Journal of Structural Engineering

Because of large variations in the longitudinal modulus of elasticity of wood it is almost impossible to determine actual values of dead and live load moments and shears in a timber bridge. An approach is presented to calculate the mean values of moments and shears and their coefficients of variation.

An experimental investigation to study reinforced concrete beams with large rectangular openings under pure torsion is reported. The beams were rectangular in cross section. Beam dimensions, and the amount and arrangement of reinforcement were held constant, but opening sizes and their locations were varied. Test results of ten beams are presented and discussed. Torsional strength and stiffness of a beam decrease with increasing opening length or depth, but appear to be marginally influenced by its eccentricity. The beams fail by the formation of a mechanism with four hinges, one at each corner of the opening. Good predictions of the ultimate torque can be obtained by using the theoretical model proposed by the writers in a companion paper.

General relationships between individual joint reliability and overall system reliability in a redundant structure with no repair program are presented. Using a fatigue reliability model, a Monte Carlo analysis provided a distribution of time to failure for various degrees of redundancy. Random variables in the model account for uncertainty in the process of determining fatigue strengths of the joints. The distribution parameters for these random variables are representative of welded tubular joints in offshore platforms. Figures are shown which relate the target safety index of a joint to the reliability against various definitions of “functional failure” of the structure. Also included is an example of how the probability of a second failure occurring within a specified time interval after an initial failure can be predicted. This can provide insight in determining the necessary frequency of inspections.

The collapse load of a reinforced concrete square spread footing under column load is derived by using the theory of plasticity. Several upper bound solutions corresponding to different yield line patterns are obtained. Since the footing slab is rigidly connected to the column end, only the so‐called rigid collapse modes are considered. The solution having the lowest collapse load gives a bending moment at the face of the column equal to that used in American practice. Lower bound solutions are also developed which together with the upper bound solutions show where the exact solution might be. The influence of nonuniform soil pressure under the footing slab upon its carrying capacity is also investigated. A comparison between the theoretical results and existing test data indicates the average measured collapse load is higher than the least upper bound which may partly be attributed to the change in contact pressure, especially near failure. It also proves the bending moment used in some foreign design codes and text books is on the unsafe side.

A model for prediction of a yield load in bolted wood joints is reviewed and modifications to the theory presented. The model predicts a joint load at which the bolt and/or the wood under the bolt behaves plastically. Experimental verification with several large data sets indicate that the modified model generally predicted joint performance within 10% of the actual values. Slight conservatism was inherent due to ignoring friction between members. A discussion of potential applications and limitations is presented.

Concrete inverted T‐beams that support precast stringers on flanges of the inverted T were studied in 27 load tests to failure. Loading included combinations of flexural shear and torsional shear on prestressed and on conventional reinforced specimens. Strength analyses based on test results provide advice for design procedures and reinforcement details applicable to the flanges as well as the shear and flexural strength of such beams.

The concomitant relationship between the bending and tensile strength properties of a common machine stress rated grade of dimension lumber was studied. Test specimens, subjected to a tensile proof load with the survivors tested to destruction in bending, provided the necessary conditional information for the development of multivariate statistical models. Maximum likelihood solutions showed excessive instability in the parameter estimates, while a modified least squares approach for limited dependent variables proved to be far more stable. The latter approach lead to a general solution to the concomitant problem.

A numerical procedure for large deformation analysis of elastic‐plastic frames is presented. The procedure is based on an Eulerian formulation, which was developed initially for elastic systems and is extended herein to include elastic‐plastic effects. Local member force‐deformation relationships are based on the beam‐column approach and changes in member chord lengths due to axial strains and flexural bowing are taken into account. A computational technique for determining the nonlinear response is described in detail. The technique utilizes an incremental load approach with Newton‐Raphson iteration to satisfy joint equilibrium equations. Numerical solutions are presented for three structures and are compared to those reported by previous investigators.

This paper presents the development of an analytical model for predicting the torsional strength of reinforced concrete beams containing a rectangular opening. The method is based on the collapse load analysis. Both upper and lower bound solutions for the strength are presented. The predictions of the two approaches are then compared with the test results available in the literature. A good agreement between the theory and experimental results is obtained.

Rational shape for the load contours in L‐shaped columns is proposed using the inverse method of analysis. Determination of the ultimate loads from the appropriate interaction curves derived from the shape of load contours is shown. An alternate and simple method based on the concept of an equivalent square or rectangular column is proposed to determine the theoretical ultimate loads using the interaction diagrams in square or rectangular columns. Theoretical loads computed by the two proposed methods are compared with the test results of 45 columns.

Behavior of fabricated tubular steel beam‐columns as commonly used in offshore structures is studied for the entire range of monotonic loading up to ultimate load including the post‐buckling branch of unloading, using assumed deflection method. In the present approach, equilibrium is established only at a critical section of a beam‐column using closed form analytical expressions for moment‐curvature‐thrust relationship of a fabricated tube. The computer model developed on the basis of this approximation is compared with tests and other analytical methods, and it is found that the assumed deflection method predicts the behavior of actual tubes with good accuracy, yet it simplifies the analysis drastically. A considerable amount of data has been obtained and presented concerning the behavior of cylindrical tubular beam‐columns. It is concluded from this numerical study that initial imperfection (out‐of‐straightness), lateral load at mid‐span, and bending moment at ends affect the behavior of a beam‐column in a similar manner. As these values increase, the ultimate strength is reduced significantly while their associated load‐deflection or shortening relations become flatter.

This paper presents a state of the art review of mathematical programming methods used in the design of skeletal elastic structures in which the possibility of altering the shape, position or layout of the members is considered. Virtually every type of optimization procedure including linear, nonlinear, and dynamic programming has been applied to this design problem. These methods have been implemented using three main approaches. The first, referred to as the ground structure approach, is one in which members are removed from a highly connect structure to derive an optimum subset of bars. In the second approach the co‐ordinates of the joints of the structure are treated as design variables and moved during the optimization procedure to enable an optimum layout to be designed. The third type of method includes those which allow for topological considerations at certain points during the design process and generally keeps the design variables in two separate groups. The paper discusses the way in which each of the mathematical programming methods has been applied to these approaches.

Plane and space frames are considered. The member end rotations relative to the chords of the deformed member are assumed to be small. Large translations and rotations of the chord are allowed. The longitudinal and transverse displacements are respectively interpolated by linear and cubic functions. The axial strain due to the transverse displacement is averaged over the element length. The averaging is shown to reduce the strain energy and the element stiffness. Without it the element would generally be too stiff. The incremental stiffness matrices are derived in Lagrange coordinates for small rotations. Solution procedures based on a fixed coordinate system and a moving or updated coordinate system are presented. Numerical results indicated that the fixed coordinate procedure works well for small displacement problems. The updated procedure is necessary if large displacements are involved. Comparison of numerical results with those of other methods indicates that the methods presented are competitive.

Current methods for the design of underground structures are reviewed. It is shown that they share the same approach when including the effects of soil‐structure interaction (SSI) in the design loading. This common approach has a major handicap in that it attempts to dissociate the loading from the structural response. An alternate approach which recognizes the importance of this coupling is described. This approach leads to a design methodology which incorporates the effect of SSI in a systematic manner. Furthermore, the implementation of this methodology is straightforward and requires little or no modification to state‐of‐the‐art design and analysis computer programs.

A computer method is presented for the analysis of cable‐stayed prestressed concrete bridges for time‐dependent effects of creep and shrinkage of concrete and relaxation of prestressing steel. Nonlinear behavior due to change of geometry and change of stiffness arising from bending by axial forces is included.

The ordinary moment distribution method for co-planar bending can be expanded into a three dimensional analysis to include pure torsion and warping torsion as in rigid steel frames. Torsional rigidities with both pure and warping terms can be calculated according to member properties and boundary conditions. Together with member bending rigidities, distribution factors at a joint are obtained. Finally, carry-over factors are found through equilibrium.

A realistic prototype high-rise building was designed and modeled using linear elastic (and also nonlinear) degrading stiffness idealizations. Using an effective damper mass ratio of 0.026, three different techniques were used to design an optimum tuned-mass damper (TMD) for the prototype. All were found to give essentially the same design. The response of the idealized prototype building to a strong ground motion was computed with and without a TMD. The TMD did not reduce the prototype's maximum response. Based on these results, vibration absorbers do not seem effective in reducing the maximum seismic response of tall buildings.

An analysis is performed to study the behavior of two parallel but not colinear shear walls coupled by a cross wall subjected to lateral loading. It is shown that the cross wall essentially acts as a shear transfer medium. The effectiveness of coupling the two parallel walls depends on the height-to-width ratio of the cross wall and criteria for full coupling is presented.

Multivortex (MV) windfields have recently been established as frequent characteristics of intense tornadoes, introducing new issues in tornado risk analysis and loading characterization. A potentially important issue in the quantification of MV loading characteristics regards the probability that a structure will be hit by one of these high velocity secondary vortices. Using a simple model of multivortex flows, analytic relationships have been derived to facilitate the calculation of multivortex tornado loading hit probabilities for structures and facilities. A numerical integration method as well as an approximate solution have been developed to compute the cycloidal areas traversed by secondary vortices. Example calculations using current estimates of MV parameters suggest the conditional strike probabilities for point targets within the intense windfield core region are about 0.4 for a continuous single secondary vortex. To estimate the total MV wind loading risks, these conditional probabilities are combined with estimates of multivortex frequency and tornadoe strike probability.