the surface of tension side, and σ_B=tensile strength under uniform stress. From stress-strain curves of compression and tension, the tension curve being somewhat extended, the moment-deflection curve and the rupture moment were calculated. These calculated values conform very closely with experiment.

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The same problems were treated formerly. At that time, however, fatigue under non-uniform stress distribution was not yet clearly understood, and it was considered that the whole stress distribution over the cross section had an effect on fatigue. Now the relation between fatigue and stress distribution is clear, and, in this paper, endurance limit diagrams under bending and under torsion were computed generally. The results of calculation agree very closely with experiments.

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Endurance limits under combincd torsion and bending were computed from the author's hypothesis. The cyclic bending stress being taken in abscissa and cyclic torsional stress in ordinate, the computed endurance limit curve becomes an are of ellipse, and this agrees very closely with experiments.

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The machine parts under rolling contact are often subjected to repeated bending, for example, the shafts supported with balls or rollers without inner races, the rollers of cold rolling mills, the rails, etc. These parts are subjected to repeated bending stress and repeated compressive stress simultaneously. In this paper the authors obtained experimentally the fatigue resistance of the materials under such stress conditions. The materials applied to the experiments were three kinds of steels and the following results were obtained : there is a critical bending stress for each material above its fatigue limit, and when the applied bending stress is greater than the critical stress, the compressive stress due to rolling contact is not injurious for the life of the materials, and when the applied bending stress is smaller than the critical stress, it is very injurious.

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This investigation was carried out to clarify the most suitable conditions of surface rolling for the purpose of increasing the fatigue limit. The materials used were four kinds of carbon steels having 0.2∼0.6% carbon content. The torsional fatigue limit was obtained by endurance tests and the tests due to a rapid method, i.e., the method of measuring temparature-rise. A surface rolling apparatus was designed specially for this investigation. Results obtained are as follows ; 1. The torsional fatigue limit may be increased greatly by surface rolling, and for this purpose it is desirable to roll at 550∼620 kg/mm², (the maximum stress calculated by the hertz formula), and the larger value corresponds to the higher carbon content. 2. The maximum increment of torsional fatigue limit by rolling was about 27% independently of carbon content, but was smaller in heat-treated material. 3. The larger the surface rolling pressure, the larger the hardness of rolled surface, but it becomes nearly a constant value when the rolling pressure exceeds 550∼620 kg/mm². 4. The rolling pressure under which the maximum torsional fatigue limit is obtained coincides with that causing the hardness of surface to approach a constant value.

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In the 1st report, the authors showed the surface rolling conditions for cbtaining them aximum torsional fatigue limit of carbon steel and the hardness of rolled surface. In this report, they carried cut a rotating bending test with rolled specimens and charified the rolling conditions for obtaining the maximum bending fatigue limit. The effect of roller shape, the effect of annealing after rolling, the effect of rolling speed, the decrease of diameter by rolling and the finishing of rolled surface were made clear. The materials used were the same steels as in the previous report and a cast iron. Results cbtained are as follows, 1. The bending fatigue limit of carbon steel and cast iron may be increased greatly by surface rolling, and surface rolling at a suitable rolling pressure, 620∼700 kg/mm² for the former material and 300 kg/mm² for the latter, respectively, will produce the maximum fatigue limit. 2. The increase of bending fatigue limit by surface rolling was about 38% maximum on carbon steels independently of carbon content, and the increase was about 9% on cast iron. 3. Increasing the radius of curvature of roller, the surface rolling pressure producing the maximum fatigue limit becomes smaller, but its decrease is slight. 4. Annealing at low temperature after rolling does not affect the fatigue limit, but if the annealing temperature exceeds 300°C, the fatigue limit decreases. 5. Speed of rolling had no effect on the fatigue limit in the range of 770∼7800 mm/min in circumferential velocity of specimen. 6. Decrease of diameter by surface rolling was made clear. 7. If a smaller feed is adopted, the finishing of rolled surface becomes better, but it attains the best state in the following condition, (Contact width of roller and rolled specimen)/(Feed of roller)≅6 Therefore, a feed less than this need not be chosen.

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In the last paper concerned with the same problem, the authors have reported that the residual stress caused by plastic deformation tends to decrease remarkably by the repeated application of stress exceeding the magnitude of the endulance limit of the material. Machine parts in general, however, are subject to the repeated stress smaller than the endurance limit. The present paper will display the results of experimental study on the variation of the residual stress, being caused by stretching or by bending steel specimens to the range of plasticity, due to the repetition of the stress smaller than the endurance limit. The residual stress was measured by means of X-ray. Thus it has been made clear that, even by the repetition of the stress smaller than the endurance limit, the residual stress decreases with increase of the number of stress repetition. By the repetition of the stress of the magnitude near half of the endurance limit, however, the decreasing rate is extremely small, and therefore, we may assume the variation of residual stress does not occur. Moreover, the authors have found that both tensile and compressive residual stress behave in quite a similar manner under repeated stress.

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In designing machine parts and structures, the time-strength often comes into question. The authors made many fatigue tests on specimens of steel and cast iron under repeated tension, and obtained their S-N diagrams. Then the authors came to the conclusion, that (1) the S-N diagram of cast iron, both in logarithmic scale, consists of the two straight lines, i.e., a horizontal line which represents the endurance limit and a straight line, the value of which at N=1 is equal to the tensile strength, (2) the S-N diagram of steel, both in lograrithmic scale, consists of three straight lines, i.e., a horizontal line which represents the endurance limit, another straight line which represents the tensile strength, and a sloped straight line, the extent of which at N=1 is equal to the true breaking strength.

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This paper gives some results of experiments on indentation hardness, which were carried out under especially light loads. The contents of these results a redivided into the following two parts. One represents the hardness obtained by the measurment of the depth of indentation and the other is of that obtained by the measurement of the diameter of indentation. From these results, it may be said that the hardness number takes under light load compression a value considerably smaller than that of ordinary load compression and the formula P=ah+bhⁿ assumed by the auther may be applicable in such a case since it coincides closely with the experimental data. The value of index n in the above formula is, in all cases, less than 2 and may be taken ⪈3/2 for light load.

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In this paper, the author intends to describe the results of experiments regarding indentation hardness. These tests were carried out under load smaller than that in the case of the previous report. The depth of indentation was measured by using the method of Newton's ring. The range of load is as follows ; i.e. P/D²=0.006-0.202 kg/mm² where P is the load applied and D the diameter of the ball used as the indenting tool. The author recognized in the present experiments that the hardness number based on the depth of indentation, as the measure of which the permanent displacement was adopted, took, on the contrarya, tendency of increasing with the decreasing of load in the range of considerably light load. The relation between the hardness and the depth of indentation in these cases is expressed as the results of the theoretical consideration by H=q₀+q₁h²+q₂h^-1. where H stands for the hardness number, h the depth of the permanent indentation and q₀, q₁ and q₂ are all constant depending on the nature of materials. Experimental data showed a fairly good coincidence with this expression.

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The author presents the following expression as a new proposition for indentation hardness ; i.e. [numerical formula] in which H_N represents the new hardness number, σ the compressive stress, ε the total and ε_p the permanent strain. He investigated theoretically the relation between this new hardness number and the wide-spread indentation hardnesses which would be obtained by using any one of the indenting tools suchas a ball, a cone, or a prism, etc., and deduced an expression which gives a relation between hardnesses. As an example, he carried out both the compression and hardness tests for copper, mild steel and special steel specimens and compared those results with the above formula. Let H_B be a hardness number obtained by ball compression and H_p that due to a prismatic indenting tool, then the formula connecting these hardnesses will be expressed as [numerical formula] where [numerical formula] and λ, λ' are constant depending on one or both of characteristic of materials and angle of prismatic indenting tool.

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In this paper the influence of the holding force on the deep drawing cylindrical shell is investigated both experimentally and theoretically. In experiment the holding force was kept constant during each drawing operation and sheet copper 0.46 mm thickness was treated. The experiment was made in order to know how the range of suitable holding force and the contribution of the holding force to the drawing force varied with the diameter of blank. On the other hand we deduced the drawing force at any instant by means of Mises' theory, and could explain theoretically how the contribution of the holding force to the drawing force varied with the diameter of blank.

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最近自動車ならびに他の車両においていわゆる防振ゴムを使用することが多くなった, しかして防振ゴムの動的な特性が明らかでないためその設計に当り適当な基準となるべき計算式が確立されていないように考えられる.ここにおいて筆者等は自動車発動機架に使用されるある種の防振ゴムについて動的な実験を行いその性質を調べた.この際ゴムの非線型性と履歴曲線をえがくことを念頭において動的な特性を静的特性より適当な計算式によって求めることが一つの実験的な係数の導入により容易に行えることを提唱したものである.

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The writers propose a new theory concerning the internal friction and have deduced a formula giving theoretically the logarithmic decrement of vibration. The formula involves a term deduced equally from the thermo-elastic theory representing the decrement due to the retardation of the deformation and decreasing approximately in inverse proportion to the frequency. It also includes another termconcerning decrement due to the solid friction approximately independent of the frequency. The logarithmic decrement of carbon steel, cold drawn or water quenched and annealed at low temperature, is measured in several frequencies, and it is ascertained that the internal stress can be determined from the constants defining the position of the decrement curve due to the retardation and the amount of the decrement due to the internal solid friction.

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Applying the theory concerning the internal friction to the damping of string vibration under mean stresses, the writers have theoretically deduced the logarithmic decrement of string vibration and found that the damping of vibration almost independent of the initial tension of the string. According to the thermcelastic theory, however, it is concluded that the logarithmic decrement is expressed by another term decreasing in inverse proportion to the increase of the initial tension. The results of the present experiments verifies the validity of the theory. The effects of heat treatment and cold working on the tone of piano cords were investigated also.

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The authors compared the subject three kinds of heat-treatment on plain carbon spring steel SUP-3, Si-Mn spring steel, and SUP-6 which are commonly used as leaf springs of railway cars and motor vehicles, by measuring hardness, impact strength permanent set due to bending test, and micro-structure, and particularly investigated toughness. They also examined the mechanical properties on the relation between size of specimen and isothermal transformation. By comparing the toughness with notched bar impact Strength and bending Strength with nearly same range of hardness, the best result was obtained with austempering. When Si-Mn spring steel is treated, it is not difficult to get bainite structure, while with plain carbon spring steel, we may be not able to get bainite structure unless the specimen is very thin.

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In order to study on the effect of temperature rise in drawing on wire properties, a wire (99.6% Al) was heated at various temperatures up to 500°C with a die, and drawn at once. At 270° to 300°, by the dissolution of impurity Si etc., the electric conductivity rises to a maximum, and mechanical properties are limited by the softening effect, except the Young's modulus and σ_{0 01}, Above such temperatures, in spite of slow cooling, there is a precipitation hardening and occurrence of cooling stress. The preferred orientation increases, [100] orientation takes the place of [111], and this ratio is three to one. This influences the decrease of Young's modulus and conductivity. Near 100°, the fibre structure is somewhat poor, and conductivity falls also. Compared with tensile broken ones, the approximation of deformation and that the skin of wire recieves a heavy tension after flow out from a die are found.

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