Journal of Structural Engineering

A direct matrix method for the calculation of the elastic critical loads on rigid frames is presented. The effect of the secondary axial forces in columns is readily included. The procedure leads to a linear eigenvalue problem where the smallest root from a product matrix represents the critical load. The computational aspects of the method are considered, and the analysis is reduced to the setting up of two main matrixes. The first matrix is directly evaluated from the geometrical and loading properties, and the second is the linear elastic stiffness matrix under a fictitious system of transverse forces. Economy in the setting up of the stiffness matrix is achieved by treating individual columns as substructures. The method is applied to three example frames, and the numerical results are compared with those obtained from stability‐function solutions.

A method for designing a trussed type structure subject to stress and displacement constraints has been developed and applied to typical examples of structural optimization. The method is based on the transformation of a constrained minimization problem with homogeneous constraints into an unconstrained minimax formulation. The latter problem is then solved using the norm optimization method. Conceptually, the technique substitutes the constrained minimization problem by a sequence of unconstrained formulations. The method is simple to implement, and does not suffer from problems inherent to the more classical penalty approach. An implementation on wellknown examples emphasizes the main features of the method.

The dynamic responses of a prototype space‐frame offshore structure to both measured and simulated stochastic wave forces are evaluated. A linearized, nondeterministic frequency domain analysis is made on a two‐dimensional model of a prototype offshore production platform located in the Gulf of Mexico. Linear ocean waves are modeled as a zero‐mean, stationary, ergodic Gaussian process represented by a one‐dimensional wave energy density spectrum. Simulated stochastic wave forces are computed via the Morison equation which is modified to account for both the effects of wave‐structure interaction and for the equivalent linearization of the drag force in the timeaverage, mean‐square sense. The dynamic equations of motion for the wavestructure system are solved by the normal mode‐superposition technique. The coupled generalized damping matrix is diagonalized through an optimization procedure. Iterative procedures are used to determine the equivalently linearized drag term and to uncouple the generalized damping matrix. Dynamic responses of the prototype production platform are compared using both simulated and measured wave pressure force spectra.

The ultimate carrying capacity of cable networks under dynamic loading is investigated. Geometric as well as physical nonlinearities are considered. The explicit Newmark's β method, with $\beta =0\text{,}$ is used to integrate the equations of motion. The method has the advantage in that there is no need to form or store the overall stiffness matrix or perform any iteration inside the time interval. The internal forces are calculated by considering direct equilibrium in the deformed position. Numerical tests are performed for two wellknown cable networks. Comparative results are presented when different piecewise linear approximations to the nonlinear stress‐strain curve are used. The influence of the linear elastic, nonlinear elastic, and nonlinear elasto‐plastic material properties on the ultimate dynamic behavior of cable networks is also presented.

The static behavior of single anchor fasteners in concrete is investigated up to pull‐out failure by means of a mathematical model. Form‐fit, expansion and adhesive anchors are considered. The nonlinear behavior of the composite system, due to concrete cracking and crushing (tensile and compressive failure), is described by appropriate constitutive laws. A finite element approach is used to calculate the nonlinear response of the system. Only concrete failure is considered, anchor and bond failure are excluded. The relevant system parameters for each kind of fastener are studied. The load‐carrying capacities and cracking zones determined with the aid of the mathematical model are compared with those obtained from experiments. The present analytical results agree well with experimental results.

The concept of providing story‐deep and bay‐wide discrete staggered panels to resist lateral loads in tall buildings has been introduced. Three systematic arrangments of panels have been investigated and critically assessed for their feasibility and advantages as compared to the conventional shear wall system. By suitably positioning and dimensioning the staggered panels lateral deflections can be controlled. Significant reduction in the shear wall base moment is achieved in the proposed system. However, the skeletal members attract more end forces which is not a serious shortcoming. Concentration of stresses occurs at the corners of a panel where columns and girders meet; but the stress‐diffusion is steeply rapid. Idealization of discrete panels as rigid bodies or wide columns with rigid arms makes the frame stiffer. A finite element method of analysis using Macleod's pair of elements, which considers inplane rotation, has been found suitable. The shear panels can be made functional as in the case of apartment constructions. Large unobstructed floor areas can be created by staggering the frames in plan.

Time history response of an elevator rail and counterweight model is studied using numerical and experimental methods. Beam finite elements are used to model the rail and the counterweight. When in contact, the rail and the counterweight are assumed to be connected by very stiff springs. Wilson‐θ method is used to perform the forced response computations. The long computing times result from the need for extremely short time steps used to integrate the nonlinear equations. In addition to the development of simple models and the use of Guyan reduction method, two techniques are introduced to reduce computing time. The numerical and experimental results compare both favorably and qualitatively.

The process of accounting for subjective information, insight, and wisdom in structural engineering decision making is a matter of debate. One effort to include verbal ideas involves the use of the fuzzy set theory. This paper may be considered as a primer for applications in structural engineering. The first part provides a justification for the theory and then simple fuzzy operations are developed and contrasted with those of conventional set theory. Two applications are then developed. The first considers the fuzzification of objective information where cylinder test results on concrete are used as a basis for the evaluation of the actual strength in a structural member. The two may not be the same and the subjective argument to assess the concrete strength of the beam is treated by fuzzy logic. The second concerns an engineer's assessment of the damage to a structure and subsequent repairs. Here a plan for starting such a problem is provided within a rule‐based assessment system called SPERIL version I. Finally, some of the problems of practical fuzzy set analysis are analyzed and then placed in a general scheme for uncertainty identified.

The 1981 failure of walkways in a Kansas City hotel occurred because of inadequate connections between hanger rods and bridge beams. This paper briefly reviews the collapse and examines means of strengthening the connections, such as had been suggested in the aftermath. The additions of a heavy washer plate and of an end plate are analyzed by approximate plasticdesign methods, and the results of simple tests on replicas are reported. Generally, good agreement among analytical implications, experimental results, actual loads, and conclusions by the National Bureau of Standards was found. The various indications of capacity are compared.

A description of the discovery of the delamination of the 3‐ft (76‐m) thick concrete dome portion of a nuclear power plant containment. An investigation was made as to the causes of the delamination, the strength of the delaminated structure, and repair techniques. Repairs were made consisting of epoxy injection of cracks in the lower 2 ft (51 m) of the dome, providing radial anchors between the lower portion of the dome and the upper “cap,” the delaminated portion, which was removed and replaced with new concrete.

The sources of nonlinearities in the behavior of bolted steel connections are briefly studied, and a connection model is proposed. The model is used to demonstrate the nature of the nonlinear behavior of bolted connections, including coupling effects between moment and axial force. Using double angle connections, the applicability of the model to the analysis of plane frames, including the important problem of predicting the behavior of a specific connection, is examined. Numerical examples demonstrate the effectiveness of the model.

A mathematical model taking into account flexural and shear deformation, rotary moment of inertia, and axial loads is developed to calculate the natural frequencies of isolated walls. Results of free vibration tests of nine 1/3‐scale reinforced concrete isolated walls are evaluated using the mathematical model. The measured “uncracked” fundamental frequency varied from 90%‐100% of the calculated value. Results of the free vibration tests are also compared with calculated frequencies using simplified formulas available in standard textbooks. It is shown that damping increases with the amplitude of the free vibration and with structural damage. It is concluded that shear deformations have a significant effect in the calculation of natural frequencies, particularly for walls with large boundary elements, and linear analyses based on “uncracked” properties may give unreasonably conservative values for earthquake design because of rapid reduction in natural frequencies caused by cracking.

A simple procedure is presented for estimating the reliability of windsensitive structures whose orientation is not specified. The procedure is based on a second moment reliability approach and makes use of: (1) Aerodynamic coefficients obtained experimentally as functions of wind direction, and (2) climatological data consisting of sets of largest annual speeds associated with winds blowing from each of the 8 (or 16) compass directions. An illustration of the procedure, based on sets of actual data, is presented. It is then shown that the tools presented in the paper can be applied to develop, from directional, aerodynamic, and climatological data, nominal aerodynamic coefficients which in effect reduce wind loads with respect to those inherent in current U.S. practice, in a manner that reflects the directional dependence of both the aerodynamic behavior of structures and the extreme wind climate, while being consistent with respect to failure risk. These tools are first developed for the general case where the orientation of the structure is not known. It is then shown that criteria for risk‐consistent design for buildings with specified orientation can be derived immediately as a particular case from the criteria applying to structures whose orientation is unknown.

The results of an analysis of wood joist floors, including the effects of the nonlinear force‐slip relationship for nails, are presented. The finite‐element analysis procedure includes an iterative scheme for solving the resulting nonlinear equations, thereby satisfying equilibrium and compatibility. To assess the ability of the model to predict deflections above the service load level, the computed deflections were compared with those measured in tests of full‐scale point‐loaded and uniformly loaded floors. These comparisons were made at the known failure loads of the test floors. Also, a comparison was made between the results of a linear analysis of each test floor in which the connector stiffness was assumed constant throughout the load range and the experimental deflections. The nonlinear analysis proved superior, particularly for the uniformly loaded floors.