Journal of Structural Engineering

Fixed‐end restraint effect on the load carrying capacity of steel arches loaded into the inelastic and the finite deformation range is studied by an accurate nonlinear finite element approach. This approach takes into consideration the two important factors on material nonlinear phenomenon, namely, spread of yielding zones in the cross section and along the longitudinal axis of the arch and unloading caused by strain reversal. Special characteristics of the interaction between bending moment and axial thrust, the changes in deflectional mode, the progress of yielding and unloading zones with load level, and local failure at the springing are thoroughly examined. The load‐deflection behavior until the stability limit load is reached, has been analyzed by linear theory, the second order elastic theory, and an accurate nonlinear theory.

Four different analytical models are presented for architectural precast cladding on highrise buildings. An interstory shear stiffness model, an incremental failure model, a hysteresis model and a slotted connection model were used to study cladding performance from the linear elastic range up to failure. The models were added to a finite element model of the structural frame of a 25‐story steel frame office building to account for the lateral stiffening effect of the building facade. Cladding stiffness values were based upon a comparison of measured and computed vibration frequencies for the building. Results of the study include peak interstory drift plots and a representation of the cladding failure state for the case of moderate earthquake ground motion input. Cladding stiffness was found to have a substantial effect on building dynamic properties and linear seismic response.

The rate of energy released as delaminations grow in FRP chimney liners subjected to the thermal environments of flue gas is computed by an indirect finite‐element approach developed by Rybicki and Kanninen using a single conventional finite element model. The energy release rates are proportional to the work required to close the displacement components of the gap at a double node near the crack tip. The results show that delaminations less than a certain size, depending on the flue gas temperature, are not susceptible to blister formation and unstable growth. Moreover, the growth of delaminations is bounded. The final size of a blister depends upon the flue gas temperature and the level of degradation of the fracture resistahce of the material that occurs over time in a thermal environment. Square shaped delaminations are found to be less susceptible to growth than the rectangular shaped delaminations orientated perpendicular to the angle of wind of the structural laminate. Initial deflection reduces the energy release rate almost proportionally to the ratio of initial deflection to total deflection.

A finite element is developed that accurately models the strain states it is designed to represent regardless of its initial configuration. In other words, the interpolation polynomials are unchanged hy element distortion. The formulation of this element is based on the transformation of a specified set of linearly independent strain states into the desired stiffness matrix. This stiffness matrix exactly reproduces the strain energy content and the pointwise strain of the continuum for the strain states designated in its formulation. This insures that the polynomial bases of the approximation remains constant. Instead of computing the strain quantities at a number of points in the element, the strain distribution information is given in terms of rigid body and strain gradient terms for a designated point. This form of the strain data supplies information about the state of convergence in the problem and the location of regions of high strains. The computational speed of the linear strain element is competitive with the isoparametric formulation procedure.

Based on equilibrium and compatibility, a general analysis procedure is developed for cracked prestressed and partially prestressed concrete composite sections in the elastic range of behavior. Direct equations are derived for the strains and stresses in the constituent materials taking into account the change in prestressing force, due to the application of loads. Solutions for the special cases of uncracked composite sections, cracked and uncracked noncomposite sections as well as expressions for the cracking and decompression moments are also presented. A parametric analysis is conducted to study the effects of various parameters on the stresses and stress ranges in the constituent materials. An example is developed to illustrate the application of the method.

An improved single‐degree‐of‐freedom (SDOF) approach is presented for the analysis of shallow‐buried reinforced concrete box‐type structures under the effect of blast and shock environments. The method is based on rational models for structural resistance functions that describe the combined effects of flexure, shear, and in‐plane compression on the system response. The approach is demonstrated by employing it for the analysis of seven different events for which experimental information is available, and the accuracy of the method is evaluated by comparing numerical and experimental results.

The current AASHTO design loads were developed more than 40 yrs ago based on truck traffic in operation in that period. The code, however, has produced safe designs despite the vastly increased legal loads and reduced levels of maintenance. New structural analysis procedures and continuous pressure to increase the legal load limits justify a code review to maintain the current safety levels for all design applications. This is accomplished by using a reliability analysis with data from large scale field measurements on actual truck loadings and bridge responses. The data obtained from these measurements is projected to calculate the maximum expected live load in the lifetime of the structure and used to calculate a safety index. Safety indices for typical spans are first calculated for designs that satisfy the current AASHTO code. A target safety index is extracted from these values and a new design procedure is proposed to achieve this target index uniformly for all the spans considered. A parametric analysis shows that the proposed changes are insensitive to small variations in the data base if the average current safety level is acceptable and can be used as basis for future code changes.

A numerical procedure for determining the hysteretic behavior of axially loaded, pin‐ended bracing members is outlined. The relationships between axial loads and deformations are computed recognizing the different states corresponding to appropriate load‐displacement conditions covering both buckling and yielding. Accurate numerical representation of the hysteretic response curve of bracing members is confirmed. By incorporating bracing elements in representative elastic rigid‐jointed plane frames, the contribution of braces to lateral load resistance in seismic excitation conditions is examined using numerical integration techniques. The efficiency of bracing systems is demonstrated. Both the lateral displacements and the loads induced in the main frame are less than those in the equivalent unbraced structure. Accurate prediction of post‐elastic behavior of bracing members has significant practical application potential particularly in industrial structures where the concept of an initially stiff yet structurally efficient system capable of degrading under extreme lateral loading conditions to a more flexible, but still load resistant structure, is very attractive.

The paper investigates the elastic lateral buckling of simply supported monosymmetric I‐beams under moment gradient. Independent solutions are obtained using the finite integral method and the Rayleigh‐Ritz energy approach. The elastic buckling moments depend on the degree of beam monosymmetry, ρ, the beam parameter, $\overline{K}\text{,}$ and the end moment ratio, β. Buckled mode shapes reveal that the buckling deformations of the beams have complicated forms. It is found that the present design moment modification factor formula cannot satisfactorily predict the buckling capacities of monosymmetric I‐beams. An alternative approximate buckling formula is proposed.

In current practice, stresses from elastic analysis are used to design reinforcement in concrete shells based on pointwise limit state behavior. This practice may be justified in view of the lower bound theorem of plasticity and the fact that elastic stresses are equilibrium stresses. Reinforced concrete, however, is not a perfectly plastic material, and the lower bound theorem cannot be strictly applied. To verify the adequacy of current practice, therefore, an analytical program was undertaken at North Carolina State Univ. A finite element computer program, which accounts for cracking of concrete and yielding of reinforcement, and that incorporates a cracking model consistent with the limit state design equations, was developed. The program was used to analyze various plane stress and shell problems. Many cases of hyperbolic paraboloid shells were also studied and are reported in this paper. It is shown that in all the saddle shell cases analyzed, the calculated ultimate capacity exceeded the design ultimate capacity. This proves the adequacy of the current practice at least for the saddle shells studied. Other conclusions of the parametric studies performed are also presented.

Analysis of the interaction between a precast wall cladding panel and a reinforced concrete frame under linear static and dynamics forces has been performed. Two computer programs (LDYN and LSTAT) were written to evaluate the effects on the lateral displacements and dynamic characteristics of a moment resisting frame when the cladding is incorporated into the analysis as a structural component. The data indicates a significant change in lateral displacement, natural frequency, member force distribution and connector forces when compared with a frame neglecting the structural characteristics of the cladding.

Measured distributions of load among two, three, five, or seven bolts in a row parallel to the direction of the applied load are presented for joints of various width Douglas‐fir main members and two widths of steel splice plates. An analytical method of predicting the load distribution is also presented. The results show that each row has a unique load distribution dependent upon the variation in load‐slip curves and fabrication effects. The analytical method is shown to predict the distribution as long as sufficient knowledge of the individual fastener load‐slip relations is available. Results indicate that present design procedures for rows of bolts are not conservative.

A new stiffness matrix for the analysis of thin walled beams is derived. Starting from the principle of virtual displacements, an updated Lagrangian procedure for nonlinear analysis is developed. Inclusion of nonuniform torsion is accomplished through adoption of the principle of sectorial areas for cross‐sectional displacements. This requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each end of the element. Problems encountered in the use of this and similar matrices in three‐dimensional analysis are described.

A geometric stiffness matrix for a beam element has been derived in a related paper. The derived matrix implies quasitangential behavior of bending moments and semitangential behavior of torques. Use of this element matrix in a three‐dimensional, large displacement analysis can result in an apparent lack of joint equilibrium. Alternative definitions for moments are studied for the purpose of resolving this problem. It is verified that equilibrium of a rotated angle joint can be achieved if each joint moment is defined as a semitangential moment.

Epoxy injection techniques are widely used to repair concrete or masonry structural components damaged by earthquakes, wind, or other types of overloads. When properly performed, the effectiveness of such epoxy injection techniques has been demonstrated by numerous laboratory experiments and a multitude of successful field applications. Except for elevated temperature, fire, and creep effects, most strength properties of epoxy repaired concrete components exceed those prior to damage. Since epoxy adhesives are organic thermosetting resin systems, they are highly susceptible to softening and pyrolysis at elevated temperatures. The effects of temperature and fire on epoxy repaired concrete beams is discussed herein with a presentation of test results of both small‐ and large‐scale specimens. These test results show that both shortterm strength and stiffness of epoxy repaired beams reduce rapidly at uniform temperatures exceeding about 250 °F (121 °C). Under fire conditions, the strength reduction is primarily influenced by the presence or lack of fire protection coatings and the thermal gradient. Analytical techniques are presented for strength analysis of epoxy repaired beams under a variety of temperature and fire exposures.

The reliability of a structure with many potential failure modes is usually assessed by evaluating an upper bound and a lower bound on the failure probability of the structure. Although it is known that a better estimate of the failure probability can be obtained with third‐order linear bounds, the excessive computational requirement of trivariate integrals (trisections) has so far restricted their use in normal practice. In this paper a nonlinear bound for trisections in terms of bisections (bivariate integrals) is presented with examples. Furthermore, the bound developed for the trisections has been used in the third‐order linear bound to produce a better second‐order lower bound (nonlinear) for the reliability of structures, and the results are compared with other published results.

An efficient analytical model is presented which determines values of steel stresses, steel strains, bond stresses as well as slip values along an embedded reinforcing bar in a reinforced concrete beam column joint under severe cyclic excitations.