Journal of Structural Engineering

The parametric instability of a curved girder subjected to equal and opposite periodic moments at the ends is examined. It is shown that the relationship of the frequencies at which parametric resonance occurs differs from the frequency relationship of ordinary resonance. For small values of the applied couples at the ends, the parametric resonant frequency is twice the natural frequency. The method presented can also be used to determine the natural frequencies and static buckling moment for a curved girder. Special analytical solutions and numerical results are obtained and presented in nondimensional forms.

A review of current code requirements on lap splices and their limitations in seismic design is presented. A simple analytical model of an embedded bar is examined and correlated with available experimental data. The force transfer mechanisms of lap splices and the effects of properly placed transverse reinforcement to avoid brittle failure are studied. The author concluded that: (1) Concentrated transverse reinforcement at the ends of lap splices and in contact with the longitudinal reinforcement is structurally beneficial; and (2) sharp offset bends must be avoided to prevent fatigue failure in the lapped reinforcement and to prevent excessive bursting forces in concrete in the event of severe tensile load reversals.

A stochastic model of the live load process in buildings provides a basis for the study of load duration. The combined load model is comprised of a sustained load process and multiple extraordinary load processes. Complete probability distributions of total time above a fixed reference load, duration of a single excursion upcrossing the reference load, and number of excursions for a fixed design lifetime are derived. These quantities are necessary for computing long‐term deflection and settlement of structures and critical load combinations for creep‐rupture materials, such as wood. The derived distributions are applied to several common building occupancy types. Results indicate the sensitivity of some duration characteristics to the extraordinary load and the need for even further refinement of the stochastic load process model.

Abnormal loads, which usually are not considered in structural design because of their low probability of occurrence, may initiate a catastrophic failure if they occur. A case study shows that the probability of structural failure due to a gas explosion in a residential compartment may exceed probabilities associated with unfavorable combinations of ordinary design loads. Therefore, specific provision in design standards to mitigate the effects of abnormal loads appear warranted.

Procedures are presented for the safe design of shell membrane reinforcement and for the determination for a given shell of the safe load capacity as controlled by membrane reinforcement. The procedures are based on the strength design method of the ACI 318‐77 Building Code. Design strengths of the reinforced concrete membrane relative to tension and shear are explicitly identified. Membrane design and capacity procedures are confirmed by comparison with test results. Non‐realistic results for design membrane reinforcement are shown to occur when shear strength is not explicitly included in the membrane design strength.

An analysis is presented of the factors that have contributed to the finite element method not being used as a design office tool for the elastic analysis of floor systems. Suggestions are made which attempt to make the finite element method more attractive for this purpose. A computer program incorporating some of these features is reported on and its use is demonstrated in the analysis of an example design problem. The relative merits of the finite element method and more traditional analysis techniques are considered.

The Southwell, Modified and Massey extrapolation techniques are derived for a doubly symmetric beam with a transverse force applied at an eccentricity to the shear center. A finite element algorithm which takes into account small initial geometric imperfections is presented using simple matrix algebra. The load vs. deflection path for elastic cases, can be traced for beams with varying kinematic boundaries, loadings, and distributions of small initial geometric imperfections. Comparison of the Southwell, Modified, and Massey Plots are made using finite element results for the problem of an I‐section cantilever beam with a concentrated end load applied at the bottom flange. The Southwell Plot appears to be superior as a nondestructive procedure for the determination of the buckling load.

The paper presents a simplified method for determining transverse shear intensity in the shear keys of multi‐beam bridges due to the AASHTO and Ontario highway bridge design vehicles. The method, which is applicable to right single span bridges, is based upon the orthotropic plate theory; it consists of the calculation of the value of a dimensionless characterizing parameter from the bridge properties, and the reading of the design values of transverse shear intensities from provided charts.

Snow loads for structural design are calculated as the product of the ground snow load and a snow load coefficient that transforms the ground load to a roof load. This paper presents a statistical analysis of annual extreme water‐equivalents (reported as inches of water) of ground snow measured at 76 weather stations in the northeast quadrant of the United States through the winter of 1979–1980. The analysis suggests that the lognormal distribution is preferable to a Type I distribution of extreme values for describing annual extreme ground snow loads at a majority of sites. Sampling errors and the selection of design loads from the statistical analysis are also described.

Inelastic cyclic loading in reinforced concrete members, which may occur in ductile frame structures under severe seismic conditions, causes shear deformation to develop in hinge zones. Experimental results illustrating this are presented. The form of the shear vs. shear deformation curve changes with repeated inelastic cycling. With each such cycle, the shear displacement is increased and most of this deformation occurs when the shear force reverses in direction. This accounts for a large part of the stiffness degradation of flexural members. For beams with closely spaced stirrups which are proportioned to resist all the shear, and where shear stresses are not high, strength degradation does not appear to be a problem. Two different forms of plastic hinge may occur in structures forming sway mechanisms under earthquake conditions. In the first, the hinges are subjected to both positive and negative rotations, while, in the second, inelastic rotations in one direction accumulate in the hinge. It is only in the first case that stiffness degradation occurs due to shear deformation.

This paper is concerned with a statistical study on initial deflection of plate members, such as stiffened plates and diaphragms, in steel girder bridges recently fabricated in Japan, in order to provide some information for establishing the realistic values of both initial deflection and ultimate strength of steel‐plated compression members. The resolution of initial deformation into a number of linearly independent modes, the concept of equivalent initial deflection, and the elasto‐plastic finite displacement theory developed by the writers can apply efficiently to the estimation of the ultimate strength.

A general method of collapse load analysis was proposed by the writers in an earlier paper for reinforced concrete indeterminate frames in which the members are subjected to combined bending, torsion, and shear. The application of the method to the case of fixed‐ended beams, curved in plan and subjected to a point load, is described in this paper in detail. The theoretical predictions are then compared with the writers' test data as well as those available in the literature. In general, the method gives a good prediction of the behavior and strength of reinforced concrete (nonprestressed) curved beams at collapse.

Over the years, observations of earthquake damage suggest that structures on large foundations respond to ground motion with less intensity than do smaller structures. The limited data obtained from instruments support these observations. The theoretical investigation described constitutes an attempt to establish the feasibility of employing the τ‐averaging traveling seismic wave procedures to investigate the effects of combined lateral motion resulting from translation and rotation of a simple structure. The results of the investigation indicated that the effects of induced rotational motion (computed by this technique) are not important at frequencies less than 1 Hz. Various approaches for combining the responses are studied, involving direct superposition approaches and coupled motion approaches. The results of this limited study suggest that the 5% accidental eccentricity, as specified in building codes, appears reasonable.

The effect of wind direction on structural reliability is studied as a problem of a vector wind force process outcrossing a structural resistance boundary which may be direction‐dependent. When the structural orientation is not known or the winds have no directionality but the resistance is highly direction‐dependent, results from simple parametric studies indicate that the upcrossing (or failure) rate is approximately proportional to the effective “direction window” width and there is a significant reduction in response level (or risk of failure) compared with the results based on a “worst direction” assumption. However, a lower bound exists to the outcrossing rate as the window vanishes. When the structural orientation is known and for location where winds show strong directionality the outcrossing rate and failure probability could be very sensitive to the structural orientation. Implications of the findings in the formulation of code procedures are mentioned.

The shearing stress analysis of glue‐laminated wood beams in the elastic‐plastic range is presented, and the theoretical method for calculating the ultimate shearing stresses is developed. The validity of the theoretical method was verified by a test program using 16 models. The test results support the theoretical prediction. It is proved that the elastic theory on which the present design criteria of bending wood beams are based does not explain adequately the true structural behavior of wood beams in the elastic‐plastic range. This theory is verified through tests of glue‐laminated wood beams of defect‐free material and of commercial quality. The theory is proved for beams of defectfree material, and it is of significant value since it makes it possible to compute the shearing stress for a fully plastic case under ultimate load.