Journal of Structural Engineering

Based on the continuum approach, a general analysis is presented for a pair of laterally loaded, coupled shear walls, supported on either rigid or flexible foundations, with one or two stiffening beams at arbitrary positions on the height. Closed solutions are given for the three common load cases; a uniformly distributed load, a triangularly distributed load, and a point load at the top, simulating both wind and earthquake actions. Numerical examples show that structural performance can be improved considerably by the addition of two stiffening beams, the greatest benefits being achieved when the beams are located at roughly one‐third and two‐thirds of the height, when the structure is supported on rigid foundations. The corresponding optimum position for a single stiffening beam is between 0.4 and 0.5 of the height of the structure. The optimum beam positions occur at lower levels if the structure is supported on flexible foundations.

In the recent design of a major tubular roof structure involving parabolic hollow structural section (HSS) arches, a cranked‐chord K‐type connection near the support points was identified for further evaluation by laboratory testing. A stiffened form of the connection was tested in triplicate and deemed to satisfy the design criteria. Subsequently, a study was initiated to establish an appropriate design method for such connections, without stiffeners. Fourteen specimens have been tested, involving ten cranked‐chord K‐connections and four similarly sized T‐connections as control specimens, with the aim of establishing whether these cranked‐chord connections behave as conventional K‐connections or as T‐connections, or a combination of both. It is shown that cranked‐chord connections can be designed as overlapped K‐ (or N‐) connections using the current International Institute of Welding (IIW) recommendations, subject to their parameter limits of validity. An argument is also made for a slight relaxation of these limits of validity.

In the study of the performance of walls constructed of brick veneer with metal‐stud backup, both experimental and analytical methods have been used. In the analytical studies, mathematical models have been developed to simulate the behavior of the wall systems. In this paper, three mathematical models are presented for: (1) Performing parametric studies; (2) simulating the composite action of the wall system; and (3) modeling the inelastic behavior of the wall after the development of a crack in the brick veneer. A method for predicting the cracking load of the brick veneer also is presented. The results of the parametric studies show that boundary conditions, tie stiffness, construction method, and the flexural rigidities of the wall system affect the system's performance. Composite action between the components of the wall systems do not appear to be significant. The inelastic behavior of the wall system shows that significant lateral load is transferred to the metal‐stud backup wall after the brick veneer cracks. The failure loads of the brick veneers were predicted to a good degree of accuracy.

An extensive test program on a range of cold‐formed rectangular and square hollow sections subjected to combined bending and concentrated force is described. The concentrated force was applied by welding a square hollow section (called the branch member) to the center of the member under test (called the chord member) and perpendicular to it. The chord member was simply supported with the concentrated force at the center of the span. The span was varied in order to determine the interaction relationship between bending moment and concentrated force. Tests under pure moment and pure concentrated force were performed for control purposes. The ratio of the width of the branch member to the chord member (β) used varied from 0.5 to 1.0 so that failure modes ranging from local bending and buckling of the face of the chord member to web crippling were observed. In addition, the thickness of the chord‐member sections was varied so as to produce a range of section slenderness and failure modes from buckling to yielding. The results are compared with the design procedures in the 1986 AISI Specification, Australian Standard AS1538 of 1988, CIDECT Monograph No. 6 of 1986, and other proposed procedures. In addition, a comparison with plastic mechanism models is provided.

A new model has been developed to study the elasto‐plastic interaction between the local and Euler buckling modes in a cold‐formed thin‐walled channel column under concentric and eccentric loading. Plate (local) and column (overall) imperfections have been considered in the analysis. The locally buckled column can be treated as an assemblage of half wavelengths of local buckling of perfect column under uniform compression. Given these considerations, the elasto‐plastic M‐P‐Φ curves of the short sections that form the column are derived in the elasto‐plastic range by using the large deflection elasto‐plastic finite strip method developed by the writers. Then a beam‐column approach associated with finite integration is presented to predict the strength of the column by means of the M‐P‐Φ curves of the short sections of the column. An experimental program was carried out, and the moire fringe method was extended to a large area encompassing the whole length of the column. The comparison of experimental with theoretical results shows very good agreement.

The critical load of a steel frame structure is dependent on joint details and flexibility. For a conventional type of skeletal structure made up of beam and column elements, the geometrical change is normally negligible. However, the variation of the joint stiffness may be significant near the ultimate limit state. In such cases, the rigorous second‐order nonlinear analysis for determining the maximum load is cost‐ineffective, while the bifurcation load approach is erroneous, because the change in connection properties with respect to the applied loads is not known. This paper introduces a numerical procedure called the semibifurcation method for the determination of the buckling load of steel frames that does not suffer from the drawbacks of either method. In the proposed technique, the variation of the joint stiffness is taken into account in the calculation of the buckling load of a steel frame. This leads to a significant saving of computer time without a notable reduction in accuracy for most conventional and braced steel buildings.

The strength of a short composite steel‐concrete beam column is affected by variations in the strengths of concrete and steel, the cross‐sectional dimensions of concrete and steel section, the placement of steel section and reinforcing bars, and the strength model itself. The effects of these factors on the variability of the ultimate strength of square short composite beam columns in which steel shapes are encased in cast‐in‐place concrete are studied. The results indicate that the specified concrete strength, the structural steel ratio, and the end eccentricity ratio influence the probability distribution properties of short composite beam‐column strength. The end eccentricity ratios of 0.5 or less are critical since they have a very significant effect on the beam‐column strength. As expected, the beam columns with slenderness ratios near the ACI Building Code upper limit for short columns produce lower strengths than the corresponding cross sections.

An important characteristic of structures that exhibit material nonlinearity is that the internal stresses are redistributed when the stiffness properties of the members change. Based on this physical characteristic of structures, an efficient analytical method for the nonlinear analysis of structures is presented here. In his analytical method, the overall response of the structure is determined by considering: (1) The elastic response of the structure to external loads; and (2) the stress redistribution that results from the member yield excursions. One advantage of this method is that the stress redistribution may be represented in terms of the elastic stiffness matrix of the structure and not the tangent stiffness matrix. Another advantage of this method is that the only parameters that have to be evaluated and updated throughout the analysis are the member stresses and the member deformations. Hence, there is no direct evaluation of the structure displacements or the tangent stiffness matrices.

It is accepted practice to test field‐cast cylinders in the laboratory under control conditions, then assume that the determined strength is representative of the compressive strength of the concrete in the structure itself. In recent years, pullout tests have been increasingly used to evaluate the compressive strength of in‐place concrete. In this paper, it is emphasized that concrete subjected to a pull‐out force experiences a complex state of behavior, the existence of which cannot be attributed to a uniaxial state of stress. First, a brief review of the experimental studies is presented, and the relevant theoretical studies are evaluated. This is followed by a discussion of the numerical modeling scheme adopted in the present study. Finally, along with a parameter study, the writers describe the progressive failure of concrete subjected to pullout tests based on their plastic‐fracture predictive finite element analysis.

Reliablity procedures are developed for girder bridges. Load models are based on the available statistical data. The derivation of load models is described in other papers. Resistance models are developed by simulations using the available test results for materials and components. The girder behavior is described by a moment curvature relationship. Bridge capacity is determined in terms of the maximum truck load before failure. The analysis is performed for a single unit truck, a semitrailer, and combinations of these trucks. For a given truck position, the load is gradually increased until the deformation (maximum deflection) exceeds the critical level. The developed resistance models are used in the reliability analysis. Reliability indices are calculated for noncomposite and composite steel girders, reinforced concrete T‐beams, and prestressed concrete girders. The calculations are performed for girders and structural systems. Reliability indices for the system are higher than for girders. The effect of correlation between girder strengths is analyzed. Girder bridges behave as parallel systems. Sensitivity functions are developed for various parameters related to the considered girders. The developed approach is demonstrated on typical girder bridges.

The objective of this paper is to present preliminary analyses of a set of acceleration response records obtained during the October 17, 1989 Loma Prieta earthquake $(M_s=7.1)$ from the 60‐story vertically tapered, pyramid‐shaped Transamerica Building—a landmark of San Francisco. The building was instrumented in 1985 with 22 channels of synchronized sensors consisting of 13 uniaxial ac‐celerometers deployed throughout the structure and connected to a central recording system and three triaxial strong‐motion accelerographs at three different levels of the structure. No free‐field accelerographs are at the site. The acceleration records permit the study of the behavior of this unique structure. The predominant translational response of the building and the associated frequency at approximately 0.28 Hz are identified from the records and their Fourier amplitude spectra. The records do not indicate any significant torsional motion. However, there is rocking type soil‐structure interaction, and an associated frequency of approximately 2.0 Hz is identified from the Fourier amplitude spectra of the differential motions between the ground level and that at the basement. In addition, the response spectra for the basement motions indicate significant resonance in both directions at a period of approximately 0.5 seconds.

A detailed analysis of the recorded seismic response of the Transamerica Building during the October 17, 1989 Loma Prieta earthquake is presented. The system identification algorithm used for the analysis is based on the discrete‐time linear filtering approach with least‐squares approximation, and assumes a multi‐input, single‐output model for the building. Fifteen modes in the north‐south direction, and 18 modes in the east‐west direction are identified from the records. The analysis shows that the building's response to the earthquake was dominated by a coupled mode of vibration at 0.28 Hz in the southwest‐northeast direction, which is almost parallel to one of the diagonals in the building's square cross section. The reason for this behavior is the symmetry of the building's structural characteristics, as well as the strong polarization of the S‐waves of the earthquake. Several higher modes of the building were excited during the strong‐motion part of the earthquake. The results also show a significant amount of rocking in the building at a frequency of 2.15 Hz.

A semianalytical procedure is presented for the axial buckling of elastic columns with step‐varying profiles. Profiles with continuous variations can be approximated, to any desired degree of accuracy, by a series of step variations. The formulation leads to a general procedure that can be applied to any continuous or discontinuous profile regardless of the number of steps. Since the step changes of the profile are represented by distributions, the differential equation cannot be solved in the ordinary sense. The differential equation is therefore converted to an integral equation. The solution of the integral equation is obtained by polynomial functions. The formulation involves a significant amount of algebraic manipulations. This problem is alleviated by using a symbolic manipulation system to carry out the algebraic manipulations. The integral kernels are obtained for the different boundary conditions. Formulas for buckling loads for members with variable profiles and different boundary conditions can be obtained in terms of the section and profile parameters. The example problems present the solution of some common columns with variable cross sections. The procedure can be used to derive the elastic and geometric stiffness matrices for beam columns with variable cross sections as well as for other elements.

The behavior of back‐to‐back double‐angle bracing members subjected to out‐of‐plane buckling under severe cyclic load reversals is investigated. Eight full‐size bracing members made of double angles of A36 steel with welded stitches and end gusset plates were tested under large cyclic deformations representative of severe earthquakes. Two types of section configuration were investigated, which included conventional and strengthened back‐to‐back sections. The first specimen was designed according to the current design practice, and the effects of stitch spacing and width‐thickness ratio were studied by changing those parameters in subsequent specimens. The tests showed that early fracture due to severe local buckling of the outstanding legs was the common mode of failure of conventional back‐to‐back angles. Local buckling was so dominant that stitch spacing did not play a major role. Smaller width‐thickness ratio reduced the severity of local buckling, leading to an increase in ductility and energy dissipation capacity. Strengthening of conventional back‐to‐back angles by welding two inclined plates did not improve member response because of asymmetrical buckling.

The concept of inelastic response spectra is now well recognized. The inelastic response spectra can be generated from the peak ground motion parameters by employing amplification factors and deamplification factors. The present study aims at generating amplification factors for two ensembles of artificial earthquakes using the actual probability distribution of the peak displacement response of a viscously single‐degree‐of‐freedom system. It is shown that the knee periods of each spectra of the ensemble vary considerably from those of the mean spectra. This results in considerable difference in the amplification factors in the velocity region. The amplification factors determined using the actual probability distribution of the elastic spectra are within 10% of those obtained using the statistical analysis.

Eighteen grouted pile‐to‐sleeve connections were tested to examine the influence of combined loading, relative shear‐key location between pile and sleeve, pile‐sleeve eccentricity, and grout strength. The results indicated that combined loading had no detrimental effect on ultimate capacity of a grouted connection. Ultimate capacity was not affected by the position of shear keys in the pile relative to those in the sleeve or by thickness variations in the grout annulus. The capacity of connections varied with the square root of the grout strength. Results were compared with recognized empirical formulations. The results indicated that safety factors could be reduced and yet maintain acceptable safety indices. Examination of tested grouted‐connection specimens indicated that the major load‐resisting mechanisms are grout commpression struts and friction that develops at the grout‐steel interface. A simplified analytical model was developed using concrete constitutive relationships, and various geometric and material parameters were investigated. The analytical results indicated that increases in shear‐key height or reduction of shear‐key spacing may not lead to higher ultimate strength of the connection.

A finite element formulation for the large‐deformation analysis of space‐frame structures is presented. The formulation is based on second‐order geometric nonlinear theory and Vlasov's theory for thin‐walled beams (i.e., large displacement of members with small strains, which includes the warping deformation influence). The influence of member‐distributed loading on the geometric nonlinear response of space‐frame structures also is included. An updated Lagrangian formulation is used to model large joint translations and rotations. Prismatic beams of arbitrary cross section are considered. Rodriguez's modified rotation vector is used to represent angular deformations, which avoids rotational discontinuities at the joints of deformed space‐frame structures. Numerical results and algorithmic details are presented in a companion paper.

In the companion paper, a finite element formulation for analyzing prismatic thin‐walled space‐frame structures with arbitrary cross sections, was developed that maintains rotational continuity and eliminates moment imbalances at the corner nodes of space‐frame structures. This paper focuses on the development of the global stiffness equations consistent with an updated Lagrangian representation of second‐order geometric nonlinearity, solution of the nonlinear equations with a quadratically converging work‐increment‐control technique, updating the element coordinate transformation matrices, nonlinear transformation of element stiffness equations from the shear center to any arbitrary point on the cross section, and the presentation of sample numerical results for an L‐shaped space‐frame structure.

A previous analysis of the means and confidence limits of bridge deflections and axial shortening due to uncertainty of material parameters is extended to consider the combined effect of random variability of material parameters and random spatial variability of material compliance. The latter effect is calculated in a simplified manner adpating the scheme of latin hypercube sampling and using a limited number of terms in the spectral decomposition of the power-response function of creep compliance in space. It is found that the effect of spatial random variability is rather small compared to the effect of randomness of material parameters. In practice it can be neglected, although the present approximate calculation is not difficult.