Journal of Structural Engineering

In nonlinear analysis of rigid‐jointed space frames, the assumption that rotations of a body are additive has been widely adopted by researchers in updating the end rotations of frame elements at each incremental step. Such an assumption remains valid only for incremental steps with small rotations. For cases with finite rotations, it is necessary to consider the noncommutative nature of rotations in three dimensions. Based on Euler's finite rotation formula, unique, analytical expressions that are valid for updating the geometry of the frame element involving finite rotations are derived in the present paper. With these expressions, the displacement increments solved from the structure equations of equilibrium at each incremental step can be decomposed into the rigid‐body modes and member deformations, thereby providing the basis for recovering and updating the element forces. The validity of the present procedure is demonstrated in the postbuckling analysis of a circular arch, involving large rotations in a three‐dimensional space.

A new calculation procedure is described that provides an alternative to full‐scale testing for composite slabs with ribbed decking used in buildings. The procedure consists of combining shear‐bond test results with a numerical analysis to predict the behavior and strength of composite slabs. It may be used to analyze either single spans or multiple spans. The procedure incorporates certain simplifications and assumptions that allow for a reasonable yet conservative prediction of both behavior and strength. In particular, chemical bonding between the concrete slab and decking and concrete tension behavior are ignored because they are brittle in nature. Advantages of using this procedure rather than full‐scale test results are versatility and reduced cost, the estimation of deformations at working loads, the inclusion of additional variables such as end anchorage (over the end supports), additional positive moment reinforcement (in the span), and reinforcement in negative moment regions (near interior supports). This calculation procedure may also be used for the development of new decking and to improve the performance of slabs with existing decking. Examples of calculations are presented for single‐span composite slabs.

The results of selected tests on full‐scale one‐way single and continuous span composite slabs with ribbed decking are presented. Variables investigated in these tests include the number of spans, the presence of embossments in the decking, end anchorage (both welded and shot‐fired shear connectors), and negative moment reinforcement near interior supports. An example comparison is given between a standard test and the calculation procedure combining shear‐bond test results with a finite element analysis (the calculation procedure was presented in part I). The importance of composite slab internal moment resistances as a function of the applied load is examined. For a composite slab, three internal moment resistance elements are of importance: the decking, concrete slab (including additional reinforcement), and the interaction between decking and concrete slab. Parametric analyses based upon the calculation procedure predictions are performed for three decking geometries using limiting slenderness ratios. Decking types were chosen to represent a wide range of shear bond connection characteristics. Slenderness ratio is defined as the span length divided by the total composite slab depth. The effects of eleven parameters are investigated for each decking and slenderness. Effects studied include the load‐carrying capacity at service deflection limits (L/250), ultimate deflection limits (L/50), and maximum load‐carrying capacity.

The closed‐form solution is derived to the problem of stiffness design of coaxially coeccentric asymmetric shear buildings (CCS buildings) for specified fundamental natural frequency and eigenvector. The complete quadratic combination (CQC) estimates of the mean maximum interstory drifts in a so‐designed CCS building subjected to an ensemble of design‐spectrum‐compatible moderate earthquakes are regarded as functions of the lowest eigenvalue and translational eigenvector, parameters for adjustment of those CQC estimates. An almost direct and efficient method of stiffness design is developed for a CCS building such that all the CQC estimates of the mean maximum drifts of the corner columns based upon a prescribed design spectrum will be equal to the prescribed distribution of design drifts. The validity of the design procedure is demonstrated with the results of time history analysis on so‐designed CCS buildings. A design amplifier factor for specified distribution of lateral torsional drifts is defined and is shown to be useful for describing directly the effect of eccentricity on the seismic response‐drift constrained designs of CCS buildings.

The analytical solutions for the deflections and for the critical load over which structural prismatic masonry collapses without reaching the compressive strength are presented. The analysis is developed by assuming that the member does not resist tensile forces and exhibits a nonlinear (monomial) gross stress‐strain relationship in compression and that the forces act with great eccentricity (cracked sections). The least square fit method is utilized to validate the nonlinear gross stress‐strain relationship. Dimensionless graphs providing the instability vertical (or lateral) load and the maximum deflection for a given lateral (or vertical) load and making it possible to analyze similar problems are presented for a set of exponents of the gross stress‐strain relationship. It is shown that solutions without lateral force and with linear behavior of the masonry is a particular case of the general solution here proposed. The reliability of the solution is validated by comparison with ample experimental data.

A step‐by‐step modeling and analysis procedure for nonlinear finite element analysis of complete constructed facilities is presented. A comprehensive microcomputer‐based software that was developed for this study is briefly described. The procedure is demonstrated by conducting analyses of an existing reinforced concrete (RC) slab bridge. The experimental knowledge base gained from nondestructive tests conducted on this bridge is used to construct and validate the analytical models. A sensitivity study is carried out to explore the effects of various modeling parameters on the structure response. Analysis results indicate that the manner of modeling support conditions significantly affects the bridge strength. The collapse mechanism of the bridge that is predicted agrees with results from destructive tests conducted on a similar RC slab bridge.

The development of an empirical formula for predicting the seismic‐induced slip of concrete gravity dams at the rock interface, often required by the presence of weak rock joints immediately underneath the surface, is presented herein. Based on the “sliding block” concept and the equivalent single‐degree‐of‐freedom system criteria, a series of parametric studies on gravity dams were performed, using a broad seismic data base with simultaneously applied horizontal and vertical ground motion, and reflecting both Eastern North American as well as California‐type conditions. The seismic slip results were statistically processed, using the multiple variables regression technique, in terms of ground‐motion parameters, such as peak acceleration, velocity and displacement, duration and predominant frequency, as well as structural response, such as fundamental frequency of vibration and the lateral acceleration required to cause incipient frictional slip. Since the results compare favorably with existing “sliding block” formulas, such as Richards‐Elms, Newmark, and Wong, the applicability of the proposed seismic slip formula may be extended to earth‐retaining walls and embankments as well.

The lateral‐torsional response of base‐isolated structures, with sliding isolation system due to bidirectional lateral ground motion, is studied. The objective of the study is to identify the key system parameters that lead to significant torsional coupling in sliding base‐isolated structures. The analysis procedure adopted can capture the highly nonlinear behavior of sliding systems in plane motion. The nonlinear biaxial stick‐slip characteristics of sliding bearings and the velocity dependence of coefficient of friction are accounted for. The study considers multistoried structures with variable number of bearings subjected to the effects of earthquakes with various frequency content and different peak ground accelerations. It is shown that, although the total superstructure response is reduced significantly due to the effects of sliding base isolation, torsional coupling can be significant depending on the superstructure eccentricity and the lateral‐torsional flexibility of the superstructure and the base.

Fifteen representative bridges throughout the state of Illinois were instrumented with foil strain gages to determine their frequencies of loading and the magnitudes of stresses induced by traffic over a 3‐ to 8‐hour period, depending on traffic volume. Fatigue prone details, such as cover‐plated wide flanges, were instrumented. For each stress range increment gathered by the data‐acquisition system, the cumulative damage sustained over an extended number of years is compared with the number of available fatigue cycles for that stress range using published $S=f\left(N\right)$ data for various details and the Palmgren‐Miner linear damage rule. A new equation for factor of safety for welded structures subject to fatigue is proposed, taking dead load, live load, and bridge detail fatigue strengths into account. A new method of assessing future fatigue damage in bridges that takes traffic growth and increased truck weights into account is also proposed.

When a lateral force acts on a cross‐bracing system, one brace member is subjected to a compressive force while the other is subjected to a tensile force. The tension brace provides a restraint to its compression counterpart at the point of intersection, if they are connected. This interaction of braces reduces the effective length of the compression brace member and should be taken into consideration to avoid overconservative designs. This paper presents a numerical method based on the energy principle for the determination of buckling load and effective length factor of the compression brace member. Typical design charts are given for a quick estimation of the effective length factors. Moreover, closed‐form solutions are presented for the special case of symmetric brace systems.

A new method of connecting members, at certain joints of a lateral force resisting structure, improves the response to seismic excitation. These connections that permit a small initial slip (displacement or rotation) are called sequential connectors. A sequential system is a structure consisting of units coupled in parallel in which at least one unit is attached by sequential connectors, and at least one other unit is attached by standard connections. A standard structure is transformed into a sequential system by replacing one or more (but not all) standard connections by sequential connectors. The effectiveness of sequential coupling, in some cases, is comparable to sensor‐initiated active controls. Sequential systems exhibit an interesting and even surprising response to dynamic excitation. The paper outlines the characteristics of sequential systems and provides a numerical comparison of their performance with an identical structure using standard connections; the structure using standard connections shows a displacement response that is 40% higher. If the response of the two systems is identical, the standard system requires 40% more material.

Experimental and theoretical investigations conducted over a 20‐year time period by several investigators provide sufficient data and information to define, for practical engineering purposes, the behavior of architectural laminated glass under lateral pressures. Investigations included definitions of material properties, theoretical stress analyses, experimental stress analyses, and destructive tests involving monolithic, laminated, and “layered” glass plates of several geometries. The preponderance of data and information indicate that: (1) Architectural laminated glass behaves in a manner similar to monolithic glass of the same nominal thickness under short‐term lateral pressures (representative of wind loads) at and below room temperature; (2) the temperature at which behavior changes from being similar to monolithic to significantly different from monolithic under short‐ term lateral pressures is not clearly defined, but is around 49°C (120°F); and (3) architectural laminated glass behaves in a manner similar to monolithic glass of the same nominal thickness under long‐term lateral pressures (representative of snow loads) at temperatures of 0°C (32°F) and below.

The present paper provides a method for the identification of failure modes that contribute significantly to the estimate of the system probability of failure in rigid‐plastic structures. For structures where loads and resistances are random variables, a decision rule is presented for the identification of failure modes in series systems based on their contribution to the system probability of failure. Stochastic programs based on this decision rule for failure mode selection are developed for the identification of failure modes in structures. Examples illustrate the use of these mathematical programs in identifying significant failure modes in rigid‐plastic structures where axial force‐moment interaction is included.

The writers presented in an earlier paper a mathematical model of friction of sliding bearings under conditions of compression and bidirectional motion. The model could account for the dependence of the coefficient of friction on the velocity and direction of sliding. The model was capable of reproducing the behavior observed in experiments with unidirectional motion, however, no experimental validation of the model was provided for bidirectional motion. The present paper presents experimental results on Teflon sliding bearings under simultaneous compression and high velocity bidirectional motion that provide a complete verification of the presented model. Furthermore, the experimental results show the existence of bidirectional interaction between the orthogonal components of the frictional force at the bearing interface. The importance of these effects is studied in the analysis of an isolated structure. The structure is subjected to a number of pairs of horizontal earthquake excitation components that are representative of seismic zone 4, soil type $S_2$ seismic motion. It was found that neglect of these effects leads to underprediction of the isolation system displacement and overprediction of the structural shear.

A nonlinear finite element model is developed to investigate the stability behavior of a novel type of structure, namely prestressed sandwich arch. A prestressed sandwich arch is formed by buckling its individual layers into an arch shape and assembling them as a sandwich composite. A corotational formulation of a two‐node, three‐layer sandwich beam element is adopted. Isotropic material properties are assumed, and shear deformations of the core and facings are both included. The discontinuity in shear strains at the layer interface is accounted for by introducing a shear warpage angle. A bilinear constitutive law is used that assumes a linear strain‐hardening behavior, once the elastic limit is reached for the corresponding layer. The effects of torsional warping, transverse normal deformations, and local modes of failure are excluded. Postbuckling analysis is performed by using the augmentation technique. The model has been tested for the classical problem of clamped‐hinged sandwich column. Numerical analyses show relatively high load‐carrying capacities for sandwich arches.

The performance of steel angles is of great interest to the field of electrical transmission tower design. In a lattice structure, the most common type of member used is the single angle. In such an application, the angles are subjected to both tension and compression. The ultimate compressive load capacity of single steel angles subjected to eccentrically applied axial load is investigated in this paper. Seventy‐five full‐scale tests were done with data collected in the elastic, inelastic, and postbuckling regions of the member's performance. Test specimens were made of A36 steel angle sections connected to the end plate by bolts. The end plates were supported using a ball joint in an attempt to model end conditions that were unrestrained against rotation. The results of the tests were compared with predicted load capacities obtained from ASCE Manual 52 for the Design of Steel Transmission Towers (1988), which is the design guide for lattice steel transmission towers.

The paper calculates how an aging concrete structure that has an uncertain constitutive law and random material properties responds to the random process of environmental humidity history. The time evolution of stochastic porehumidity distributions is solved from a linear diffusion equation. The stresses produced by the shrinkage strains are calculated taking concrete creep into account. The environmental humidity process is described by three components: one Poisson square‐wave random process and two random‐phase processes, having periods of one year and one day, the latter of which is found to have a negligible effect. The response to the random‐phase process is calculated by the spectral method combined with equal probability sampling. The Poisson‐process component is important for very long times since it produces a response whose standard deviation grows as the square root of time; the nonstationary random‐phase component stabilizes after about 10 years. The influence of the random‐phase process reaches a depth of about 20 cm below the concrete surface; that of the Poisson process reaches only about 5 cm. The randomness of the material parameters and the uncertainty factor of the material model influence the entire structure. A numerical example of a cylindrical wall is given and simplified explicit formulas for estimating the response statistics are derived.

Unlike most structures that may be considered as a single point with respect to the size of a weather system, transmission structures may extend hundreds of kilometers and traverse more than one weather system. This presents unique problems in evaluating the structural system reliability of the line. In the present paper, an approximate relationship between the reliability of a fully utilized supporting structure in a transmission line and the reliability of the complete line is developed. The relationship accounts for the spacing between the supporting structures, the number of structures in the line, the correlation between the structure strengths, and the spatial extent of the extreme loading events. The problem is first formulated using an event‐based approach, in which each storm that hits the line is considered independently, then it is converted to an extreme value problem. The simplicity of the resulting solution and the current availability of the required data make the proposed relationship a valuable tool in system‐reliability‐based design (SRBD) of the line.

The aerodynamic response of long‐span suspended and cable‐stayed bridges can be significantly improved by streamlining the deck geometry. In some cases, a full streamlining may not be practical and, as a compromise, partial streamlining is considered. The present technical note is concerned with the aerodynamic response of the deck of a cable‐stayed bridge. The results of a wind‐tunnel study employing a section model of the deck are presented. The experimental data include the deck response in heave and flow patterns about the stationary and oscillating decks. The effects of modification of the deck geometry (addition of streamlining fairings and removal of traffic barriers) on the vortex‐induced response of the deck are discussed. It is shown that partial streamlining of the deck geometry may result in an increase in the deck aerodynamic response.