Journal of Structural Engineering

An efficient strategy to obtain static nonlinear response is presented. It is applicable to trusses made up of elements with piecewise linear force‐deformation characteristics and subject to proportional loads or piecewise linear load paths. The strategy uses the fact that the response is piecewise linear; it only computes response at the ends of the linear segments and obtains intermediate response by linear interpolation. The key part of the strategy is identifying the structure stiffness matrix and the load direction in each linear segment. This is done with an iterative procedure based on a changing local deformation criteria.

Structural systems are typically redundant, and collapse usually occurs after a sequence of failures. This has led to failure‐path approaches in which one identifies important sequences of element failures leading to collapse and estimates the probability of structural failure as the probability that one of these important sequences occurs. In this paper, failure‐path approaches are extended from the two‐state element representation (in which an element is either safe or failed) to a multistate representation in which the element has piecewise linear force‐deformation characteristics. This allows realistic modeling of nonlinear element behavior including buckling, inelastic strain softening, strength degradation, etc. The basic event is the force/deformation in an element exceeding its limits and causing a change in the structure stiffness. An exact formulation of this event (and an approximate formulation for use in computations) is presented. The possibility of load decrements (e.g., due to buckling) and structure state changes during the decrements is included. The branch and bound search algorithm is used to identify important sequences of structure state changes leading to collapse and efficient first‐order reliability methods are used for probability computations.

Geometric characteristics of orthotropic shells introduce computational difficulties (discretization of the stiffeners, computing time, interaction at the ring and stringer junctions with the sheathing, etc.). Navigation‐dam gates, tidal surge barriers, etc., are hydraulic steel structures composed of orthotropic sheathings, which can now be more easily computed with the development of the LBR‐3 stiffened sheathing software. This method is one of harmonic analysis and is founded on the Fourier series expansions. It is based on the analytical solution of the governing differential equations for orthotropic cylindrical shells. These differential equations result from the DKJ method (Donnell, von Kármán, and Jenkins) and allow taking into account the torsional stiffness, the lateral bending stiffness, and the exact position of each stiffener. New developments that permit the designing of stiffened cylindrical structures with many boundary conditions are presented. After the numerical verifications, an example of a tidal surge barrier design is presented.

The effect of the sequential application of dead load due to the sequential nature of construction is an important factor to be considered in the multistory frame analysis. Unfortunately, however, this effect has been ignored by many engineers in practice in the past. One of the ways to include this effect properly in the analysis is to carry out the analysis through step‐by‐step procedures in accordance with the sequential application of dead loads as the construction proceeds. These procedures, however, require elaborated computations and more solution time. A simplified approach, termed as correction factor method (CFM), to solve the problem without elaborated step‐by‐step analyses has been proposed in this paper. This method utilizes the correction factors established by regression from the data obtained from the existing buildings to modify the results from the ordinary analysis to produce more accurate solutions. Some numerical tests are presented to show the validity and effectiveness of the method.

The force‐deformation equations of a two‐noded three‐dimensional (3‐D) beam‐column element with both central and end rotational springs, which take account of the effects of the axial load on the lateral element stiffness, are derived. Current position‐based equations are developed that give both the nodal forces and end shortening for a deformed element under the action of a significant axial force. The tangent stiffness matrix for this element is derived from the force‐deformation relations by following the procedures adopted by Oran for a two‐noded beam‐column prismatic element. Where appropriate, a successful analytical comparison with either Oran's or Chilton's expressions is made for the cases of no axial force, infinite end joint stiffness, and finite/infinite central joint stiffness. The stiffness expressions of this element can be used to represent several commonly used members in real structures by employing the appropriate stiffnesses of the central and end springs. The use of the new equations presented can lead to a significant saving in the core storage required for the analysis of structural assemblies with flexible joints.

The axisymmetric buckling behavior of clamped shallow spherical shells under uniform pressure is investigated using Marguerre's shallow‐shell equations of 1939. The deflected shape of the shell as well as the stress function are described by linear combinations of Bessel functions and modified Bessel functions that satisfy all the relevant boundary and continuity conditions. The buckling characteristics of these caps are examined using a fully nonlinear Galerkin solution procedure, a classical bifurcation analysis, and a reduced‐stiffness bifurcation analysis. This allows the elucidation of the imperfection sensitivity and nonlinear behavior of this important class of shell structures. A systematic parametric analysis highlights the interplay between these contrasting approaches, and demonstrates the lower boundedness of the reduced‐stiffness analytical procedure for predicting imperfection‐sensitive elastic‐collapse pressures and its potential importance as a design methodology. A simple closed‐form solution is given for this analytical lower bound. This compares favorably with a large collection of available experimental results but demonstrates the variability and possible inadequacies in some of the existing design rules for spherical shell structures.

Using current American Association of State Highway and Transportation Officials (AASHTO) allowable stress or load‐factor bridge‐rating methods, many of the nation's bridges are deficient in their load‐carrying capacities. These evaluation methods are direct extensions of their respective design procedures and are inherently conservative for many of the bridges in existence. Recently, reliability‐based procedures have been developed to better estimate actual site‐specific bridge‐loading and resistance characteristics. For compact bridges, the ultimate limit state for these procedures is the formation of a flexural hinge. However, slab‐on‐steel girder bridges are highly redundant structures and show a large reserve capacity in the postelastic range. This paper presents models that extend these reliability‐based procedures to analyze bridge systems for inelastic ultimate limit states. A system‐shakedown limit state is presented where, after some initial inelastic deformations, the deflections stabilize and future loadings are resisted by pure elastic action. An example bridge is analyzed for the first hinge, shakedown, and plastic‐collapse limit states to illustrate the system models.

A mathematical model is developed to predict the load‐deformation $(P‐\Delta )$ relationship of single‐bolted connections in wood structures subjected to bending/tension loading. The connections under consideration exhibit a nonlinear $P‐\Delta$ pattern from the origin. Analyses are made using a plane‐stress, two‐dimensional, orthotropic, linear‐elastic finite‐element model. An incremental‐iterative secant stiffness approach is employed to trace the nonlinear behavior. The principal response investigated is $P‐\Delta$ at the free end of the wood member. Computations are performed on a CYBER 205 supercomputer. The validity of the computer model is determined via comparisons to experimentally obtained $P‐\Delta$ curves. Two wood species were included in the experimental phase of this study: a softwood (lodgepole pine) and a hardwood (hard maple). Additional variables examined in this study included: lumber width (nominal $2\times 4$ and $2\times 6$), moisture content (MC) (12% and green), and washer size [0.12 in. (3.05 mm) thick, 1.375 in. (34.9 mm) diameter; and 0.08 in. (2.03 mm) thick, 1.245 in. (31.6 mm) diameter]. It was concluded that the simplified model developed in the study reasonably predicted the shape and magnitude of the $P‐\Delta$ relationship of the connection under bending/tension loading. The average weighted error throughout the entire range of deflections studied was less than 17% in most of the 16 specimens evaluated.

Delamination of walls, where the outer concrete sloughs off, can occur in concrete post‐tensioned silos whose tendons are embedded in the silo wall rather than being placed around the outside of the curved wall. One potential source of this wall concrete failure is bending moment generated by kinks (due to improper splicing) in tendon ducts. This bending moment causes radial tensile stress concentrations. The writers have studied the problem analytically by the finite element method. Initial studies involved three‐dimensional (3‐D) models of the failed area with a linearly elastic material model. Subsequent studies use a two‐dimensional (2‐D) mesh and a nonlinear concrete material model that can account for compression crushing, tensile cracking, and aggregate interlock. Variation in kink angle and prestressing force are investigated. Tensile stresses of sufficient magnitude to initiate cracking failure of the concrete are discovered. Specific recommendations and construction details to minimize the occurrence of the problem are suggested.

The effect of environmental histories on the load‐duration behavior of structural lumber is presented. Select Structural Douglas‐fir nominal 2‐by‐4 lumber was tested in bending for this investigation. Constant load tests were conducted in a variety of constant and cyclic environments to define environmental effects on the load‐duration behavior and determine model constants. Constant environments were found not to have any substantial effect on the load‐duration behavior if their effect on short‐term strength is accounted for properly. However, cyclic moisture conditions caused a marked decrease in time‐to‐failure. That is, additional damage associated with so‐called mechano‐sorptive creep strain often observed in wood is present in the load‐duration behavior. A cumulative damage modeling approach was used to model the effect of mechanical, thermal, and moisture loadings on the load‐duration behavior. A damage parameter is introduced to account for the additional damage associated with cyclic moisture histories.

The modeling and dynamic analysis of a concrete arch dam, the impounded water, and the foundation rock is an important step in the earthquake‐safety evaluation of the system. An analysis assuming the dam is a monolithic structure often shows large tensile stresses in the arch direction. Arch dams are generally constructed as cantilever monoliths, however, and the joints between the monoliths cannot develop the tensile stress predicted from a linear analysis. The joints are expected to open during an earthquake, releasing the arch stresses and redistributing forces. In this study, a nonlinear element is developed to model the opening and closing of contraction joints. The joint elements are combined with linear shell, solid, and fluid finite elements to model an arch dam system. The assumption that the monoliths are linear substructures significantly reduces the computation required to solve the nonlinear equations of motion. The earthquake analysis of a typical concrete arch dam shows the importance of contraction‐]joint opening and the release of arch tensile stresses.

In recent years, probability‐based load‐and‐resistance‐factor‐design (LRFD) method has been successfully applied to the design of hot‐rolled steel sections and cold‐formed steel members in the United States and foreign countries. In order to develop the LRFD criteria for the design of cold‐formed stainless steel structural members and connections, a research project was conducted at the University of Missouri‐Rolla since 1986 under the sponsorship of the American Society of Civil Engineers (ASCE). This newly developed LRFD Specification with Commentary has been adopted by ASCE as a new standard in 1990. It supersedes the 1974 edition of the Specification for the Design of Cold‐Formed Stainless Steel Structural Members issued by the American Iron and Steel Institute. The basic theory of probability‐based design approach and the development of the ASCE LRFD criteria for cold‐formed stainless steel structural members are presented in this paper.

During the last few years a project on experimental investigation of the ultimate capacity of dented beam‐columns was performed at Veritas Offshore Technology and Services A.S. in Oslo, Norway. The purpose of the project is to determine experimentally the moment versus axial force versus rotation relationships for dented tubular steel members. The diameter thickness ratio of the tubular tested corresponds to that of typical members in jacket structures with D/t ratios of 31 and 47. The steel quality of the pipes is St 52 and St 35 respectively. A total of 35 ultimate load tests are performed. Four tests are performed with undented specimens for verification of the test procedure. Eighteen tests are performed with a dent depth equal to 10% of the pipe diameter and 13 are performed with a dent depth equal to 20% of the diameter. The information from these tests may be used in the evaluation and verification of residual strength of damaged offshore structures.

The response of bridges exposed to thermal environment conditions is studied. Analytical methods are developed to obtain temperature distributions and the maximum bridge temperature ranges. Thermoelastic analysis is conducted to obtain the temperature induced movements and the associated stresses in bridges. Parametric studies are conducted for different bridge geometries, temperature distributions, and support conditions. A field test is conducted on a bridge to verify the analytical models. The analysis suggests that concrete bridges sometimes are designed for smaller temperature ranges and corresponding thermal movements than may be expected in practice. The analysis suggests that steel bridges with composite concrete decks sometimes are designed for larger temperature ranges and thermal movements than may be expected at many locations in the United States. Skew and curved bridges often exhibit magnitude and direction of movement that is different than commonly expected. Additional guidelines and recommendations are provided regarding the analysis required to accurately predict thermal movements and the placement of bearings and expansion joints. This study will help engineers better understand thermal movements and stresses developed in bridges.

Probabilistic system‐reliability methods have the potential to assist designers in better understanding the ultimate global behavior of bridges, thus leading to more economical, rational, and reliable structures. Nonetheless, these techniques are not currently broadly used in North American bridge engineering practice. Using a sample cable‐stayed bridge design, a study is conducted to assess the practicability of system‐reliability analytical methods to assist in the design of cable‐stayed bridges. Ductile and brittle cables are considered in series and mixed system analyses, respectively. The sample bridge selected is found to be very reliable; the most likely failure mode identified is somewhat counterintuitive. More importantly, considerable insight into global ultimate behavior is provided by these analyses, and the effect of various design assumptions on global structural safety can be assessed. Some obstacles to the transfer of system‐reliability procedures to the state of practice are identified.

Excessive vibrations and deflections associated with human movements have recently become of great concern in modern structures. The recommended design values for human loading in the current U.S. building codes and standards were developed over half a century ago and are based on strength requirements alone. Recent investigations have led to load models for individuals and small groups of people using laboratory measurements on small‐ and medium‐size force platforms. The current research project is directed towards testing the group harmonic load model and recommendation of design values. We designed and built a floor system instrumented with strain gages and displacement transducers to measure dynamic loads due to large groups of people. The floor system is analyzed experimentally and analytically. The imposed dynamic forces are determined using both data from the displacement transducers and the strain gages. The measured group harmonic loads compare closely with the computer simulation model of our previous study. Based upon work presented, structural design live loads are suggested for crowd harmonic movements for both strength and serviceability criteria.

A design method for the reinforcement-steel area in a concrete section with a generic shape is proposed. The section is subjected to axial load and biaxial bending. The materials are assumed to be nonlienar elastic. The method is based on the failure condition prescribed by the ACI Building code (maximum compressive strain in concrete ${\phi }_{\mathrm{cf}}=0.003$). It permits finding the amount of reinforcement and the location of the neutral axis in a rapid manner, avoiding the usual trial-and-error procedures based on the failure of surfaces and strength-interaction diagrams. The solution is obtained by resolving a system of nonlinear equations by means of the Newton-Raphson method. The method was run using a computer program, and provided fast convergence in all the many tests carried out. Computational effort is not considerable, and a personal computer can be used for the design. A numerical example is reported.