Journal of Structural Engineering

A beam‐column element with springs connected in series is presented for efficient and effective geometric and material nonlinear analysis of steel frames with semirigid connections. When incorporated into a computer program for nonlinear analysis of steel framed structures, the effects of semirigid connections and material yielding can be accounted for in a simple and direct manner. Proposed mathematical models for various joint types and assumed patterns for material yielding can also be simulated independently, while the combined effect can be included in the analysis automatically. The obvious and direct method of adding the connection and plastic springs to the element matrix and to condense out the internal or dummy degrees of freedom for the final element matrix is also discussed in this paper and noted to be computationally infeasible due to the finite accuracy in computer analysis and the odd values of very large and small stiffness encountered during an ultimate analysis. This paper proposes an efficient and simple method to trace the equilibrium path of steel frames, allowing for geometrical, material, and joint stiffness nonlinearities up to the ultimate load. The benchmarked problem (Vogel's six‐story frame) is analyzed and extended to include the effects of semirigid connections, which is new and is recommended to be used for validation of computer programs for this type of analysis.

Structural response to one‐ and three‐dimensional (3D) simulated motions in San Bernardino Valley, Calif., from a hypothetical earthquake along the San Andreas Fault with moment magnitude 6.5 and rupture length of 30 km (18.6 mi) is investigated. For three stations that are close to each other and to the fault line, various measures of ground motions (e.g., peak values, intensities, durations, and effective frequency bands), elastic and elastoplastic response spectra, and the response of a 10‐story, three‐bay frame are calculated. Because the simulation results are reliable up to 1 Hz, only long‐period structures, with periods of 1 to 10 sec, are considered. The results show that the ground motions and the structural response vary dramatically with the type of simulation and the location. In general, one‐dimensional (1D) simulations underestimated the response and resulted in values as low as one‐fifth of those of 3D simulations. The difference in the structural response at three stations was found to be as high as a factor of six. The reasons for such large differences are the trapping of seismic waves in the basin and the constructive interference of surface waves traveling in different directions, none of which can be accounted for by 1D models, and the strong influence of source directivity.

The present paper is concerned with the analysis of thin‐walled beams of arbitrary open or closed cross section undergoing elastoplastic deformations. The general approach to the solution of the problem is based on the finite‐element method and incremental solution techniques. A new model of describing the warping of a cross section that allows for shear deformation is applied. Linear and elastoplastic stiffness matrices are given using Von Mises yield condition with isotropic hardening. Numerical examples are given to demonstrate the accuracy and efficiency of the present method. The numerical results show excellent agreement with experimental results. A shear lag phenomenon, as special case of general analysis, is considered as well.

Using a database containing test results of 58 specimens, simple mathematical expressions that explain the resistance of multiplanar tube‐to‐tube joints with circular hollow sections under axial brace loading are sought. The joints concerned are multiplanar TT‐ and KK‐joints consisting of two uniplanar T‐ or K‐joints that lie in different planes. The uniplanar joints have an identical configuration and loading of the braces. Multiple regression analysis is performed to obtain prediction equations. The proposed ultimate strength equations are shown to be in good agreement with the test results. The prediction models are based on a simple mechanical model of a ring that enables an extrapolation of the geometric variables' application ranges. The proposed ultimate strength equations are compared with existing prediction formulas. For the proposed validity ranges of the ultimate strength equations, the multiplanar coefficient μ, the factor by which the uniplanar joint strength has to be multiplied to obtain the multiplanar joint strength, ranges from 0.5 to 1.3, indicating that multiplanar effects are indeed significant.

The development of appropriate computer models to predict the response of buildings to fire is now making it possible to analyze specific structures under realistic fire‐exposure conditions. By means of experimental tests carried out at the University of Braunschweig on simply supported composite beams connected to reinforced concrete slabs, a theoretical study for estimating the effective slab width of composite concrete beams exposed to fire has been set up using a finite‐element analysis. The satisfactory agreement between the experimental and the calculation results confirms the efficiency of the finite‐element theory for determining the fire resistance of composite beams. The influence of the top transverse reinforcement in the concrete slab on the fire resistance and crack propagation are examined. The application of the results in designing fire safety of buildings is also discussed.

At the Luleå University of Technology, research has been performed on thermal stresses and thermal cracking in maturing concrete in the last decade. Laboratory tests have been carried out providing material data for calibration of a proposed theoretical model for thermal stress analysis in young concrete. The laboratory tests included creep tests, free thermal volume change tests and relaxation tests. In the theoretical model, the thermal properties and the transient mechanical properties of the young maturing concrete as well as the restraint within the concrete element are considered. The model has been implemented in a computer program permitting the analysis of different concreting scenarios of which some examples are shown. In the examples, influences of different measures against cracking as well as influences of changes in temperature conditions, restraint, and mechanical behavior of concrete are quantified. For some cases in the computational studies it may be concluded that, for control of early‐age thermal stresses and cracking in a structure, it is highly inadequate to consider only the early‐age distribution of the temperature field within the studied structures.

This is the first of two papers addressing the efficient and simultaneously accurate analysis of reinforced concrete frames through the use of adaptive nonlinear analysis techniques. The present paper discusses the requirements of adaptive analysis and highlights the essential need for a beam‐column formulation that accurately models the behavior of reinforced concrete members in the range where the response can be considered elastic and fully recoverable. A new elastic formulation is therefore proposed for reinforced concrete beam‐columns; it assumes a quartic shape function for the transverse displacements and differs from conventional finite‐element formulations in the use of the constant‐axial‐force criterion. The quartic formulation is capable of modeling a typical reinforced concrete member of arbitrary cross‐sectional shape and reinforcement layout with only one element, including the effects of concrete tensile cracking, the nonlinear compressive response of concrete, and the beam‐column action. Verification examples using the nonlinear analysis program ADAPTIC demonstrate the accuracy of the proposed formulation and its ability to model an entire reinforced concrete member using one element.

This is the second of two papers concerned with the application of adaptive techniques to the nonlinear analysis of reinforced concrete frames. The first paper presented a new nonlinear elastic formulation capable of representing an entire reinforced concrete member with one element, and the present paper discusses the use of such a formulation within the framework of adaptive inelastic analysis. This is followed by a description of an inelastic cubic formulation based on the layered approach, which complements the elastic formulation within the proposed methodology. The concept of automatic mesh refinement is then outlined, and comments are made regarding the applicability of the elastic formulation under low amplitude dynamic or cyclic loading. Finally, the accuracy and efficiency of adaptive analysis is verified through static and dynamic analyses using the nonlinear analysis program ADAPTIC. Comparisons are made where appropriate with the results of existing analysis methods for reinforced concrete frames to illustrate the advantages of the proposed methodology.

The results of an exploratory experimental and analytical study of six concrete‐graphite/epoxy (CG/E) composite beams are presented. Four of the beams incorporated a reinforced concrete slab to simulate the effect of bridge decks or floor slabs. The test variables were the shape of the graphite/epoxy (G/E) elements and the strength of concrete. The G/E beams were connected to the concrete slabs by an epoxy resin. The composite action and the effect of concrete strength on bond, stiffness, and strength were studied. The results showed that it may be possible to predict the response of these beams using familiar and existing theories. The use of epoxy resin to bond concrete deck to G/E elements was only partially effective. Mechanical connectors or other reliable means are needed to develop composite action between G/E elements and concrete. Many other issues such as optimized fiber orientation and means of improving the local stiffness and strength of thin‐walled G/E elements need to be addressed.

A simple method that evaluates the slenderness $K$ factor for leaning columns with sidesway uninhibited and partially inhibited is presented. The proposed method is applicable to the stability analysis of columns with pinned end connections in frames with rigid, semirigid, and simple connections. The proposed method and formulas are general and simple to apply yielding results within 1% of the theoretical values. The minimum amount of lateral stiffness or bracing required to make a leaning column totally braced (i.e., with $K=1$) is also discussed. Three design examples using the American Institute of Steel Construction's (AISC's) Load Resistance Factor Design (LRFD) method are presented in detail that demonstrate the effectiveness and accuracy of the proposed method.

A simple integrated procedure to analyze the problem of soil‐pile‐foundation‐superstructure interaction is presented. The procedure combines the available theories for the computation of the dynamic impedances and kinematic‐seismic response factors of pile foundations with a simple six‐degree‐of‐freedom structural model. The procedure is used to predict the response of the Painter Street Bridge located at Rio Dell, California, which was excited by the 1992 Petrolia earthquake. The predicted response with the proposed procedure is in very good agreement with recorded data, and the significance of considering the frequency dependent pile‐foundation impedances in predicting the superstructure response is demonstrated.

An algorithm has been developed for the stable analysis of reinforced‐concrete cross sections of arbitrary shape. The algorithm is based on a modified event‐to‐event scheme and is free of the convergence problems that have been observed with some iterative solution methods. The algorithm allows loading under displacement, load, or mixed displacement/load control. The algorithm is implemented in a program for the analysis of reinforced‐concrete sections, called ArcS. The cross section is modeled using a fiber discretization method. Each fiber is associated with a uniaxial material model. Common concrete and steel models are available and new material models are simple to add. The algorithm is discussed together with a description of the program capabilities. Examples are provided to demonstrate the algorithm.

The modeling of uplift pressures within a dam, on the foundation on which it was constructed, and on the interface between the dam and foundation is a critical aspect in the analysis of concrete gravity dams. The procedures for modeling uplift pressures are well established for the traditional hand‐calculation methods, but this is not the case for finite element (FE) analysis. In this paper, the procedures for including uplift pressures in the hand‐calculation methods, as prescribed by various government agencies, are reviewed and compared. Three separate models for including uplift pressures in a FE analysis are proposed. The use of these models is demonstrated in cracked‐base analyses of two different dam geometries with identical material properties. A linear elastic fracture mechanics criterion is used to determine the final crack length rather than the strength criterion used in the hand‐calculation methods. The results of these analyses are compared with one another and with results published elsewhere for one of the two geometries but with different material properties.

The computational effort to analyze a sandwich panel can be greatly reduced if an equivalent 2D thick‐plate bending model is used instead of a detailed 3D finite‐element model. The success of the transformation from a sandwich panel to a 2D thick‐plate bending model depends on the equivalent elastic constants used. In this note, these elastic constants for Z‐core sandwich panels are summarized. The elastic constant for the shear stiffness in the weaker direction for Z‐core sandwich panels is derived. To ascertain the validity of the elastic constants, the results obtained from the 2D thick‐plate bending model with different boundary conditions are compared with a detailed 3D finite‐element model. From the results, it is shown that excellent agreement is obtained between the two models.

The effects of different approaches to rating reinforced concrete slab bridges are explored by using an existing bridge as an example. Nonlinear finite‐element analysis (NLFEA) has been conducted on a field‐calibrated model of the bridge to obtain the ultimate capacity, which is compared with the rating factors obtained from American Association of State Highway and Transportation Officials (AASHTO) guidelines. The demand used to obtain the rating factor depends on how the structure is idealized in the analysis. The capacity can be interpreted at either the local level (material strength or cross‐sectional strength) or at the global level (failure of the structure due to attainment of a collapse mechanism or due to regional shear failure). It is observed that different approaches yield significantly different rating factors and the reasons for the noted differences are discussed.