Showing papers in "Journal of the Structural Division in 1970"

Reinforced Concrete response to simulated earthquakes

Abstract: A series of reinforced concrete specimens has been subjected to static tests as well as periodic and simulated earthquake motions to develop realistic analytical models for the earthquake response of the elements and materials involved. During some of the dynamic tests the specimen responded with a displacement of the order of six times the initial yield deflection. The stiffness and energy absorbing capacity of the specimens changed considerably and, at times, very rapidly during the dynamic tests. A realistic conceptual model for predicting the dynamic response of a reinforced concrete member should be based on a static force-displacement relationship which reflects the changes in stiffness for loading and unloading as a function of the previous loading history. The dynamic response calculated on the basis of the proposed force-displacement relationship resulted in satisfactory agreement with the measured response. With the hysteresis loops defined by the proposed force-displacement relationship, it was not necessary to invoke additional sources of energy absorption for a satisfactory prediction of the dynamic response.

Analysis of Frames with Partial Connection Rigidity

Abstract: A computer oriented method is described for the analysis of frames with partially rigid beam-to-column connections. The moment-rotation relationship for the partially rigid connections is approximated by a bilinear model. Slopes of these models are graphically determined and used to define connection rigidities. Element stiffness matrices are derived which include the effect of these partial rigidities. The modified element stiffness matrices are then used in a direct stiffness method of solution. Analysis for stability of frames with partial connection rigidity is carried out using the classical method of determining bifurcation states. The modified element stiffness matrices incorporating the effects of partial connection rigidities are directly used in the analysis. Problems ranging from rigid frames to pin connected frames can be solved by the same appproach and examples are presented to show the results.

Axial Load Design for Concrete Filled Steel Tubes

Abstract: The ultimate load of axially loaded concrete filled steel tube columns was investigated and design equations are proposed which are based on summing the tangent modulus buckling loads of the concrete core and the steel tube. The tangent modulus loads are calculated using the AISC code method for the steel tube and a parabolic stress-strain relationship for the concrete. The proposed design equations are shown to give reasonable agreement when compared with test results and it is shown that other design formulae do not give better agreement. A method for calculating the limits of slenderness ratio which determine whether an increase in concrete strength due to triaxial confinement is likely is also given.

Vibrations of Timoshenko Beams and Frameworks

Abstract: A general matrix formulation suitable for a use of the digital computer is presented for dynamic analysis of frameworks composed of prismatic members. The dynamic stiffness coefficients are derived in the form of nondimensional parameters corresponding to the effects of rotatory inertia, shear deformation, and of bending deformation. The individual parameter may be dropped when the appropriate effect is not considered; hence, the stiffness coefficients can be applied to a problem with various considerations of Timoshenko theory, Rayleigh theory, bending and shear, and of Bernoulli-Euler theory. Input data for the computer include the configurations of the framework and the elastic properties of constituent members. The method may be applied to irregular frameworks composed of sloping members with and without sidesway. Numerical examples presented indicate that the effect of rotatory inertia and of shear deformation on the frequencies of frameworks without sidesway is more significant than that of swayed structures.

Elastic Lateral Buckling of Steel Beams

Abstract: A general numerical procedure for the determination of lateral-torsional critical buckling loads for elastic beams of singly symmetric I-section is presented. The procedure mades use of finite element techniques, and is applicable to beams with arbitrary vertical and lateral supports and arbitrary loading. Expressions for elastic and geometric stiffnesses are developed, the solution of the eigenvalue problem is considered, and examples are presented. The method can be extended to the inelastic case.

Orthotropic Elastic Properties of Wood

Abstract: Results of a large scale study of orthotropic elastic properties of wood are presented. The general theory for elastic behavior of wood is presented for compression loading at general angles to ring and grain. Experimental work, for four species of wood, utilizing a total of 588 specimens is presented. Comparison of theoretical and measured strain is provided and a statistical analysis of the data is developed. Agreement between the theoretical and experimental strain was reasonably good for loading within a principal orthotropic plane; however, large errors seem to exist for general loading out of the principal planes. The study suggests new research efforts are needed to incorporate the nonhomogeneous characteristics of wood in the theory. Refined experimental techniques are also needed to better evaluate the elastic behavior of wood loaded at general angles to the orthotropic axes.

Reliability Analysis of Frame Structures

Abstract: Methods of analysis are presented which permit the rapid evaluation of overall reliability of complex redundant structural systems made up of components and subject to loads described by the linear combinations of continuous, random statistical variables. Structures in this category include fail safe designs; and trusses, frames, plates and shells analyzed by ultimate or limit design methods. The particular example chosen to show this capability is the indeterminate frame structure subject to moment induced plastic hinge failure mechanisms. In particular, approximate methods of reliability analysis are developed which consider explicitly the correlation between interrelated failure modes. Excellent agreement with exact results are achieved. Both normal and non-normal statistical distribution are considered in detail. A number of examples are presented which demonstrate the practicality of reliability base structural design.

Statistical Methods in Structural Fatigue

Abstract: Because of the scatter of fatigue test data, statistical methods are required for the interpretation of the data. A method, which features the Weibull distribution as the basic statistical model, is analyzed. This point estimation method is applicable in cases where the sample sizes are relatively large. Methods for estimating the parameters for the two and three parameter Weibull distributions are summarized. Furthermore, estimates of the confidence intervals for the parameters in the case of the two-parameter family are presented. The paper is a state-of-the-art summary of the methods of employing the Weibull distribution for analysis of experimental data with emphasis on practical application.

Theoretical Analysis of Suspension Roofs

Abstract: The finite deflection theory analysis of a spatial system of nets on the basis of nonlinear theory and a more accurate representation of the material's stress-strain relationship is presented. The structures considered comprise cables and truss members which are assumed incapable of resisting bending. The theory is valid regardless of the magnitude of the displacements as long as the stresses are within the elastic limits. An actual stress-strain curve is used for members stressed beyond the proportional limit. A derivation is given for the tangent stiffnes matrix of a space structure at a state of deformation. The joint equations of equilibrium are transformed into linear equations at any intermediate state of deformation, and a solution tangent to the load-deflection curve is obtained. The displacements are determined by means of an iterative technique. The analysis is given for three problems: (1) Cable; (2) prestressd suspension roof; and (3) truss stressed beyond the proportional limit.

Structure and Foundation Interaction Theory

Abstract: Two methods are described in which the response of plane, framed structures to load can be assessed by accounting for superstructure and substructure as a single compatible unit. Both methods are based on the assumption of linear-elastic behavior in superstructure and raft. The Winkler model is used to represent the behavior of the soil beneath the raft. The first method uses equilibrium equations to describe separately the response of structure and raft. Sufficient relationships to solve the complete problem are obtained by adding the compatibility relationships at the junction of raft and superstructure. In the second method, statically admissible contact pressure distributions beneath the raft are successively modified to converge upon the situation where the deformations at the junction of raft and structure are compatible. Both methods are designed for hand calculations.

Behavior of Laced and Battened Structural Members

Abstract: Theoretical analysis is presented of the elastic behavior of both the laced and battened structural member considering the effects of axial load, shear deformation, and connection rigidity of subelements. The analytical solution is used to obtain modified slope-deflection equations to generalize a relation between applied forces and joint displacements. A nondimensional parameter, the shear flexibility, is defined so as to characterize the shear flexibility of the members and to take account of the effects of axial force, local joint connections, and local connection flexibility of the battened members. The fundamental linear second-order differential equation for the deflection curve of the member which includes the effect of shear deformation has been derived. Using boundary conditions for the general solution of deflected shape of the member, the solutions are set up in the forms of slope-deflection equations. Elastic buckling loads for the structural members have been evaluated for various boundary conditions.

Reliability-Based Structural Design

Abstract: Safety is described in terms of reliability or probability of survival for multimember multiload condition structures with loads and strengths as random variables. These include weakest link structures which fail if any member fails and fail-safe structures which survive even after the failure or yielding of some members. A proposed design method is to proportion member sizes with a mathematical programming approach to minimize weight subject to an overall probability of failure constraint. Examples presented include trusses designed by weakest link failure analysis and limit designed redundant or fail safe rigid frames. A sequence of numerical integrations evaluates the failure probability for any form of load and strength frequency distribution. Results show the optimum design versus allowable failure probability, coefficients of variation and frequency distribution for load and strength and the effect of failure mode correlation which is due to different members being affected by the same loading.

Inelastic Stiffened Suspension Space Structures

Abstract: A numerical procedure is presented for determining the deformational response of three-dimensional suspension structures, stiffened and unstiffened, as the loading is increased from the initial state to the ultimate carrying capacity. The analysis accounts for the nonlinear stress-strain relationship of the cables and, in the case of stiffened structures, the elasto-plastic behavior of the flexural members. The equilibrium equations are based on the deformed state. The structure is assumed subjected to static concentrated loads, applied in any direction, at the joints of the stiffening framework. The effects of support movement are considered in the analysis. Numerical studies of stiffened and unstiffened structures are included.

Shear Lag in Stiffened Box Girders

Abstract: METHODS FOR THE ANALYSIS OF SHEAR LAG IN WIDE FLANGES ARE REVIEWED AND A TREATMENT IS PRESENTED WHICH INCORPORATES THE EFFECT OF THE WEB UPON THE STRESS DISTRIBUTION IN THE STIFFENED FLANGE OF A BOX GIRDER BY REPLACING THE WEB WITH AN EDGE STIFFENER ON THE FLANGE. ATTENTION IS DRAWN TO THE EFFECT OF SEVERE SHEAR LAG IN THE CURVATURE AND DISPLACED SHAPE OF A CANTILEVERED BOX GIRDER. A SERIES OF TESTS ON MODEL GIRDERS IS DESCRIBED AND THE RESULTS ARE COMPARED WITH AN APPROXIMATE "STIFFENER-SHEET" ANALYSIS, A MORE RIGOROUS ORTHOTROPIC PLATE ANALYSIS, AND A PLANE STRESS FINITE ELEMENT ANALYSIS; THE LATTER IS USED TO ANALYSE FLANGES UNDER MORE COMPLEX CONDITIONS. A THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS CONFIRMED THE OBSERVED CURVATURES AT THE SECTION OF HIGH SHEAR LAG. /ASCE/

Effects of reinforcements on ductility of concrete

Abstract: To study and compare the reinforcing action of stirrups, randomly distributed short fibers, and compression reinforcement in improving ductility of plain concrete, over-reinforced and under-reinforced beams and prisms were tested in continuously increasing as well as cyclic loading. Reinforcement appears to increase ductility primarily by retarding growth of longitudinal microcracks. As a result, although overall ductility of over-reinforced beams was improved by the addition of compression steel, its presence did not significantly influence the behavior of concrete in the compression zone. Stirrups and fibers substantially improved the ductility of concrete as evidenced by the increased ultimate compressive concrete strains and toughness. Spacing of reinforcement appears to have a small influence on cracking and on ductility for a spacing less than about 1 in. Only small size beams and prisms were tested in this investigation.

Substructure Analysis by Matrix Decomposition

Abstract: The method uses the substructure transformation inherent in the Choleski decomposition and involves a partial release of the interior coordinates. A comparison is made between the decomposition method and the standard one which requires the full release of all interior degrees-of-freedom before the boundary problem is solved. It is concluded that the decomposition method requires less numerical calculations and manipulates less data than the standard method. In addition, the numerical calculations for the substructure decomposition method can be performed within the context of the Choleski decomposition method and requires few new computer routines.

Impact from Railway Loading on Steel Girder Spans

Abstract: Results of tests on 37 spans indicate that the distribution of impact magnitudes on railway girder bridges can be approximated by a normal distribution if speed and span length are constant. If speed is increased, impact is increased. If span length is increased, impact is decreased. Impacts on open deck and ballast deck spans are compared. Impact is defined in terms of increased (or decreased) structural response to moving load as compared with static load or in terms of vertical acceleration of the load system. Factors contributing to impact from railway loading are described. Application to a probabilistic design code is suggested.

Response of Offshore Structures to Random Wave Forces

Abstract: Response of offshore structures to random wave action is presented. A theory for evaluating the response of these structures in deep water is described by the linear wave theory and the Gaussian processes. Hydrodynamic forces are computed through the Morrision-O’Brien-Britschneider formula. Some results of this application to several towers are given.

Lateral-Load Analysis of Asymmetric Multistory Structures

Abstract: The object of the present paper is to provide a more complete three-dimensional continuous method for structures comprising simple or coupled, prismatic or nonprismatic, shear walls and frames arranged asymmetrically in the floor plane. The unknowns of the problem are three continuous functions of horizontal displacements; two for the translations parallel to the structure axes, and one for the angle of twist. These functions are derived from a system of three third-degree nonhomogeneous differential equations with constant coefficients. The homogeneous part of the solution relates to an eigenvalue problem of a third-degree matrix, involving nine arbitrary constants obtainable from the boundary conditions. The particular solution depends on the type of loading; a uniform lateral load yields a second-order polynomial and a trapezoidal load yields a third-order one. With the three functions known the three displacement functions for each of the stiffening elements and elastic media can be calculated and the internal forces established. The present method is applicable to structures with nonuniform geometric properties by dividing them into uniform zones, solving for each zone separately, and determining the relevant constants from interzone boundary conditions.

Modal Response of Structures

Abstract: In this note, an attempt is made to provide additional information concerning the contributions of the lower modes to the total response of a shear building to earthquake loading.

Theoretical stresses and strains from heat curving

Abstract: HORIZONTALLY CURVED STEEL GIRDERS FOR CURVED HIGHWAY BRIDGES CAN BE ECONOMICALLY FABRICATED BY BUILDING A STRAIGHT GIRDER AND THEN HEATING APPROPRIATE FLANGE EDGES TO INDUCE A RESIDUAL CURVATURE AFTER COOLING. THE RESULTS OF A THEORETICAL INVESTIGATION OF THE RESIDUAL STRESS, STRAIN, AND CURVATURE DUE TO THIS HEAT-CURVING PROCESS PROCESSES ARE PRESENTED. THE ANALYTICAL MODEL USED A PERFECT ELASTIC-PLASTIC, TEMPERATURE-DEPENDENT STRESS-STRAIN RELATIONSHIP FOR THE STEEL, AND TEMPERATURE PROFILES IN THE GIRDER FLANGES BASED ON HEAT-TRANSFER THEORY FOR A SEMI-INFINITE PLATE. THE EFFECTS OF MAXIMUM EDGE TEMPERATURES TO 1,150 DEGREES F OVER INCREASING WIDTHS OF THE FLANGES OF A TYPICAL GIRDER WERE DETERMINED. THE RESIDUAL STRESSES AFTER HEAT CURVING WERE TENSILE NEAR THE FLANGE EDGE AND COMPRESSIVE ELSEWHERE, EXCEPT NEAR THE CENTER OF THE FLANGE, WHERE TENSILE STRESS SOMETIMES REMAINED. THE FINAL CURVATURE, WHICH WAS DETERMINED FROM THE RESIDUAL STRAIN DISTRIBUTION, GENERALLY INCREASED WITH MAXIMUM TEMPERATURE. /ASCE/

Research on Steel-Concrete Composite Beams

Abstract: This summary of British research on composite beams covers the period 1960 to 1968, during which emphasis was placed on the behavior of uncased beams at ultimate load (for buildings) and under repeated load (for bridges). The publications of the Drafting Committee for the British Code of Practice for Composite Construction are reviewed and related to the AISC and AASHO specifications. A more detailed account is given of the research at the University of Cambridge on uncased and concrete-encased beams. It is concluded that sufficient work has been completed to enable an ultimate-strength design method for continuous floor structures for buildings to be codified for composite construction in uncased mild steel and normal-density concrete. Further research is required on the composite behavior of lightweight concrete, high-yield steel and metal-deck flooring.

Efficient Solutions for Linear Matrix Equations

Abstract: The most efficient means of solving most systems of linear equations arising in structural analysis is by Gaussian elimination and subsequent back substitution. A method is presented for its implementation. Direct solutions are obtained with sparse matrix factors which preserve the operations of the Gaussian elimination for repeat solutions. The method together with techniques for its application are graphically described. Its use in many types of engineering problems requiring solutions to systems of linear equations will: (1) Minimize the amount of central computer memory required; (2) provide a more flexible means of manipulating large matrices; and (3) dramatically reduce computer time.

Elastic-Plastic Analysis of Frameworks

Abstract: A general matrix-network procedure is formulated for tracing the load-deflection characteristics of frameworks loaded through the elastic range and inelastically to the plastic collapse stage. An iterative incremental analysis procedure is employed, with the load-displacement characteristics of the structure piecewise linearized over finite loading increments. Consecutive nonproportional loading systems comprised of any arrangement of concentrated member and joint loads are considered. The classical plastic hinge concept is extended to incorporate the interaction of flexural and torsional moments and axial force. The force and plastic deformation increment vectors at each plastic hinge are constrained to remain perpendicular and parallel, respectively, to the yield surface normal vector during finite loading increments. A procedure is developed for periodically drawing the force vector at any plastic hinge an arbitrarily specified distance back from the yield surface tangent plane, while maintaining equilibrium and compatibility in the structure. The analysis procedure incorporates provision for distinguishing between partial and total collapse mechanisms.

Local instability of horizontally curved members

Abstract: AN ANALYTICAL STUDY OF THE ELASTIC BUCKLING BEHAVIOR OF THE FLANGES OF HORIZONTALLY CURVED I-SHAPED GIRDERS IS PRESENTED THE PREBUCKLING FLANGE STRESSES IN THE LONGITUDINAL AND RADIAL DIRECTIONS DUE TO BENDING AND NONUNIFORM TORSION ARE DETERMINED USING AN ELASTICITY APPROACH THE MAGNITUDES OF THESE STRESSES ARE COMPARED WITH THOSE RESULTING FROM A STRENGTH OF MATERIALS APPROACH USING THESE STRESSES AND THE FINITE DIFFERENCE METHOD, BUCKLING COEFFICIENTS, K, ARE OBTAINED BY TREATING THE FLANGES OF THE GIRDER AS ELASTICALLY RESTRAINED CURVED PLATES THE INFLUENCE OF CURVATURE AND THE RATIO OF BENDING STRESS TO WARPING NORMAL STRESS ON THESE BUCKLING COEFFICIENTS IS EVALUATED THE BUCKLING COEFFICIENTS ARE COMPARED WITH THOSE FOR RECTANGULAR PLATES WIDTH TO THICKNESS REQUIREMENTS BASED ON PREVENTING LOCAL BUCKLING IN THE ELASTIC RANGE ARE ALSO OBTAINED /ASCE/

Behavior of Wood-Concrete Composite Beams

Abstract: Thirteen wood-concrete composite T-beams were fabricated and tested. Epoxy resin was used to bond the wood web to the concrete flange. By proper design, it was possible to stress the concrete in compression and the wood in tension as long as the bond between wood and concrete remained effective. It was found that the beams function as composite sections and carry substantial loads before failure. Four failure modes are identified: Sliding shear, beam shear, tensile wood failure and concrete compressive failure. Beams glued while the concrete was fresh performed at least as well as beams glued after the concrete had set. Longitudinal nails used as additional shear connectors substantially increase the horizontal shear resistance between wood and concrete. Reinforcing wood strips also increase the sliding shear resistance. The effect of other variables remain to be considered.

Flexible Plate Finite Element on Elastic Foundation

Abstract: A step-by-step linear incremental procedure for large deflection analyses of plates on elastic foundations using finite elements is presented. The incremental stiffness matrices for a conforming rectangular plate finite element, which are appropriate for large deflection analysis, are formulated and presented explicitly. Evaluative analyses are made by using the incremental stiffness formulations and piecewise incremental procedures. Examples include uniformly loaded rectangular plates with different length-to-width ratios, various boundary conditions and foundation moduli. Comparisons are made in those cases where the alternative analytic solutions are available. Good agreements are found.

Tapered Box Girders of Deformable Cross Section

Abstract: A general theory of torsion of tapered box girders of deformable cross section, its experimental substantiation, studies of the ultimate strength of box girders, and the use of the theory derived for analysis of a really big bridge, are presented. Warping stresses and distortion stresses from transverse flexure are computed. A simple criterion is derived for load distribution on the bridge to ensure the greatest effects of bending and torsion. It is possible to use computers for practical computations; the presented solution is simplified and expressed in the form of formulas for less important cases. The analysis is applicable to straight tapered box girders of deformable cross section, and also for continuity over intermediate supports, and arbitrary end support conditions. It is also applicable to girders with rigid cross section.

Unbalanced Tensions in Transmission Lines

Abstract: A nonlinear analysis of an electric transmission line is presented for conditions involving imbalance in conductor tensions. The analysis is applicable to lines containing structures of arbitrary geometry and stiffnesses. Structure and insulator displacements are considered. Stiffness properties of structures, conductors, and insulators are derived. Equilibrium equations to be used in the analysis are formed. Two numerical methods of analysis, an iteration method, and a step-by-step linear increment technique are applied to the equilibrium equations. Both methods which have been programmed on a digital computer are applied to an actual transmission line containing flexible tubular steel structures. The iteration method has been found to be superior to the step-by-step method for the example analyzed. Analysis of this line has also shown that neglecting deflections of flexible structures with suspension insulators introduces substantial error.

Fatigue Tests on Prestressed Concrete I-Beams

Abstract: Six fatigue tests of prestressed concrete I-beams containing web reinforcement are reported. Each beam was initially subjected to a high overload, and then subjected to 2,000,000 cycles of a design equivalent repeated loading. The beams failed by either flexural or shear fatigue. The flexural fatigue life of the test beams was less than expected from available information on the fatigue strength of strand. The tests demonstrated that prestressed concrete beams have a remarkable shear fatigue resistance. Prestressed beams, with enough web reinforcement to develop their flexural capacity, can be subjected to overloads which cause extensive cracking without subsequent danger of a shear fatigue failure under design loads. Shear fatigue failures do not occur suddenly. There is considerable warning, as indicated by increasing deflection and increasing inclined crack width, before failure occurs. In these and other tests, shear fatigue failures did not occur when the range in inclined crack width was less than 0.006 in. under application of repeated loads.