Journal of Structural Engineering

The elastic lateral buckling capacity of coped steel beams with various coping details is examined by conducting a theoretical parametric study using the elastic finite element program BASP. Cope length, cope depth, and span length were found to have a significant influence on the lateral buckling capacity. In some instances the reduction due to coping can be more than 90% of the uncoped buckling capacity. Simple interaction equations, which utilize the individual lateral buckling capacities of the coped region and the uncoped length, are developed for design.

Very little experimental data are available regarding lateral buckling of coped beams. In order to investigate and understand their behavior, six lateral buckling tests were conducted on a $W12\times 14$ section with different coping details. The results of each test are compared with a finite element computer solution and a proposed design method. Other available test results are also used in the comparison. Results of the tests indicate that the reduction in buckling load due to coping can be very significant depending upon the coping details. It is also found that the adjacent span restraint can increase the buckling load of coped beams significantly. The computer solutions agree with the test results both in buckling loads and buckled shapes. Comparison also indicates that the design method proposed is conservative.

The entire spectrum of incremental collapse behavior of elastic‐perfectly plastic multistory rigid‐frame structures can be described by energy methods. The separation between safe and unsafe load ranges coincides precisely with the transition from bounded to unbounded hysteresis energy absorption. The energy method is preferable to alternate methods that rely on linear programming methods for computation of the envelope, which bounds “safe” loading regimes. This is because the energy method leads to a sharp demarcation between shakedown and incremental collapse, which can be exploited to produce a highly efficient computer program. Illustrative results from the application of the energy method are given for a three‐bay, three‐story rigid‐frame structure.

This paper reports the results of 172 flexural tests of 790 mm by 1,590 mm ($31\mathrm{in}\text{.}\times 62\mathrm{in}\text{.}$) concrete block masonry walls. In addition to evaluating tensile strength both normal and parallel to the bed joint, the parameters included in the study are three sizes of block; three percentages of solid; four block strengths; two types of mortar; hollow blocks and ones grouted with three strengths of grout; and special conditions such as stack pattern, partial grouting, and empty head joints. The results confirm the orthotropic nature of masonry where for hollow blockwork, tensile strength parallel to the bed joint is two to four times higher than tensile strength normal to the bed joint. Grouting of the blockwork resulted in a greater increase of strength for tension normal to the bed joint so that these ratios are between 1 and 1.5. While the percent solid of the block has a marked influence, the tensile strength is not found to be significantly influenced by block size or block strength for the range tested. Grout strength is found to have little influence, particularly for tension normal to the bed joint. Comparison of the test values with allowable stresses recently adopted in North American building codes tends to raise questions regarding the justification for the allowable stresses for tension normal to the bed joints. Conversely, the practice of equating grout‐filled hollow masonry to solid masonry tends to ignore the very large benefits derived from the continuity provided by the continuous columns of grout. A general discussion of behavior and design concludes this paper.

A truck passing over a bridge induces loads which vary with time. To test the ability of available analytical techniques to estimate fatigue life under such loading, crack growth rate tests are conducted with eleven compact‐type specimens using constant and variable amplitude load‐time histories. One variable amplitude load‐time history used in these tests is recorded from an in‐service bridge; other histories used are constructed to isolate minor cycle amplitude and minor cycle mean relative to major cycle mean as test variables. The data show that the mean level of minor cycles within a complex cycle significantly affects the damage caused by the complex cycle, causing the standard rainflow counting‐Miner's rule fatigue life estimating technique to be unconservative. Furthermore, cycles below the constant amplitude fatigue stress range threshold are shown to be damaging when applied as part of a variable amplitude load‐time history. It is proposed that complex load‐time histories be converted to single equivalent cycles through a damage index.

A total of 24 tests have been carried out to investigate the shear resistance of rectangular mortar beams reinforced with three combinations of steel fibers and conventional stirrups; the tests have also been designed to study the effect of partial replacement of cement by pulverized fuel ash (PFA). The experiments have demonstrated the advantages of combining steel fibers and stirrups for shear reinforcement. The partial replacement of cement by PFA results in improved workability and higher long term strengths. Based on the test observations, a rapid method of assessing the ultimate shear strength of reinforced concrete beams containing both stirrups and fibers as shear reinforcement is suggested. Good correlation has been obtained between observed test values and the predictions using the method suggested in this paper.

Features of the phenomenon of interactive buckling of thin‐walled columns are briefly reviewed. The theoretical results are compared with the recent test results from University of Sydney and earlier results from Cornell University. The agreement is very good indeed. The role of imperfections in producing scatter in the prediction of the ultimate capacity of the columns is illustrated. Design procedures, one developed at Cornell University in the seventies and the other recommended by the new American Iron and Steel Institute Code, are examined in the light of the new results. In order to account for the interaction of plate elements, it is suggested that exact local critical stress be used in the effective width formula. To obtain a reliable and safe estimate of the column strength, it is proposed that the collapse load given by the design methods be multiplied by an appropriate factor. This factor must be a function of the key parameters governing the problem. A statistically derived expression for this factor is also suggested.

The test results for 21 full‐scale concrete block walls subjected to uniformly distributed loading normal to the surfaces of the walls are reported. The variables included in this experimental study include three wall lengths of 6.0 m (19 ft, 8 in.), 5.2 m (17 ft, 1 in.), and 3.6 m (11 ft, 10 in.) with a constant 2.8 m (9 ft, 2 in.) wall height. In addition, tests were performed with simple support conditions on all four boundaries, on the bottom and two sides, on only the two sides, and on only the top and bottom of the wall. Also, one series of tests was done with precompression loading in the vertical direction. Three repetitions for each combination of parameters were performed to provide a better statistical sample. The test results were compared with both elastic‐plate and yield‐line analyses. In these analyses, the bending strengths used were taken from tests of masonry assemblages constructed to allow testing of individual joints under bending normal to the bed joint and parallel to the bed joint. Both the load for first cracking and the failure load were investigated. A general evaluation of the comparable allowable wind loadings permitted by current building codes is also included.

Three transversely stiffened A572 Grade 50 steel girders were tested to obtain full moment‐rotation curves for use in the autostress design of continuous‐span bridge girders. The flange and web slendemess ratios were close to the limiting AASHTO values for transversely stiffened girders. The tests included a variety of conditions that affect rotation characteristics: (1) Symmetric and unsymmetric cross sections; (2) long and short spans; (3) relatively large and small amounts of initial out‐of‐flatness; and (4) relatively large shear stresses. Each specimen reached a maximum moment very close to its yield moment and then was able to sustain large plastic rotations as further deflections were imposed to obtain the unloading portion of the momentrotation curve. A simple equation was developed to represent a lower bound for the plastic rotation capacity of the specimens at various moment levels. Two alternative ways of utilizing ah effective plastic moment based on this equation in autostress design procedures are suggested.

An energy method has been used for an elastic formulation of buckling analysis of a simply supported sandwich plate with crossply faces, including the interlayer shear deformation of adhesive layers and the transverse normal and shear deformations of the core. A quasielastic method is used for the solution of viscoelastic analysis of the sandwich plate. Results of the viscoelastic buckling analysis under in‐plane loads are presented for various lay‐up sequences of face plates. Dependence of buckling load on face lay‐up sequence, adhesive bonding stiffness, load ratio, and plate geometry is examined, including the effect of change of buckling modes.

A nonlinear formulation is presented for the analysis of railroad tracks. The finite element discretization is used for a rail element which includes all the deformation modes of the rail. The stiffness of the fasteners, ties, and roadbed is included by a set of springs. A parametric study is carried out to examine the effect of the nonlinear deformations and degradation on stresses and deformations.

A general method for the large deflection analysis of inelastic plane frames is presented. The large deflection analysis is based on the Eulerian formulation in which a member tangent stiffness matrix is constructed with reference to the current deformed configuration. The exact differential equation and the moment‐thrust‐curvature relations of a member subjected to large relative deflection are used for deriving the member tangent stiffness matrix. A member tangent stiffness matrix for W‐sections of elasto‐plastic material is constructed as an example and its application to the large deflection analysis of inelastic frames is demonstrated by several examples. A simple form of the member tangent stiffness matrix is deduced from the above exact formulation by utilizing the assumption of small member relative deflections. It is shown that the simple one can yield excellent results compared to those obtained by the exact formulation. Hence it is reasonable to adopt the assumption of small member relative deflections in the large deflection analysis of inelastic framed structures.

Equal‐leg angle cruciform members are known to be prone to torsional buckling. The primary parameters controlling torsional buckling mode are the width/thickness ratio of the outstanding legs, and the degree of warping restraint provided by the supports, the interconnectors, and the separation gap between the angles. Results are reported of an analytic and numerical study on the effects of warping restraint on the torsional stiffness and on the torsional buckling capacity. The study investigates the effect of different warping restraints, interconnector spacings, and gap separations on the torsional rigidity of four equal‐leg angle cruciforms. The effective torsional rigidity is used in analytic predictions of torsional buckling critical stresses, which are compared with finite‐element, geometrically nonlinear analyses. Recommendations are made for design, and future research directions are suggested.

A study of the effects of soil‐structure interaction on the dynamic response of linear base‐isolated structures is presented. The structures are supported at the surface of a homogeneous and viscoelastic half‐space and are excited at the foundation. The conditions under which the interaction effects are of sufficient importance to warrant consideration in design are defined. These conditions appear to be different than corresponding conditions for conventional structures, and in particular, the interaction effects in base‐isolated structures are not as important as those in conventional structures.

The unit volume weight of the material in a structural body is modeled as a random field, and the boundary of the body is modeled to be random. Both sources of randomness contribute in an interacting way to the variance of any considered self‐weight load effect. A specific type of random vector‐field modeling of the uncertain boundary is particularly useful. It enables an application of Gauss' integral theorem to reduce the problem of the uncertain boundary to a problem of the enhanced uncertainty of the random volume weight field considered solely within the expected structural body.

An analytical solution, based on the flexibility method, is developed to design and analyze open, conical, metal shells having segments of different thicknesses. The shell is used typically as a hopper, which is rigidly attached to the lower end of a concrete silo and is subjected to pressure loading and self‐weight. A computer program, based on the analytical solution, is written to facilitate the design and analysis of the shell. The results of several specific problems show that it is always feasible to use segments of decreasing thickness for the metal hopper of concrete silos to save materials without adding stiffening members at the geometrical discontinuity junction.