Journal of Structural Engineering

The methods used for designing prestressed sections are discussed and classified. It is shown how the number of variables makes hand design inefficient, especially for nonprismatic members. A computer program is described that can assist a designer in producing efficient nonprismatic designs rapidly and easily.

A method is presented for the direct economical design of entire nonprismatic prestressed concrete flexural members. The cost of the member includes the costs of steel, concrete, and formwork. The section of the member is computed at several points in the span, as required by the loads, and is adjusted in a simple fashion to minimize the cost. Examples are presented using typical unit costs.

This paper intends to derive the nonlinear differential equations of equilibrium for a horizontally curved I‐beam. Based on the principle of virtual displacements, the equilibrium of a bar is established for its deformed or buckled configuration using a Lagrangian approach. Central to the consideration of the effect of curvature is the expression of various quantities in cylindrical coordinates and the incorporation of radial stresses in the virtual work statement. The governing differential equations are obtained for the curved beam as the Euler‐Lagrange equations of the functional using a variational procedure. Rationality of the present theory is demonstrated for some typical examples, where the sources of errors in existing theories are traced. Also illustrated is the inconsistency involved in a conventional finite element analysis in which a curved beam is represented by several straight beam elements.

Computation of the full response of concrete frame structures to severe dynamic loads requires consideration of softening in addition to plasticity and hysteresis. Critical softening parameters and ground frequencies are determined for simple flexural structures. For unidirectional loads, the critical softening parameter depends on the severity of the applied load as represented by the ratio of maximum applied force to maximum resistance (or by energy of impulse to maximum elastic strain energy), on the plastic plateau length (ductility) on any limit to the softening region, and on the duration of load in the case of a rectangular load function. Conversely, for a given softening slope, a critical severity of load, critical plateau length, or critical duration of load may be identified. For the response to reversible loads, a stiffness matrix for flexural elements with finite softening lengths is used in the analysis. The softening of individual hinges is reflected in the overall hysteresis loop of a structure. Elastic‐softening structures perform well in absorbing energy at relatively high frequencies.

A review of the basic concepts involved when constructing nonlinear load‐deflection curves of framed structures by the finite element method is presented. The study is limited to the geometrically nonlinear behavior of elastic structures. Three different procedures are considered: the linear incremental method, the nonlinear incremental method, and the direct method. For each method the governing equations are derived, and the procedure used to plot the load‐deflection curve is outlined.

Adhesively bonding a cover plate to the tension flange of a steel girder and high‐strength bolting the ends to prevent debonding was experimentally shown to increase the fatigue life by a factor of 20 over that of welded cover plates, from Category E to Category B. The number of end bolts should be that needed to develop the cover plate's portion of the maximum moment at the theoretical cut‐off point. Previous parametric analyses of single‐span and two‐span‐continuous multigirder bridges has shown that improvements in cover plate design, which raise the fatigue strength to that of Category B, make them fatigue‐proof to highway truck loading.

Directed loading may have significant effects on the buckling resistances of beams and columns. Rotations of directed loads during buckling induce transverse components that may stabilize or destabilize the member. Previous studies of flexural‐torsional buckling are limited to specific situations. In this paper, a simple method is developed of modifying general finite element computer programs to account for the effects of directed loading on flexural‐torsional buckling. Computer results show that the buckling resistances of beams and cantilevers under downwards loading are increased when the load direction points are below the load application points and decreased when above. Members with top flange loads directed from above may have very low buckling resistances. Approximate equations are developed for simply supported beams and cantilevers. The accuracy of the computer predictions for cantilevered I‐beams is confirmed experimentally.

Results of experimental shaking table tests and analytical studies of the biaxial response of a reinforced concrete frame having rectangular columns and inelastic motion induced by earthquake excitation are summarized. The objective of this research program was to evaluate biaxial loading effects on R/C column behavior and implications for aseismic design. Inspection of the response and comparison to a test with uniaxial motion found that biaxial motion seriously affected column and frame behavior. The column capacities (strength, stiffness, deformability, and energy dissipation) were reduced and the response demand was increased compared to those with uniaxial motion. Results indicate that present code‐endorsed methods of analyzing and designing frames independently along their principal axes may result in an unconservative product when biaxial motion occurs.

Displacement functions used for simply supported finite strips are combined with those of a rectangular plate‐bending element. The resulting finite strip‐element combines a number of advantages of both finite strips and finite elements. Owing to orthogonality relationships of the trigonometric functions used in the formulation, partial uncoupling of the equations occurs, enabling any number of sine series terms to be taken without increasing computer storage requirements. The free edge condition is approximately satisfied as a natural boundary condition, while the clamped edge condition is exactly satisfied using Lagrange multipliers. Three examples are considered demonstrating the accuracy and efficiency of the method.

A study of the dynamic response of offshore towers to wind‐generated random ocean waves is presented. The analysis is performed in the frequency domain and the equations of motion are solved using equivalent linearization techniques. Two methods of reliability analysis are considered in this study: a statistical fatigue damage analysis using the American Welding Society model (high‐cycle fatigue analysis) to demonstrate the influence of the design stress level for fatigue‐critical members on the fatigue reliability and a first‐passage failure probability with periodic inspections. For the latter, a crack growth analysis is performed using the fracture mechanics method to estimate propagated crack size and corresponding residual strength under random service loading conditions. The effect of periodic inspections is very important if a fatigue crack already exists. It is also shown that there is always a limit in the number of inspections beyond which no significant improvement can be achieved.

In the case of reinforced concrete frames, full moment redistribution may not take place, and any critical regions may fail because of insufficient rotation capacity before a collapse mechanism is formed. Considering the limited rotation capacity of concrete sections, a method is developed to verify and analyze the identified dominant mechanisms that are impossible to form. A reliability model for the rotation failure prior to mechanism collapse is proposed, and the safety margin equation, in relation to and consistent with the mechanism, is generated on the basis of the partial utilization of moment redistribution at the failure stage. Rotation failure modes are combined with other possible mechanism modes, and the structural reliability is reassessed. The proposed method is illustrated with two examples. It is found that a check of plastic hinge rotations and remodeling of the failure modes improve the accuracy of predicting the system reliability of a reinforced concrete frame. However, the improvement is only marginal in the case of simple frames.

Reversed cyclic torsion tests on nine normal‐weight and three lightweight reinforced reinforced concrete beams are reported, along with nonreversible cyclic torsion tests on four reinforced concrete beams and two companion static tests. The variables studied were the peak torque, the range and the frequency of loading. Basic information concerning concrete and steel strains, the angle of twist, the torsional stiffness, the cracking torque, and the ultimate torque in cyclic torsion has been reported.

Design specifications for columns include nomographs for calculating effective length factors. The method, which is simple to use, requires the designer to evaluate G at each end of the column, but only positive G‐factors result, and in the case of sway‐prevented structures, effective length factors are always less than one. In practice, some columns may have values of K greater than one, corresponding to negative values of G. This paper expands the present graphical method so that the correct set of K‐values can be determined. An iterative procedure is presented, based on linearized stability functions that effectively account for the presence of axial forces in the restraining members. The improved G‐factor method is illustrated by numerical examples that are not, in general, covered by the nomographs where the beams are assumed to offer significant restraint.

Wood diaphragms are used in low‐rise, wood‐framed buildings to resist the lateral forces produced by wind and earthquakes. Since wood buildings are known to be efficient in absorbing the energy produced by these loadings, it is of importance to more fully understand the dynamic behavior of their components. Presented in this paper are the results from an experimental study performed to measure the dynamic characteristics of ten plywood and gypsumboard‐sheathed diaphragms. Four walls, three floors, and three ceilings were tested to determine natural frequencies and damping ratios. Results indicate that natural frequencies for the diaphragms proportions tested range from 8–29 Hz and vary depending on diaphragm displacement level. Using results of regression analysis, natural frequencies for various diaphragms may be predicted. Damping ratios were calculated and were found to range from 0.09–0.34.

The influence of inelastic load-deformation behavior on seismic energy imparted and dissipated is assessed. Stiffness degrading and bilinear hysteretic models are considered. The load-deformation model has a pronounced influence on the energy imparted to the system and on the energy absorbed by inelastic action. The use of the simpler bilinear model in evaluating the seismic energies is restricted to systems within certain ranges of natural frequency and displacement ductility.