Journal of Structural Engineering

Refinements are presented on a model proposed originally by Wozniak for the seismic analysis of fluid storage tanks, which forms the basis of the provisions in the American Petroleum Institute design code API 650. It is found that use of the rules in API 650 may lead in some cases to underestimations of the maximum compressive stresses in the shell, and to overestimations of the tensile stresses in the straps of anchored tanks. The stiffness of these straps relative to that of the shell is shown to play an important role in the maximum compressive stresses that can be expected in the tank wall. In the case of unanchored tanks, the larger compressive shell forces result from the limited mass of fluid that can be mobilized before the buckling load in the shell is reached.

A fracture mechanics‐based theoretical model is presented to predict the crack propagation resistance of fiber‐reinforced cement‐based composites. Mode I crack propagation and steel fibers are treated in the roposed model. The mechanism of fracture resistance for fiber‐reinforced concrete can be separated as: Subcritical crack growth in the matrix and the beginning of the fiber bridging effect; post‐critical crack growth in the matrix such that the net stress intensity factor due to the applied load and the fiber‐bridging closing stresses remains constant; and a final stage where the resistance to crack separation is provided exclusively by fibers. The response of fiber‐reinforced concrete during all these stages was successfully predicted from the knowledge of matrix fracture properties and the pull‐out load versus slip relationship of single fiber. The model was verified with the results of experiments conducted on notched beams reported here as well as by other researchers. Beams were loaded in a closed‐loop testing machine in order to maintain a constant rate of crack mouth opening displacement.

A combined experimental and analytical study is made of the response to strong base motions of reinforced concrete structures having irregular vertical configurations. In the study, two frame‐wall structures are constructed at small scale and subjected to earthquake simulations on a shaking table. Measured responses of the structures are compared with responses computed by several conventional analysis methods. The methods include inelastic dynamic response history analysis, inelastic static analysis, elastic modal spectral analysis, and elastic static analysis. Based on the data presented, it is concluded that the main advantage of the dynamic methods was that they were capable of estimating maximum displacement responses, whereas the static methods cannot be used for this purpose. In all other regards, the dynamic methods offered no clear advantage over the corresponding static method. The inelastic static and dynamic methods were superior to the elastic methods in interpreting effects of the structural discontinuities.

An experimental investigation carried out to assess the effect of incorporating steel fibers on the torsional behavior of conventionally reinforced beams is reported. The study involved testing 24 beams, with partial or full replacement of longitudinal steel reinforcement and/or stirrups by an equivalent volume fraction of steel fibers. The tests revealed that the loads on first cracking observed on fiber‐reinforced beams were substantially higher than those obtained in similar beams with conventional reinforcement. Increases of up to 60% in the torsional capacity of beams were observed, when the stirrups were partially or fully replaced by an equivalent volume fraction of fibers.

The reliability of floor and roof deflections due to occupancy and snow loads, respectively, and of lateral frame deflections due to wind loads is examined. These deflections are determined for unfactored code‐specified loads, and they are not to exceed professionally established deflection limits. Firstorder, second‐moment probabilistic theory is used in the analysis. Values of the reliability index are calculated for eight‐ and one‐yr reference periods. Recommendations are made with regard to load levels to be used in the serviceability analysis of deflection‐sensitive and deflection‐insensitive structures.

Dynamic correction stiffness and mass matrices are derived in explicit form for a tapered beam element of any cross‐sectional shape. These matrices are derived using exact expressions for the required displacement functions. Variation of area and moment of inertia of cross section along the axis of the element is exactly represented by simple functions involving shape factors. Vibration analysis of an example tapered beam is performed using static and dynamic correction tapered beam element matrices, and uniform beam element matrices. The costs, and advantages and disadvantages of analyzing tapered beams using these matrices are considered.

The structural engineers of classical Rome are reputed to have been careful and methodical, but also uninspired, tradition‐bound and overly conservative. Yet the Pont du Gard, an aqueduct bridge in southern France, was boldly conceived and designed. The structure is described and several of its structural features are examined in the light of insights presumably gained only during the last few of the 20 centuries since its construction. It is concluded that the design is far from being supersafe or wasteful, and that the bridge is reasonably stressed and amazingly efficient. The findings suggest, in fact, that the designer understood structural behavior uncommonly well.

A finite strip method (FSM) is developed for the analysis of linear elastic flat plate systems that are continuous over, deflecting supports. The approach presented incorporates the effect of the support elements in a direct stiffness methodology. The stiffness contribution of the support elements have been derived and are given in the form of strip matrices, which are directly added to the plate strip stiffness matrix at the element level. This summation of plate and support stiffness contributions constitutes a substructure, which is termed a compound strip. The validity of the compound strip method is demonstrated in several illustrative problems, which include single and multipanel plates continuous over flexible and rigid beams and columns. The FSM and finite element method (FEM) compare favorably for displacement and moment.

Asymptotic equations are derived for the natural frequencies and mode shapes of an elastic, taut, inclined cable. The equations are derived from more general asymptotic results by assuming quasi‐static stretching. It is shown that for horizontal cables all previous results are recovered, while inclined cables have additional properties which cannot be obtained by using horizontal cable results. The phenomena of avoided crossings and hybrid mode formation are reviewed for inclined cables, in particular because of the significant dynamic tension amplification they induce.

The design of a full‐scale reinforced concrete building is compared to US seismic resistant design practice, and the observed behavior and measured response of the building during a series of simulated earthquake tests is compared to behavior predicted by US engineers. The test structure is the seven story building tested in Japan as part of the US‐Japan cooperative research agreement. Two west coast design offices were asked to answer five questions, which were intended to give a comparison between the design of the test structure and the design provisions of the Uniform Building Code. The results indicate that the test structure had some significant code violations with respect to detailing and strength of the shear wall. A five part questionnaire was also developed and presented to several US engineers. They were asked what type of response they expected from the test structure during simulated earthquake tests. The responses from the engineers often varied widely, but the average of their responses usually compared well to observed and measured results from the actual tests.

An orthotropic model to predict the ascending and descending parts of the stress‐strain curves of concrete subjected to biaxial or triaxial compressive stresses is presented. The stress‐induced orthotropic material properties are expressed in terms of six constants in the compliance matrix. The six material constants are expressed as functions of stress invariants at ultimate strength. The proposed orthotropic constitutive model depends on the knowledge of the three principal stresses at the maximum strength, which are obtained through the use of a strength criterion (which is sensitive to all the three stress invariants). For predicting the ascending and descending parts of the multiaxial stressstrain curves, the six orthotropic material constants in the compliance matrix are continuously changed with the help of a “fracturing index” parameter. The proposed constitutive model compares favorably with the available experimental data under multiaxial stresses.

The optimization of an archgrid consisting of a system of parallel arches running in a number of arbitrary directions is presented. It is established that the archgrid must finish with a single middle surface in the optimal solution even though the possibility of separate layers of arches is allowed in the formulation. The possibility of some arches becoming vanishing ones (of zero m cross sections) is also taken into account. It is shown that mean square slopes of vanishing arches are not to exceed unity for any one arch, while those of nonvanishing ones are equal to unity. Implicit in the derivation of these conditions are: (1) The loading system is perpendicular to the reference plane containing the support of all arches: and (2) any one arch is contained in the plane of the loading system, and its reaction component parallel to the reference plane is constant along its entire length. Two examples of optimal shapes of archgrids over square and rectangular domains consisting of arches running in four equally inclined directions are presented.