Journal of Structural Engineering

Nonlinear problems in structures are generally solved by using traditional finite‐element methods. The computations are often accurate, but they are also expensive. A simplified model could, however, be sufficient either in an optimum design problem or if only a rough analysis of the structure is sought. A simplified tool using Damage mechanics is developed for reinforced concrete analysis.

A general time‐step analysis procedure for prestressed and partially prestressed concrete composite beams is presented. The analytical model considers the effects of creep (time and cyclic dependent), shrinkage of concrete, and relaxation of prestressing steel. The model developed satisfies equilibrium of forces and compatibility of strains with time and leads to the prediction of stresses and strains in the constituent materials at any time t and number of cycles $N_t\text{.}$ For the initial time or the first cycle, the model is shown to reduce to existing models applicable to the analysis of partially prestressed beams under short‐term static loading. Solutions for uncracked composite sections as well as cracked and uncracked noncomposite sections are derived as special cases. A computerized parametric evaluation is briefly described and numerical examples are developed to illustrate the application of the method.

Reliability of framed structures is studied assuming loads and component strengths are random variables. The incremental load model is extended to semibrittle failure of components. For brittle component failure, an efficient technique is introduced. The method is also extended to simultaneous multiple loads. Strategies are established to enumerate significant failure modes of a structure. Incomplete failure modes of structures are also studied. The significant modes are used in a Monte Carlo simulation to obtain accurately a safety index for the system. Applications and numerical examples are presented.

An approach to estimating the limit and post‐limit behavior of a framed structure from its geometrically linear response is presented. The method follows from a particular restatement of the weak form of the nonlinear differential equations governing the response of the structure, and is based upon the observation that geometric effects are insensitive to redistribution of the moment field in planar framed structures. The formulation gives insight into the relationship between important observed phenomena and the complex nonlinear governing equations. A novel derivation of Home's method for estimating the nonlinear response of frames is presented and extended to the important case of nonproportional loads. The role of the linearized geometric stiffness matrix, and the buckling eigenvalues is clearly demonstrated. Several examples are given to evaluate the validity of the inherent assumptions and to demonstrate the effectiveness of the approach.

The empirical results of a test program studying the effects of rectilinear confinement in high‐strength concrete subjected to a monotonically increasing compressive axial load was reported. Twentyfour columns made of high‐strength concrete with compressive strength $f_c^{\prime }$ ranging from 12,130–13,560 psi (83.6–93.5 MPa) and rectilinearly confined with lateral ties and longitudinal rebars were tested. The stress‐strain behavior was studied with respect to the effects of the volumetric ratio of lateral ties, the concrete cover, and the distribution of the longitudinal steel around the core perimeter. Expected general improvements in the strength and ductility of the high‐strength concrete with rectilinear confinement was observed. The lateral steel confinement was not as effective as in low and normal‐strength concrete. Columns with four longitudinal rebars exhibited much less ductility than columns with eight longitudinal bars. All the specimens failed with a single shear failure plane. An empirical model for the stress‐strain curve of rectilinearly confined high strength concrete using three parameters: ($f_0\text{,}$ ${\epsilon }_0$), ($f_i\text{,}$ ${\epsilon }_i$), and ($f_{\mathrm{2i}}\text{,}$ ${\epsilon }_{\mathrm{2i}}$) was proposed. Equations for the parameters were developed.

A new and simple modeling procedure is presented for the probabilistic definition of maximum wind speed due to tropical cyclones. Using a fluid dynamic model, the history of the cyclonic winds is first reconstructed for places of interest on the coast from information of paths and intensities. A probabilistic treatment then permits an estimation of the maximum wind speed associated with different return periods, using various probability distributions. The results from this model are similar to those obtained from more elaborate m$\underset{¸}{e}$thods. The model has been successfully used as part of a large computation scheme to improve coastal wind predictions in México.

Any theory of design for reinforced concrete structures implies a minimum structural cost for which all failure modes, or limit states, are covered in the design for specified loading and geometric configuration of the structure. The critical limit states are safeguarded by adequate performance at ultimate and service design load levels through adopting a certain philosophy of design. The present paper proposes a limit‐state design method based on a design philosophy whereby direct design control is exercised on the service behavior of the structure by prespecifying the yield‐moment and rotation capacities of each of the critical sections of the structure. Both strength and deformability criteria are simultaneously satisfied in the design at the specified service and ultimate load levels. An optimal limit design formulation for the design problems is obtained. Suitable algorithms and related computer codes are used to solve the design problem having a nonlinear cost function and explicit nonlinear constraints. An example continuous beam is completely designed by the proposed method. A practical‐sized building frame example is also presented to demonstrate an application of the method to moderately complex framed structures.

The results of an experimental investigation into the strength and collapse behavior of Australian‐produced cold‐formed square and rectangular hollow section columns is described. The individual plate strengths calculated from the stub column tests on both square and rectangular hollow sections are compared with predictions based on the effective width formulae in the American Iron and Steel Institute (AISI) specification. The long column test results on square hollow sections are compared with the AISI class A and class B column curves as well as a proposal based on the Structural Stability Research Council (SSRC) multiple column curves. The sections studied had plate width to thickness ratios in a range where local buckling and yielding occur almost simultaneously, leading to rapid load shedding after ultimate. Theoretical models of the postultimate collapse behavior, based on local plastic mechanisms, are summarized in the paper. The theoretical models are compared with the collapse behavior of the stub columns and long columns.

This paper deals with the behavior and design of welded joints to the tension chord of triangular trusses, with two Warren‐type web planes and a single tension chord, made of rectangular tubes (hollow structural sections or HSS). Experimental programs are outlined in which simplified double‐T joints and triangular truss segments with double‐K gap joints were tested. Parameters investigated include the gap size, the web‐member‐width‐to‐chord‐width ratio, the chordwall‐width‐to‐thickness ratio, and the angle between web planes. The mechanics of deformations of the double‐T and double‐K joints are discussed in relation to yield line theory, and this theory is shown to give a good prediction of the experimental joint stiffnesses and strengths. Strength equations are proposed to cover tension chord gap joint behavior with respect to chord wall bending and a design example is outlined.

The behavior of reinforced concrete (R/C) shell elements subjected to membrane stresses is examined. The governing equations are derived from equilibrium, compatibility, and the constitutive law of reinforced concrete under biaxial stress states. Using these equations, load‐deformation relations of membrane elements are traced up to and past the ultimate load. There are three types of failure modes: (1) Yielding of reinforcement in both directions; (2) yielding of reinforcement in only one direction combined with the compressional failure of concrete; and (3) the failure of concrete without the yielding of any reinforcement. Using an analogy with beams in flexure, it is shown that the element behavior is ductile for the first two modes and brittle for the last mode. One of the major factors that influences the failure mode is the amount of reinforcement. Two sets of boundaries that separate the three different failure modes are identified in terms of reinforcement ratios. One set of boundaries separates the first two failure modes. This set defines the limit of reinforcement beyond which a commonly used strength formula based on the yielding of reinforcement alone is not valid. The other set, which separates the last two failure modes, defines the limit beyond which the element behavior is brittle. These boundaries are presented in a form suitable for use as design guides.

The collapse of reinforced concrete structural elements subjected to compression is linked to the instability of the reinforcement bars. This phenomenon may occur in the longitudinal region between two consecutive hoops, or may involve a number of hoops, deforming them through tension until they fail. A criterion is given which makes it possible to determine the unknown length of the region of longitudinal reinforcement involved, in relation to the geometrical and mechanical characteristics of the column. The critical load is then calculated assuming the configuration of a compressed straight bar with built‐in ends, bound on unilateral elastic supports. A comparison with the results obtained experimentally by other authors makes it possible to assess the reduction coefficient to apply to the theoretical values deduced.

Experimental results from constant amplitude fatigue tests are analyzed to account for the possible effect of residual stresses induced by welding of the specimens. It is shown that large amplitude precycling of a welded specimen can significantly change the S‐N curve for the specimen. Primarily the precycling reduces the fatigue damage caused by subsequent small amplitude cycles. Using simple hypotheses for the initial stress state and the following stress‐strain behavior, it is shown that Gerber's formula for the effect of mean stress gives results agreeing with the experimental data. Finally it is shown that consideration of residual stresses changes the S‐N curve enough to cause significant modification of the variable amplitude fatigue life predicted by the Rayleigh approximation.

Steel tanks for liquid storage often consist of a cylindrical shell attached to a steel bottom plate which rests on the ground. In many cases neither the bottom plate nor the cylindrical shell are fixed to the ground. When such an unanchored tank is subjected to seismic ground shaking, the lateral inertia of the contained liquid contributes to the overturning moment, but its weight cannot contribute to the stabilizing moment until some uplift of the bottom plate occurs. The hold‐down force, due to the weight of liquid resting on the uplifted portion of the bottom plate, provides the necessary resistance against overturning. However, this benefit of uplift comes at the cost of very high vertical compressive stresses in the tank wall at the base in the region diametrically opposite to where the maximum uplift occurs. The benefits of uplift can be reaped without some of its detrimental effects if the tank wall is preuplifted all around the circumference by means of a ring filler. An annular portion of the base plate is also preuplifted, but is not supported by the ring filler. The weight of liquid resting on that preuplifted portion of the base plate then becomes effective in resisting the overturning moment. For a 127 mm diameter Mylar tank, it is shown by experiment and analysis that preuplift increases the lateral load capacity by a factor of up to 2.

The purpose of this note is to demonstrate a method for generating stiffness matrices for nonprismatic members which can be included in any computer program for solving rigid frame problems. In creating member stiffnesses, the conjugate beam method has been employed. For generalization, numerical methods are used for solving the conjugate beams, because different types of nonprismatic members have different section properties, and therefore cannot be expressed with a single mathematical function. For the convenience of computer programmers, the writers included the fixed-end moments and shears due to concentrated loads and uniform loads.