Journal of Structural Engineering

A numerical integration method to predict the time‐related deflections of reinforced concrete beams, which includes cyclic loading and unloading, is presented. It requires little computer storage capacity. The major aspects of this method include the time‐dependent strains in the stress‐strain relationships for concrete compression and tension in terms of the creep coefficient, the creep‐moment‐curvature relationships, the deflection‐creep coefficient diagrams, and shrinkage deflections. Variations in the flexural stiffness caused by cracking are accounted for in the tension stress‐strain relationship in terms of maximum tensile stress. By applying the principle of strain superposition, the effect of loading history on the beam is incorporated into the creep coefficient for the specific concrete age at which deflection is desired. Deflections are determined from the deflection‐creep coefficient diagrams. The procedure eliminates the inconsistency in the zero strain surface location caused by superimposing deflection components from loading and unloading. Comparisons between the calculated deflections and test data from beams under cyclic loading and unloading are very good.

The local buckling and post‐local buckling behavior of short length I‐section columns fabricated by welding high tensile steel plate is described. Six sections of three different section geometries were tested to destruction by loading between rigid end plattens mounted on freely rotating bearings in a compression testing machine. Accurate measurements of welding residual strains and geometric imperfections were taken prior to testing and are presented in the paper. Comparisons of the test local buckling loads are made with a finite strip buckling analysis including welding residual strain. Comparisons of the measured axial stiffnesses and stress distributions were made with a nonlinear finite strip analysis, which includes geometric imperfections and welding residual strain. The test loads are compared with those based on the Winter effective width formulas.

A finite element analysis, in conjunction with Vlasov's theory of warping of thin‐walled beams, has been used to study the torsional stiffening of thin‐walled open‐section cores by the surrounding floor slabs. The relative influences of the most important geometrical parameters and slab support conditions are examined, and design curves are presented to allow the equivalent width and effective warping stiffness of the slab to be evaluated rapidly. The influence of the axial and flexural stiffness of the external columns is also considered. A numerical example illustrates the stiffening effect of the floor slabs on the most important design quantities for the core, the maximum rotation at the top and the warping moment (bimoment) at the base.

Present U.S. structural engineering practice assumes that live load components due to human occupancy and human movements for the design of assembly structures, such as grandstands, can be represented as statically applied uniform or line loads. A review of code values and procedures reveals a history of theoretical, experimental, empirical, and practical developments and events that provide insight into their sources and meanings. The mechanisms by which they have been implemented should prove to be interesting and informative to the design engineer and others concerned with the modernization of codes. The designer is provided with a perspective of a complex commonly used codified deterministic loading.

A hand method of estimating the period of free vibration of building structures, for use in determining the minimum base shear for their earthquake design, is presented. The method is for structures that have uniform properties through their height, and that are symmetrical in plan and symmetrically loaded so that they do not twist. The structures may consist of rigid frames, coupled walls, wall‐frames and braced frames, or any combination of these. The basis of the method is that all of the above described types of bent behave as members of a family of shear‐flexure structures whose static deflections can be predicted by coupled wall theory. A method of decoupling the static deflection into a flexural component and a shear plus flexure wall‐frame type of component is extended to dynamic behavior of a corresponding decoupled eigenvalue approach, to determine the periods of free vibration. The derivation of the method, an assessment of its accuracy, and a worked example to illustrate its application are presented.

The nonlinear interaction phenomenon in reinforced concrete frame‐wall systems in the presence of combined vertical and lateral loading is studied for a range of values of the four parameters, such as the ratio of beam and column stiffness, the ratio of column and shear wall stiffness, the slenderness ratio of columns, and the proportion of lateral to vertical load (load ratio). The method used for this study is based on finite element techniques and takes into account both material and geometric nonlinearities. The method uses the noni linear stress‐strain curve of the constitutive materials and does not use bilinear or trilinear idealizations. The important conclusions which have emerged from this study are as follows: (1) Nonlinear behavior is significantly pronounced in the frame‐wall systems with stiff walls when under a large load ratio; (2) the bracing effect of the shear wall is more effective for the case of frames having slender columns and flexible beams when under a large ratio of lateral to vertical load; (3) nonlinear idealization of the flexural characteristics of shear walls is important when the shear walls are connected to stiff frames; and (4) stiff walls undergo more reduction in their stiffness at failure than flexible walls.

Ballasted prestressed concrete single track railway bridges, consisting of several box girders with spans of 25, 50, 75, and 100 ft $(1\mathrm{ft}=0.305m)\text{,}$ were studied. The girder cross sections were designed according to American Railway Engineering Association (AREA) specifications. Two percent of critical damping corresponding to the first mode of vibration was assumed for the bridges. The track irregularities on the approaches and the bridges were generated from power spectral density functions for Federal Railroad administration (FRA) Class 4 track. A freight car model, which included the geometric and suspension nonlinearities of the car, was developed and used in the analysis. Impact percentages in the bridges due to a two‐vehicle, 100‐ton freight car train operating at 20, 40, and 60 mph were calculated. These were compared with the values obtained in an earlier investigation and those specied by the AREA.

A nonlinear stiffness matrix based computer program is used to investigate the stability of elastic space structures whose likely failure modes are determined by examining the tangent stiffness matrix of the structure near its collapse load. For a structure whose exact initial geometry is known, the actual behavior under any given load can be calculated. Where the imperfections are unknown, the initial geometry is altered by adding those combinations of small imperfections that will excite the likely failure modes. A separate analysis for each of these cases reveals the degree of imperfection‐sensitivity of the respective failure modes in the structure. Experiments were performed on three model structures and a large dome in which both bifurcation and limitpoint behavior were observed. Where the exact initial geometry was unknown, the addition of a suitable set of imperfections produced results in agreement with the experiments. In cases where the more significant real imperfections could be measured before the tests, good agreement was obtained between experiment and analysis.

A method is proposed for rehabilitation and strengthening of multiwythe unreinforced brick masonry walls in buildings where they are the primary structural element for transferring load to the foundation. Shear tests were performed to determine the strength of newly manufactured small‐scale specimens made with cement grout, sand/polyester grouts, and sand/epoxy grouts as the filler materials. Experimental tests were also performed on specimens cut out of existing (about 80‐yr old) unreinforced brick masonry walls that had been strengthened using the proposed technique. The tests were performed to determine optimum parameters such as core diameter and flow and strength characteristics of the core filler materials. The flow characteristics of sand/epoxy or sand/polyester grouts were superior to those of sand/cement grouts, but at higher costs. The primary advantages of the proposed technique include uninterrupted use of buildings, no external aesthetic alterations, and a shorter time span for the complete rehabilitation process. An ultimate strength type design technique for out‐of‐plane loads and a calculation of the equivalent modulii of the composite section is also presented.

The structural advantages and aesthetics of a triangular cross section truss have long been recognized by structural engineers and architects alike. Until recently however, it has not been considered cost effective to design and build this system over the traditional rectangular or two‐dimensional trusses. But with recent advances in welding techniques, the use of computer analysis methods, and the increased availability of structural tubing for truss members, the triangular cross section truss has seen a wide range of new applications. This article examines the advantages and disadvantages of this type of truss as well as past and present uses of the system for various structural applications.

Forty $4\times 4‐\mathrm{in}\text{.}$ wood columns were tested to observe the effects of creep on the time‐to‐failure. Models of column creep based on fundamental beam creep were devised and employed to explain the variability observed in the column behavior and to suggest when and how designers should introduce beam creep effects into design calculations. It was determined that creep would only present problems for extremely high permanent column loading; however, it was also shown that the natural curvature of columns of commercial grade lumber is a more important influence than creep on performance and design for the majority of situations. Methods of introducing creep into analysis, and of estimating variation in column behavior are described.

Strain reversal in the inelastic range may cause a dramatic drop in the tangent modulus for mild steel struts. Other material properties also affect the tangent modulus. Consequently the influence of several of these properties is examined for an electric‐resistance welded steel tube. The variables chosen are: (1) Strain hardening caused by varying the amount of tensile prestrain; (2) strain aging; (3) and the Bauschinger effect, for a specific steel type. The results of 39 stub column tests on rimmed steel specimens show that tensile prestrain reduces the tangent modulus compared with that found for the as‐received tube, but strain aging is seen to be highly significant in reducing this loss in value. The variations obtained for the tangent modulus are illustrated for low, intermediate, and high axial tresses. The variations are given as functions of the amount of tensile prestrain and whether the steel is fully aged or non‐aged. The importance of knowledge of prior strain history of a material is highlighted.

An approximate reliability model for wood structural systems is suggested. The model requires that the probability of first member failure be determined using a wood system model which includes partial composite and two‐way action. The proposed model can then be used to estimate ultimate capacity reliability from first member failure probability. System ultimate capacity is defined as failure of two adjacent members or failure of a set number of members, whichever occurs first. It is demonstrated that the use of first member failure as an ultimate limit state is not necessarily conservative. The level of the reliability with respect to the first failed member versus system reliability must be considered. The relationship between first member reliability and system reliability is an S‐curve. Some guidelines are suggested for determining safe levels of first member reliability as well as setting target reliability levels for use in development of a LRFD code.

This paper presents an iterative procedure that can be used to determine the structural response of sealed insulating glass (IG) units which are subjected to uniform lateral loads and variations of both atmospheric pressure and air space temperature. The solution is achieved by simultaneously satisfying equilibrium conditions and air space compatibility relationships. A flow chart for a micro‐computer program to accomplish the analysis is presented. Selected results show that the distribution of load between the inner and outer plates of an IG unit depends significantly on several factors, including the ratio of the glass plate thicknesses, atmospheric pressure variations, and air space temperature variations.

The present work is a photoelastic investigation of the stress distribution in deep beams with and without web openings. The general form of stress diffusion has been established and the critical zones have been identified. The critical tensile and shear stresses have been evaluated and their sensitivity to various span‐to‐depth ratios and opening positions along the span have been established. Based on stress flow pattern and contour lines of principal tensile stresses, failure mechanisms have been predicted and recommendations have been made for the design of reinforced concrete deep beams.

Experiments are conducted to study the behavior of base plates under the action of axial loads and moments by eccentric loading on the column. The parameters in the study are the thickness of the base plate and the eccentricity of the load. At the lowest eccentricity, failure was by cracking of the concrete, while at other eccentricities the primary mode of failure was by the yielding of the base plate. Comparisons of the test results with the predictions from the Working Stress Method gave a range of 1.09–1.89 for the factor of safety with a mean value of 1.35 for specimens that failed by yielding of the base plate. The strain distributions in the base plate were obtained at various stages of loading. They indicate the existence of a critical section of maximum strain, a section of zero strain and strain reversal. The eccentricity of the load seems to have a greater influence on the strains than the thickness of the base plate. The test results show that flexible base plates when loaded at high eccentricities fail primarily by yielding of the plate and that their behavior is somewhat different to that predicted by the present design methods.

A new method for the analysis of cable‐stayed bridges is presented. The method uses the potential energy of the stayed girder with an iterative procedure. It was found that the iterative procedure is convergent and that a small number of Fourier terms is sufficient. Although only linear analysis is used in solving the numerical examples, various nonlinear effects can be accounted for. However, for practical purposes, the linear solution is quite reasonable. The method is simple and quick, and suitable for use on electronic computers and even pocket calculators. The computer program prepared by the writer can solve any cable‐stayed bridge in a few seconds.

A procedure is presented for estimating reliability bounds for the probability of failure of members sensitive to load directionality effects. The property of multivariate extreme value distributions that zero values of all pairwise correlations imply statistical idependence among the variates is first used to obtain rough estimates of failure probabilities. More refined estimates are then obtained by using expressions for lower and upper bounds for the probabilities, which entail the use of univariate and bivariate probability distributions. In the latter, information is used on the pairwise correlation of load data corresponding to the various directions. In well-behaved wind climates the assumption that data corresponding to any two octants are shown to be mutually uncorrelated results in the overestimation of failure probabilities by a fctor of about two or less.