Journal of Structural Engineering

Use of the design point method for reliability analysis of laterally loaded piling is described and programmed. A versatile method of modeling uncertainty in soil lateral resistance is proposed. Using this method, the soil reaction corresponding to a given deflection at a specific depth is treated as a random variable. Input soil reactions for P‐Y curves give mean values of soil resistance, with uncertainty quantified by residual reaction probability distributions. Other random variables explicitly considered include applied lateral, vertical, and moment loads at pile top, pile stress capacity, and pile top lateral deflection capacity. Vertical load and moment can be independent of or partially correlated to lateral load. Stress and deflection failure modes are considered. In the first, failure of the pile is assumed to occur when the actual maximum normal stress at any point exceeds the pile material yield point. In the second, failure is assumed to occur when the actual lateral top deflection exceeds the deflection capacity. A nonlinear analysis by the displacement method is used, including P‐delta effect and nonlinear soil springs.

Several studies in recent years suggest that conventional design of space trusses, based on elastic analysis, may lead to unsafe design. Space truss response is adversely affected by imperfections in the presence of brittle‐type compression member buckling coupled with high degree of static indeterminacy. This paper provides a critical review of enhancement techniques evolved in recent years that aim at improving space truss response in terms of ductility and loadbearing capacity. Underdesign of critical tension members coupled with overdesign of critical compression members, diagonal member removal or eccentric diagonals, and prestress by imposed lack of fit in members are effective techniques that are relatively simple to implement. A conservative approach to the design of compression members is generally recommended.

A finite element elastic‐plastic model for separated double chord gap K‐joints of steel rectangular hollow sections (RHS), is presented. The model treats a single chord member as composed of a plate representing the inner web and a channel depicting the top and bottom flanges and the outer web, respectively. Triangular and rectangular flat shell elements are used to discretize the inner web plate, whereas plane stress elements are employed for the branch members. The channel consists of a grillage of beam elements. The analysis extends beyond the elastic limit and accounts for strain hardening and material nonlinearity. A comparison of theoretical predictions with the experimental results of 12 K‐joint specimens of a previous study shows fair agreement.

TO cope with more realistic material behavior in the structural optimization process, this paper introduces a general constitutive model based on seven parameters along with the secant stiffness method and the Rosenbrock's minimization algorithm. In addition, the concepts of reserve and residual strengths are used to study the effect of optimization on system strength and redundancy. Furthermore, stress and displacement behavioral constraints are considered both separately and simultaneously to investigate their influence on the optimum solution for brittle and ductile truss systems.

The eigenfunctions of a continuous beam are derived by numerical method. The top flange plate strip, the vertical variable depth web strip and the bottom flange shell strip are formulated by combining these functions in the longitudinal direction with appropriate finite element shape functions in the transverse direction in order to analyze continuous, haunched box‐girder bridges. The numerical examples given in this paper demonstrate the advantages of this method which are simplicity, accuracy and convenience.

The curves presented enable the buckling loads to be found for tapered columns with a uniform axial force P applied over all their length L or over all except $\beta L$ (for $0⩽\beta ⩽0.9$) of their length. The main curves cover six combinations of end conditions, $0.05⩽r⩽1$ and $h=2\text{,}3\text{,}$ or 4, where r is the ratio of the second moment of area at the smaller end to the second moment of area at the larger end and h is the power which governs the variation of second moment of area with length. An evaluation is also undertaken of the accuracy of a method which uses the curves to obtain lower bound approximations to the critical load factor for stepped distributions of axial force. These lower bounds are on the safe side, so that they can cause loss of economy but not loss of safety, and for most practical problems they are within 10% of the exact answer.

An investigation was conducted to study behavior of steel double angle framing connections under severe cyclic loading of earthquakes. The studies consisted of subjecting six connection assemblages to an increasing level of large cyclic rotations until failure occurred. The connection angles were bolted to the column flange and welded to the beam web. Structural ribbed bolts taken from an existing building and high strength A325 bolts were used in test specimens. The structural ribbed bolts failed in cyclic tension when connection experienced rotations larger than 0.025 radians. Behavior of connections with A325 high strength bolts tightened to 70% of their proof loads was satisfactory and ductile. However, in these specimens, cyclic fracture of angles started when connection rotation exceeded 0.025 radians. Results of hysteresis behavior, failure modes, and variations of bolt forces are presented. Also, information is provided on applying the findings to dynamic analysis and design of steel structures with double angle connections.

In assessing structural safety, the state of knowledge is imperfect when uncertainties arise from estimation error or model imperfection. The nature of these uncertainties is fundamentally different from those arising from inherent variabilities. A reliability index under such conditions is a point estimator of safety. Motivated by needs in structural code development, a set of fundamental requirements on the point‐estimator reliability index are formulated. Existing definitions of the reliability index are examined in this light and are found to be deficient in satisfying one or more of the requirements. Based on concepts from Bayesian statistical decision theory, a new reliability index is introduced which satisfies all the stipulated requirements. The index recognizes the fundamental difference between the sources of uncertainty and provides a rational basis for the assessment of structural safety and for development of reliability‐based codes under arbitrary states of knowledge. Methods are also developed for quantifying the uncertainty in the measure of safety arising from the imperfect state of knowledge. Existing reliability methods can be used to compute the probability distribution or variance of the safety measure. A simple example illustrates the main concepts of the paper.

Transverse shear failures of reinforced concrete plates and shells are analyzed using a layered shell element that has been modified to more accurately model shear behavior. The transverse shear stress distribution through the shell thickness is obtained by equilibrium relations, Three‐dimensional failure criteria are used to predict transverse shear failure. The element is able to predict shear failures for plates and shells with and without shear reinforcement. A new cracking model based on crack friction, shear dilatancy, and crack surface deformability is used for some of the results. The analytical results are compared with experimental results for beams, plates, and shells subjected to concentrated forces. Good agreement between analysis and experiment is obtained for plates with and without shear reinforcement and for shells without reinforcement. An improved multidirectional cracking model is needed for shells with shear reinforcement.

A rational method of analysis is proposed for the calculation of creep deflections of reinforced concrete beams under sustained service loads. The method introduces the use of a fictitious modulus relating, for a given section under bending, the initial stress in concrete with the final strain after a period of sustained load. The requirements of strain compatibility and equilibrium of a section are used, in conjunction, to determine the position of neutral axis and strain and stress distributions after creep. The long‐term flexural rigidity of the member, (EI), is determined from a knowledge of a new neutral axis and a new modular ratio and is used to calculate the final deflections. The approach for calculating long‐term deflections is similar to the current American Concrete Institute (ACI) procedure for calculating short‐term deflections. The accuracy of the analysis is verified by comparison with several experimental measurements of beam deflections. The result is good correlation between the theoretical values and measured values.

An analytical approach to calculate time‐dependent stresses and strains in initially cracked reinforced and partially prestressed concrete members with or without nonprestressed reinforcement is presented. The method utilizes Trost's relaxation coefficient approach and the aging coefficient approach of Bazant in addition to the linear creep theory. Noncoincidence of the neutral axis of stress with the neutral axis of strain is taken into account in the analysis. Necessary expressions are developed for the general case of a partially prestressed beam of unsym‐metrical I section from which expressions for the special cases of reinforced concrete members of either rectangular or T shape, with or without compression reinforcement are deduced. With these algorithms, a comparative analysis of the effects of the quantity and position of the compression reinforcement, prestressed reinforcement, and nonprestressed tensile reinforcement is made. Four examples are given to demonstrate the method of analysis.

Nondestructive test methods are evaluted for predicting the buckling capacity and buckling location of fabric‐reinforced concrete shells. The load‐deformation methods consist of measuring vertical deflections of 10—20 points on the shell surface under increasing vacuum pressures, curve fitting of the deflectionpressure response at each point, calculating a characteristic pressure on each curve, and using the lowest such calculated pressure as a predictor of shell buckling capacity. The curve fits are updated at each pressure increment and the test is continued to a pressure equal to a safe fraction of predicted buckling load, based on prior testing experience. Predicted and actual buckling pressures are compared for six experimental shells. The chosen method was selected from a comparison of four extrapolation methods, based on its least standard deviation between predicted and actual buckling pressures for the six shells. Vacuum tests can also indicate approximate buckling locations, for installing reinforcing arches before placing shells in service, and provide an inexpensive means for proof loading shells to any specified overload factor.

Specimens simulating silicone bonded structural glazing joints were tested to failure under combinations of tensile and shear displacement. Tension, shear, and moment resultants in the joint specimens were monitored throughout each test. To account for glass edge rotation effects, joints were also tested in the same manner with the addition of a relatively large preset rotation. Tests were conducted at three joint depth‐to‐width ratios, spanning the range typically encountered in practice. The results of these tests were used to develop interaction relationships for ultimate strength and displacement. The interaction between nominal tensile and shear stresses at failure is elliptical. Differences between the three depth‐to‐width ratios, on a stress basis, were minor. The corresponding interaction for ultimate displacements is approximately linear. Glass edge rotation effects, within typical practical limits, are negligible. Measured bending moments remained small during all testing, apparently as a result of a moment balance between the tension and shear forces acting on the deformed specimen geometry.

For designing steel beam‐columns, the present AISC‐LRFD, AISC‐ASD linear interaction equations are simple to use, but they have some weaknesses. The AISC‐ASD interaction equations have a jump from a long to a short member, i.e., for a very short member, the stability interaction equation does not always reduce to the strength equation. For short beam‐columns in which the weakaxis bending and axial force are dominant, and for double curvature bending, the AISC‐LRFD bilinear interaction equation may result in an overly conservative design. In this paper, a unified design interaction equation for braced steel beam‐columns subjected to compression combined with biaxial bending is proposed. An extensive evaluation of the proposed design equation, as well as the AISC equations, is made and compared with exact inelastic solutions of I‐section beam‐columns and with the results of 81 full‐scale tests of biaxially loaded beam‐columns of I‐section. It is found that the load‐carrying capacity of steel beam‐columns can be estimated simply and more accurately by the proposed unified design interaction equation.

Metal silos and tanks are subject to axial compressive stresses in their cylindrical shell walls. The buckling strength is very sensitive to geometric imperfections in the wall. The most regular and well‐defined imperfection is the local depression adjacent to a circumferential weld, caused by the plate rolling process and shrinkage of the weld.

This paper examines the elastic buckling strengths of thin cylindrical shells under axial compression, with imperfections arising at circumferential welded joints. The effects of the welded joint depression amplitude, the shell radius‐to‐thickness ratio, a change of shell plate thickness at the weld, and internal pressurization are all examined. The study is confined to cylinders with a radius‐to‐thickness ratio in excess of 100, as thicker shells are rare for these structures. It is shown that a welded joint depression is one of the most deleterious practical imperfection forms currently known.

A key step in a numerical analysis of an elasto-plastic frame using the plastic hinge concept is the calculation of the incremental resistance and plastic deformations of a beam element for a given incremental member displacement vector. An algorithm is presented, based on the assumption that during the load or time increment the change of the displacement is linear. That is, in the member displacement space, the vector is straight so that at any stage within the total increment, the current displacement increment is a scalar times the total displacement increment vector. Following an iterative process, the new member force point is made to stay on the yield surface and the corresponding plastic deformation increment is computed in a manner more strictly conformable to the theory of plasticity. The incremental displacement can be large enough so that the element may undergo the process of changing from a state of total elasticity to having one yielded end and then on to having both ends yielding. A numerical example is given.

The results of an inelastic finite element distortional buckling study of a hot-rolled I-beam used in a composite girder are given. The study shows that the relationship between slenderness and strength for distortional buckling is different from that which exists for lateral buckling, the latter forming the basis for the codified method of design against the lateral instability limit state. A relationship between slenderness and strength for distortional buckling is given, from which an accurate and simple design method is proposed.