Journal of Structural Engineering

An investigation into the factors affecting the strength of epoxyrepaired timber structures has been conducted. Two aspects are evaluated: repair methodology, and effects of member configuration. The structural repair sequence of timber consists of four basic steps: (1) Special member preparation; (2) joint sealing; (3) epoxy injection; and (4) finishing. Each of these steps is described in detail with recommended procedures to aid the engineer in both the design and inspection of epoxy repair. To evaluate the various joint configuration parameters affecting the behavior of epoxy‐repaired timber, over 200 full size repaired members and over 100 shear blocks of Southern pine were tested. The parameters studied include effects of: mechanical connectors; length of overlap; member thickness; grain orientation; timber age; and glue line thickness. It was found that the shear bond strength is on the order of the shear strength of the wood. It was also determined that the primary factors affecting strength are the ratio of lap length to member thickness and grain orientation.

The repair of timber structures requires the same careful engineering design as that of new structures. However, practically no information is available that allows the engineer to compute either allowable or actual stresses for repair alternatives. Based on both theoretical and experimental studies, a methodology for computing both actual and allowable glue line shear stresses is presented here. The actual glue line stress is computed as an average shear stress. The allowable stresses are given as formulas which are functions of the wood species, grain orientation, allowable wood shear stress, and lap length to member thickness ratio. Several epoxy formulations are considered and a method for evaluating other epoxies is presented. Numerical examples are given to illustrate the approach for both predicting the strength and designing a repair scheme. Through the use of the design techniques presented here for epoxy repair of timber, the engineer can rationally decide: (1) Whether the proposed repair will be structurally adequate; and (2) how to modify the design if the predicted load capacity of the joint is too low.

A development was undertaken to demonstrate the feasibility of using computer methods to calculate the effective length factors of elastically restrained beam‐columns. Three theoretical models for elastically restrained beamcolumns were derived to characterize the structural behavior of various types of elements used in offshore structures, such as jacket legs, piles, X‐braces, diagonal braces, K‐braces, etc. These beam‐columns are restrained by elastic rotational springs at the ends and an elastic translational spring at any given location along the beam‐columns. The expressions for the rotational and translational stiffness coefficients for the constraining elements and the characteristic equations for determination of the effective length factors for the restrained beam‐columns were derived by utilizing Livesley's stability functions. These expressions together with representative curves of effective length factors of beam‐columns in terms of constraining elastic spring constants, and calculated effective length factors for elements in example offshore structures are presented.

Recent multi‐beam bridge designs have been developed around standard prestressed, precast double‐tee sections to combat the high cost of this particular type of bridge design. Although several methods of multi‐beam bridge analysis are available, none are applicable to discretely connected or skewed bridges. A procedure for the analysis of skewed, discretely connected multibeam bridges is presented. The method of analysis proceeds through three distinct phases: (1) Development of a single beam response model; (2) modeling of connection response; and (3) generation of a governing system of equations for the total structure. The first phase is accomplished through the use of statics, and connection response is modeled by linear and rotational springs resisting relative displacement between adjacent beams. The governing equations for the response of the assembled bridge take the form of a symmetric banded linear system in which the four forces at each connection in the bridge are the unknowns.

This paper investigates fatigue strength of plain concrete subjected to flexural loading. This type of fatigue loading is of concern in the design of concrete bridges and concrete pavement slabs, since the flexural stresses in these structures can be critical. Both experimental and theoretical studies are conducted. The S‐N curves are generated from the test results and an equation is obtained by regression analysis to predict the flexural fatigue strength of concrete. A probabilistic approach is introduced to predict the fatigue reliability of concrete. The distribution of fatigue life of concrete under a given stress level was found, from the test data, to approximately follow the Weibull probability law. The method of obtaining the distribution parameters from S‐N relation for the flexural fatigue of concrete is also presented. The Weibull distribution is found to have more convincing physical features than the lognormal distribution, and may be appropriate to. describe the fatigue behavior of concrete.

The previously derived size effect law for blunt fracture is exploited for determining the parameters of the R‐curve, of the crack band model, and of Hillerborg's fictitious crack model. No measurements of the crack length or of the unloading compliance are needed. It suffices to measure only the maximum load values for a set of geometrically similar specimens of different sizes. The parameters of the size effect law can then be identified by linear regression. The inverse slope of the regression line yields the fracture energy. The regression also has a twofold benefit: it smoothes statistically scattered data, and it extends the range of the data, so that one can do with fewer tests. From the experimentally calibrated size effect law, the R‐curve may then be obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes. A simple algebraic formula for this envelope is presented. The size effect regression plot makes it also possible to determine crack band model parameters, particularly the fracture energy, the crack band width, and the strain‐softening modulus. The same is made possible for Hillerborg's model.

Base anchorage forces for three empty, stiffened steel grain silos with conical roof shells are determined by finite element analysis for nonuniform wind loading. In general, the axial tensile forces govern for tall silos, while the shear force anchorage requirements control for shallow silos. The anchorage requirements for all three types of silos are adequately predicted by use of an adjusted membrane theory for a wind loaded cylindrical shell free at its top, with axial stress at the top due to the roof wind loading. The “cantilever beam” approximation yields extremely nonconservative anchorage forces.

The effects of the shape of the descending branch of the tensile stress‐strain curve, fracture energy, grid refinement, and load‐step size on the response of finite element models of a notched concrete beam are studied. The width of the process zone and constraints imposed on crack angles are also investigated. Cracking of the concrete in tension is the only nonlinear behavior modeled. Load‐deflection curves and general cracking patterns provide the primary means for evaluating response. Comparisons with discrete crack models are made. The fracture energy, tensile strength, and shape of the descending branch interact to determine the stiffness and general behavior of the specimen. The width of the process zone has a negligible influence on the beam's response. The importance of proper crack orientation is demonstrated. The model is objective with respect to grid refinement and load‐step size. The implications of the results are discussed with respect to modeling reinforced concrete structures.

A model for inelastic response analysis of braced steel structures is presented. This model achieves realism and efficiency by combining analytical formultions with formulas developed on the basis of a study of experimental data. A brace is idealized as a pin‐ended member with a plastic hinge located at its midspan. Analytical expressions for the axial force versus axial deformation behavior of the brace are derived on the basis of the classical beamcolumn equation and a plastic flow hypothesis for the plastic hinge. Several empirical behavioral characteristics are incorporated to achieve better representation of observed cyclic inelastic behavior. The model is implemented in a computationally efficient manner so as to be suitable for studying the dynamic response of relatively large structural systems. Verification of the new model is performed on the basis of a quasi‐static analysis of an individual strut and dynamic response analyses of a braced steel frame. The model is able to accurately simulate the cyclic inelastic behavior of steel braces and appears to be reliable and applicable to dynamic analyses of braced frame structures.

The behavior of different length wide flange (WF) links in eccentrically braced steel frames with or without axial force application, were experimentally investigated using a subassemblage system simulating the frame action. The results are examined with emphasis on the influence of link length on the performance. Moment, shear, and axial force interaction, as well as the effect of strain hardening on moment redistribution, energy dissipation, and flange and web buckling are considered. Design and analysis methods for cyclically loaded links are proposed.

The inelastic seismic response of a class of one‐way torsionally unbalanced structures is presented. The structural model consists of a single mass supported by bilinear hysteretic elements. The yield strength of the model is a function of the lateral period and follows a trend similar to the design strengths suggested by design codes. The response parameters of interest are the resisting element ductility demands and the edge displacement of the model. The sensitivity of the response parameters to system parameters, such as structural eccentricity, yield strength, uncoupled lateral period, and uncoupled torsional to lateral frequency ratio, is examined for two types of ground motions. It is found that the effect of asymmetry is most pronounced for stiff structures with low yield strength. Unlike elastic response, the uncoupled torsional‐to‐lateral‐frequency ratio is not a sensitive system parameter that affects the inelastic responses. Exceptionally large ductility demand can be expected on eccentric stiff structures with low yield strength when exposed to ground motions with large and long duration acceleration peaks as exemplified by the 1977 Romanian earthquake record.

A critical part of the large‐scale earthquake simulation facility at the State Univ. of New York at Buffalo is the shaking table itself. The table is a prestressed composite sandwich structure consisting of a steel frame, a superimposed prestressed‐reinforced concrete grid, and ferrocement faces. The ferrocement was found to be particularly useful as the table surface layers. Its unique characteristics led to a very thin yet stiff facing, which greatly improved the overall dynamic behavior of the structure. The present paper describes the table's structure, emphasizing the role of the ferrocement in the system and the determination of the required static and dynamic properties using this rarely utilized material. The construction of the table and various problems encountered are also examined. The paper concludes with a comparison of the actual tested performances and the theoretical design values.

Recent building codes require that wind loads be determined by multiplying a calculated velocity pressure by the drag coefficient of the structure. It is suggested that the drag coefficients given in the codes for latticed towers are conservative. To determine appropriate drag coefficients for square self‐supported latticed towers two models were constructed and tested in a wind tunnel. Drag forces of the two models with and without heel angles as well as half of one model and tilting to different angles of the other model were determined. Results are analyzed and drag coefficients are calculated and compared to other published test results and to the ANSI A58.1 Code. Recommended equations are given for determining the drag coefficient of latticed towers with solidity ratios in a given range. For the wind direction on the diagonal axis of the tower the drag was found to be independent of the solidity ratio and, therefore, a multiplier is recommended. A multiplier is also recommended for towers with legs that have a heel angle.

A Rayleigh-Ritz free vibration analysis of a simply supported beam is carried out in this note with prestress effects included through an axial compressive load and with shear deformation and rotatory inertia considered. Suitable functional forms are assumed for the lateral displacement and the shear rotation. Results in the form of frequency parameters for various modes are presented. The variation of the frequency parameters with slenderness ratio (length/radius of gyration) and the magnitude of the compressive load (prescribed as different percentages of the critical load of the beam) is clearly brought out through numerical results. It is observed that the effect of shear deformation and rotatory inertia is quite significant for higher modes of vibration of slender beams and the effect of axial compressive load is predominant for lower modes of vibration.

This note examines the computer modeling of grids and space frames which have joints between members where there are significant offsets. This is commonly done by the inclusion of dummy members of high stiffness. Results are presented for a typical structure using a range of values for this stiffness from which their sensitivity on the chosen properties can be seen.