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Showing papers in "Journal of Engineering Mechanics-asce in 1963"


Journal ArticleDOI
TL;DR: In this article, the tensile strength of concrete is proportional to the inverse square root of the defect diameter, where the fault diameter is defined by the wire spacing of the wire.
Abstract: The tensile strength of concrete is greatly reduced as a result of internal flaws and micro-cracks. The application of fracture mechanics concepts reveals that the tensile strength is proportional to the inverse square root of flaw diameter. High tensile strengths can be realized, however, when flaws are prevented from enlarging beyond certain limits. This is accomplished by means of closely spaced wire reinforcement. For wire spacings of less than a certain predictable range, the maximum size of flaw is equal to the wire spacing. Thus, the smaller the spacing the larger the tensile strength. Theoretical results are presented in detail. The theoretically predicted relationship between tensile strength and wire spacing is substantiated by tests.

297 citations


Journal ArticleDOI
TL;DR: A theoretical discussion of the principles involved in the fracture of concrete under stress is presented in this paper, where the strength determining property for all types of loads is the critical strain energy release rate.
Abstract: A theoretical discussion of the principles involved in the fracture of concrete under stress is presented. The strength determining property for all types of loads is the critical strain energy release rate. The elastic energy is transformed mainly to surface energy, but the new surfaces include a multitude of microcracks much larger in total area than the main crack. The increase of the microcracked zone and the heterogeneity of concrete contribute to its strength. The basic difference between tensile and compressive fractures is that, in the former, the rate of strain energy release (i. e., the driving force) increases with crack length, whereas, in the latter, it is constant. This makes compression a more controlled type of fracture than is tension. In tension, the first crack is also the fatal one: hence, the stress-strain curve is almost linear. In compression, fracture is preceded by a process of progressive cracking that accounts for the higher strength and the greater curvature of the stress-strain relationship.

103 citations


Journal ArticleDOI
TL;DR: In this article, a general thermoelastic theory for thin aeolotropic plates that are heterogeneous in the thickness direction was formulated in terms of two simultaneous equations for the transverse deflection, w, and the Airy stress function, F.
Abstract: A general thermoelastic theory for thin aeolotropic plates that are heterogeneous in the thickness direction may be formulated in terms of two simultaneous equations for the transverse deflection, w, and the Airy stress function, F. From these equations, thermal coupling terms appear, in addition to the interaction of stretching and bending. Applying the theory to the case of uniform heating of long rectangular heterogeneous plates yields explicit equations for the transverse deflection, the in-plane forces, and couples that arise in a uniformly heated plate. A cross-thermoelastic phenomenon is exemplified in the stress-resultants and couples relations. The linear theory may be extended to include finite deflections. The pre-thermal and post-thermal buckling states, in a heterogeneous plate, require the simultaneous determination of w and F.

64 citations


Journal ArticleDOI
TL;DR: In this article, the measured periods of vibrations of a large number of buildings are used to compare the merits of existing formulas and of equations derived using a rational approach, and it is concluded that no single, simple, empirical equation will give reasonably accurate estimates for the periods of buildings having shear wall characteristics.
Abstract: The measured periods of vibrations of a large number of buildings are used to compare the merits of existing formulas and of equations derived using a rational approach. It is concluded that no single, simple, empirical equation will give reasonably accurate estimates for the periods of buildings having shear wall characteristics. The calculated periods of steel frame buildings are found to be proportional to the square root of the number of stories rather than directly proportional as is usually assumed. However, observed periods of such buildings indicate that the steel frame alone would contribute only about 25% of the effective stiffness. The dependence of the period on the flexibility of the floor girders is also demonstrated using a digital computer. Calculations show that these buildings behave essentially as if they had rigid floor girders, although the girders of the steel frames themselves are very flexible, so far as the period of vibration is concerned. Additional studies of the natural periods of actual structures are recommended.

59 citations


Journal ArticleDOI
TL;DR: In this article, the authors used Berger's approximation to evaluate moderately large deflections of uniformly loaded plates on elastic foundations of the Winkler type, which neglects the strain energy due to the second invariant of the middle surface strains.
Abstract: The evaluation of moderately large deflections of uniformly loaded plates on elastic foundations of the Winkler type is presented using Berger's approximation, which neglects the strain energy due to the second invariant of the middle surface strains. Because of this approximation, the problem may be formulated in terms of two decoupled nonlinear equations. Series solutions are obtained for circular and rectangular plates under various support conditions, and are numerically evaluated and presented in the form of graphs for plates of various aspect ratios with simply supported edges. Results obtained are compared with some known solutions, and it is concluded that Berger's approximate method yields results of sufficient accuracy for practical purposes.

56 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that for both simply supported and clamped circular plates the vibration can be expressed in terms of elliptic functions and a modified Galerkin procedure was used for solving the resulting equations.
Abstract: The vibration of circular plates when the amplitude is large is governed by nonlinear partial differential equations. An approximate formulation of these equations for the static case has previously been proposed by H. M. Berger. These equations are here extended to the dynamic case. A simplification in the statement of the problem is introduced by requiring that the in-plane displacement at the boundary of the plate vanish. A modified Galerkin procedure is then used for solving the resulting equations. It is shown that for both simply supported and clamped circular plates the vibration can be expressed in terms of elliptic functions. Numerical results are given for the calculation of frequencies and stresses. A method is suggested for solving forced vibration problems.

53 citations


Journal ArticleDOI
TL;DR: In this article, the Wagner theory for the bending and buckling of straight bars of thin-walled open section is extended to circular curved bars and rings, and the differential equations of equilibrium are determined by a summation of force components, whereas the natural boundary conditions are derived by the minimum potential energy principle.
Abstract: The Wagner theory for the bending and buckling of straight bars of thin-walled open section is extended to circular curved bars and rings. The differential equations of equilibrium are determined by a summation of force components, whereas the natural boundary conditions are derived by the minimum potential energy principle. The effects of nonuniform torsion, unsymmetrical loading, elastic foundation, and axial extension are included. The buckling of a ring subjected to a uniform external pressure is treated. The critical pressure is found to be the root of a cubic characteristic equation. Simplified solutions are found by restricting the generality, thereby reducing the characteristic equation to the first order.

37 citations


Journal ArticleDOI
E. J. Gumbel1
TL;DR: In this paper, the authors considered the Weibull distribution of smallest values, where the probability of surviving θ number of cycles is fixed at 1/e, and the lower limit of the distribution is defined as u\Do\N. This lower limit is of great interest for the design of structures.
Abstract: In the third asymptotic distribution of smallest values, or Weibull distribution, three parameters exist. One is a location parameter in which the probability of surviving θ number of cycles is fixed at 1/e. A second is a shape parameter, α, and the third parameter, u\Do\N, is the lower limit of the distribution. It is this lower limit which is of great interest in fatigue studies for the design of structures, since the existence of a positive u\Do\N enables the design of a structure in which, if the number of cycles is kept below this critical value for a given stress, no fatigue failure will ever occur. The three parameters may or may not be a function of stress, and appropriate changes in notation are made when applicable. The interdependence of the three parameters is also studied. Reduction to two parameters by the introduction of a reduced life and a reduced minimum life is carried through. By introducing a standardization of the number of cycles N, the number of parameters is lessened to one. A table of this standardized life then facilitates the estimation of the three parameters by the method of moments procedure.

29 citations


Journal ArticleDOI
TL;DR: In this paper, a mathematical theory that attempts to describe the detailed manner in which one vehicle follows another in a single lane is reviewed, where the motion of a line of cars is described by a system of differential difference equations.
Abstract: A mathematical theory that attempts to describe the detailed manner in which one vehicle follows another in a single lane is reviewed. According to this theory, the motion of a line of cars is described by a system of differential difference equations. The parameters entering these equations have been obtained by a series of car-following experiments. Stability criteria, as well as steady state flow relationships between density, speed, and volume of traffic, are presented. In order to test the validity of this car-following model in the case of single lane traffic flow, comparisons are made with a number of experiments and observations.

22 citations


Journal ArticleDOI
TL;DR: In this article, the condition of statical equilibrium of plane triangulated (braced) rigidly-jointed frames is studied. But it is assumed the frames are loaded centrally at the joints, and the analysis is made of the elastic behavior of the system.
Abstract: A study is made of the condition of statical equilibrium of plane triangulated (braced) rigidly-jointed frames. It is assumed the frames are loaded centrally at the joints. A nonlinear analysis is made of the elastic behavior of the system. The analysis takes account of the interactions of the members at the continuous joints. It is shown that such frames may, in general, pursue an unstable equilibrium path in the early stages of elastic buckling, and that, initially, the external loads causing buckling must be varied linearly with lateral deflections of the members. The analysis confirms that the critical loading condition, at which buckling can begin, agrees with that given by a conventional eigenvalue treatment of the problem. Tests on simple models made of high-strength steel members (to insure elastic buckling) are described. The results of these tests confirm that an unstable path is possible immediately after buckling. It is commonly assumed that the buckling of a frame occurs in neutral equilibrium; any conclusions based on this assumption should, therefore, be treated cautiously.

19 citations


Journal ArticleDOI
TL;DR: In this article, the buckling value of the external pressure acting on thin cylindrical shells has been derived on the basis of various linear bending theories for certain ranges of shell shapes.
Abstract: Expressions for the buckling value of the external pressure acting on thin cylindrical shells have earlier been derived on the basis of various linear bending theories. For certain ranges of shell ...

Journal ArticleDOI
TL;DR: In this paper, an arbitrarily thick elastic cylinder in an infinite elastic medium during the passage of plane, compressional, harmonically time-varying waves is investigated, and the maximum dynamic stresses in both the cylinder and the medium are 10% to 20% higher than their corresponding static values.
Abstract: Dynamic stresses in an arbitrarily thick elastic cylinder in an infinite elastic medium during the passage of plane, compressional, harmonically time-varying waves are investigated. Dynamic stresses around the cylinder in the elastic medium are also determined. Numerical results for two different cylinders with ratios of outer radius and inner radius ranging from 1.05 to 1.20 are presented in dimensionless form. It is demonstrated that the maximum dynamic stresses in both the cylinder and the medium are 10% to 20% higher than their corresponding static values. It is noted that the maximum values of dynamic stresses obtained under the harmonically varying waves are identical to the maximum values obtained under the step-pulse loading, both for the unlined cavity and for the thin-shell lining case. Thus, it is believed that the values presented in the paper can be used for design purposes.

Journal ArticleDOI
TL;DR: The simplex computational technique and an equivalent geometric algorithm are presented side-by-side in the solution of a sample problem so that the relationship of the two methods can be seen.
Abstract: An examination of the use of linear programming is presented for the assignment of traffic to routes in a network when the origins and destinations of the trips are known. The formulation of the traffic assignment problem as a linear programming problem is given. The simplex computational technique and an equivalent geometric algorithm are presented side-by-side in the solution of a sample problem so that the relationship of the two methods can be seen. Also mentioned is an intersection mode that permits time penalties to be assigned to individual turning maneuvers within the intersection. Essentially the intersection node is broken into several sub-nodes so that, for visualization purposes, a spacial separation can be substituted for the temporal one. Adaptations of the model for several types of intersections are presented. The intersection model can be applied equally well to the linear programming approach to assignment or to presently used techniques.


Journal ArticleDOI
TL;DR: In this paper, a series of the appropriate characteristic functions of beam vibration are used for beams with different types of end conditions, such as axial and transverse loads, for continuous beam-columns and for continuous varying flexural and foundation stiffnesses.
Abstract: Beam-columns of finite length resting on elastic foundation are analyzed by a series method. The series of the appropriate characteristic functions of beam vibration are used for beams with different types of end conditions. The method is shown to be applicable to continuous beam-columns and to the beam-columns with distributed axial and transverse loads. Cases of continuously varying flexural and foundation stiffnesses are also covered. A method is suggested for the calculation of the buckling loads of beam-columns. The method is illustrated by several numerical examples.

Journal ArticleDOI
TL;DR: In this article, the authors measured the drag, lift, and moment on twenty-four parallel vertical 1/2in. cylinders oscillating with 13-in. amplitude in a laboratory tank 5.5 ft by 16 ft.
Abstract: Drag, lift, and moment on twenty-four parallel vertical 1/2-in. cylinders oscillating with 13-in. amplitude in water were measured in a laboratory tank 5.5 ft by 16 ft. A comparison, D\Do\N, is defined as 24 times the calculated drag on one of the cylinders alone in a uniform stream flowing at the maximum velocity of the group oscillation. Drag increases from 0.3 D\Do\N, with cylinders in contact, to 0.9 D\Do\N at 4 diameter spacing, and to approximately D\Do\N at 8 diameters. At small spacings, lift decreases from approximately D\Do\N to 0.3 Do as Reynolds numbers increase from 5,000 to 15,000. At 2.8 to 8 diameters spacing, lift reaches the large value of 1.7 D\Do\N for the higher Reynolds numbers. Moments about the vertical axis of the group are 1 to 9 times the product of D\Do\N and the group radius. Vibration frequencies in all modes are at natural frequencies of the group in its corresponding modes. Staggered and square cylinder patterns give approximately the same results.

Journal ArticleDOI
TL;DR: In this article, the authors used the deflection expression of an infinite plate subjected to a concentrated force in connection with the method of images permitted solutions for a wedge-shaped plate, infinite strip, semi-infinite strip, and rectangular plate simply supported along their edges.
Abstract: Use of the deflection expression of an infinite plate subjected to a concentrated force in connection with the method of images permitted solutions for a wedge-shaped plate, infinite strip, semi-infinite strip, and rectangular plate simply supported along their edges. The closed-form solutions that were obtained for the semi-infinite and rectangular plate were evaluated and the results reveal that, in the rectangular corner plate, the corner reaction is negligible for λr\D0\N≥5. It was also found that, for λr\D0\N<4, in the corner area there appear negative bending moments which by far exceed the absolute maximum value of the negative moment of an infinite plate. The solutions of the infinite strip, semi-infinite strip, and rectangular plate were obtained as infinite series of fundamental deflections. It is noted that the series for deflections, moments, and shear forces converge rapidly, particularly in the vicinity of the concentrated forces. Advantages in using superpositions of fundamental deflections, as compared with using Fourier-type series, are noted in treating the infinite plate subjected to arbitrary loads.

Journal ArticleDOI
TL;DR: In this article, an exact solution for the seepage flow from a system of parallel trapezoidal channels through a layer of homogeneous, isotropic soil is presented.
Abstract: An exact solution is presented for the seepage flow from a system of parallel trapezoidal channels through a layer of homogeneous, isotropic soil. Under this layer there is a drain that might be represented physically by a bed of gravel or coarse sand. The flow is assumed to obey Darcy’s law and hence there is velocity potential which satisfies the Laplace equation. By constructing the complex potential and the complex velocity planes, the solution is obtained through conformal mapping. General expressions are given for the discharge and shape of the free streamline. A numerical example is presented for which the free surface and the velocity distribution on the channel’s profile were drawn. The quantity of seepage from the bottom and sides were also computed.

Journal ArticleDOI
TL;DR: In this paper, the dynamic response of statically determinate and indeterminate elastic-plastic beams is computed with a maximum degree of accuracy and with a minimum of computational difficulty.
Abstract: A method is developed whereby the dynamic response of statically determinate and indeterminate elastic-plastic beams may be computed with a maximum degree of accuracy and with a minimum of computational difficulty. The development is applied to a mathematical model of the actual beam consisting of a system of concentrated masses connected by massless segments whose stiffnesses are identical to the stiffnesses of the corresponding parts of the original beam. The equations of motion are written in the usual manner, in which the structural resistance to deformation is expressed explicitly in terms of the deflections for any elastic-plastic phase of deformation. These equations of motion are solved by means of a single step forward numerical integration procedure. A method of determining the points of elastic-plastic and plastic-elastic transitions is described that, in conjunction with the numerical integration procedure, is suitable for programming on a high-speed digital computer. Several examples are given to show the versatility of the method, including the response of a continuous beam subjected to a moving load.

Journal ArticleDOI
TL;DR: A mathematical analogy is made between the network problem and the arbitrary linear structure that allows a formulation of the structure, using the graph theory, which corresponds to the node method for a network.
Abstract: A mathematical analogy is made between the network problem and the arbitrary linear structure that allows a formulation of the structure, using the graph theory, which corresponds to the node method for a network. The formulation may serve as a basis for a general computer program for structural analysis. It provides a simple means by which research concerning the solution of large networks may be directly applied to structures (for example, Kron's Methods).

Journal ArticleDOI
TL;DR: In this article, an application is presented of a linear programming model, the multicopy mixing model developed by Charnes and Cooper, to the problem of arterial street system analysis, and an example demonstrates how the use of the model provides a simulation of traffic flow over a street network containing branches or links with capacity constraints.
Abstract: An application is presented of a linear-programming model, the multicopy mixing model developed by Charnes and Cooper, to the problem of arterial street system analysis, and an example demonstrates how the use of the model provides a simulation of traffic flow over a street network containing branches or links with capacity constraints. The example presents a specific use of the technique, that of holding the freeway volume at or below a fixed amount and developing the resulting optimum flow pattern in the system. It is shown how the results of the simulation can be used as a guide for determining what control measures, such as one way street routings, or freeway ramp closures, should be used to get optimum use of the street system. The paper also illustrates how the nonlinear travel time-volume curve (delay curve) can be piece-wise, linearly approximated and included in the traffic assignment procedure in order to closely simulate actual traffic behavior in a street network.

Journal ArticleDOI
TL;DR: In this article, the Rayleigh wave displacements produced by a concentrated load on the surface of the medium are used as influence functions to construct, by means of suitable integrations in space and time, the corresponding quantities produced by the pressure distributions from a nuclear burst.
Abstract: Displacements due to Rayleigh waves are produced by nuclear bursts acting on the surface of a semi-infinite elastic half-space producing a time decaying pressure pulse that acts over a circular surface area of increasing radius. Expressions for the Rayleigh wave displacements produced by a concentrated load on the surface of the medium are used as influence functions to construct, by means of suitable integrations in space and time, the corresponding quantities produced by the pressure distributions from a nuclear burst. Numerical results and procedures are noted and the application of the method to the design of undergound facilities is outlined.

Journal ArticleDOI
TL;DR: In this paper, the authors describe the dynamic response of lattice-type structures, assuming small displacements, by the following set of four matrix equations: (1) Equation of consistent displacements; (2) joint equation of equilibrium; (3) force displacement equation; and (4) equation of support.
Abstract: The dynamic response of lattice-type structures, assuming small displacements, may be described by the following set of four matrix equations: (1) Equation of consistent displacements; (2) joint equation of equilibrium; (3) force displacement equation; and (4) equation of support. The response function or indicial flexibility matrix is formed of terms that are solutions of the partial differential equations describing the transverse, torsional, and longitudinal vibrations of uniform, slender beams. The set of matrix equations becomes a set of linear, algebraic equations when transformed to the Laplace domain. Solutions that are carried out in the Laplace domain yield expressions for displacements, rotations, end moments, and forces in terms of the transform variable. Inversions are carried out in terms of series expansions of orthogonal functions. External damping, together with forcing function cut-off, is introduced to assure the uniform convergence of the series for all values of time. The application of the equations to the externally damped cantilever beam and to the unsymmetrical portal verifies the validity of the method.

Journal ArticleDOI
TL;DR: In this article, it was shown that if the viscous damping in a linear elastic system can be represented in the form C = Σ β i (BS) i in which S and B represent the stiffness and universe of the mass matrix, respectively, and the β i are scalar constants, then the mode shapes for damped and undamped vibration are identical.
Abstract: Analysis shows that if the viscous damping in a linear elastic system can be represented in the form C = Σ β i (BS) i in which S and B represent the stiffness and universe of the mass matrix, respectively, and the β i are scalar constants, then the mode shapes for damped and undamped vibration are identical. The assumption of small damping is not imposed. It is shown how the damping matrix can be constructed when the damping ratios in the normal modes of vibration are known.

Journal ArticleDOI
TL;DR: In this article, a description of the basic properties of moire patterns used in strain analysis is presented, and the uniqueness and continuity of displacements are noted, compared with topological elevations.
Abstract: A description of several of the basic properties of moire patterns used in strain analysis is presented. The uniqueness and continuity of displacements are noted, compared with topological elevations, and the ordering of fringes is demonstrated to follow. The meaning of lines of zero slope in the pattern is shown to be an aid in strain analysis. Singular points of the elliptical, hyperblic, and double-tangent type are described. Singular lines are noted as an extension of singular points. The effect on the moire pattern of rotation of the master and model grid systems is presented in terms of Mohr’s circle. The use of symmetry in order to obtain additional information from the pattern is demonstrated, including an example of a complete analysis from one pattern, wherein the proper regard is given to symmetry. The description is illustrated with patterns from a ring and a disk under diametral load, a strip with a hole subjected to uniaxial tension, a plate with two concentrated loads on one edge, and a disk subjected to four-point loading.

Journal ArticleDOI
TL;DR: In this paper, a mechanism of fracture is proposed that accounts for variation in time required to complete fracture and for the difference in static and dynamic ultimate stresses that have been reported by various investigators.
Abstract: Evidence indicates that small model systems using the same material, same explosive, and similar geometry give good quantitative predictions of strains in a number of rocks, but only qualitative predictions of fracture. It appears that an equation of state that is applicable to blasting in rocks does not involve strain rates, but that fracture is time dependent. Fracture caused by rapidly applied loads cannot, in general, be predicted by assuming that materials fail at a certain state of stress or strain. Some additional "property" of the material must be known. The consistency between nonsimilarity of fracture in model systems, and the existance of such a "property" is pointed out. Experiments demonstrating variation in time required to complete fracture of plaster bars with applied stress are described. A mechanism of fracture is proposed that accounts for variation in time required to complete fracture and for the difference in static and dynamic ultimate stresses that have been reported by various investigators. Some predictions that follow from this mechanism of fracture are presented.

Journal ArticleDOI
TL;DR: In this article, the transient response of nonlinear, nonconservative structures, idealized as lumped parameter chains, is treated by a combination graphical-numerical method, and a scaling law is derived for nonlinear multi-degree-of-freedom systems.
Abstract: The transient response of nonlinear, nonconservative structures, idealized as lumped parameter chains, is treated by a combination graphical-numerical method. The step-by-step solution of the set of ordinary second-order nonlinear differential equations is in the form of trajectory curves in multiple phase-plane space. Examples of one and two-degree-of-freedom systems with cubic hardening springs are treated in which the forcing function is a prescribed foundation velocity. Relative displacement response curves obtained from an analog computer show good agreement with the graphical-numerical results. A scaling law is derived for nonlinear multi-degree-of-freedom systems. Prescribed restrictions are imposed on the parameters and input of the model system and the prototype system. Application of the scaling law is made for a system consisting of a finite number of masses connected by cubic hardening springs and linear dashpots.