Journal of Structural Engineering

Lognormal probability distribution functions for both ground snow loads and the ground‐to‐roof conversion factor are used to establish lognormal probability distribution functions for roof snow loads. Site specific values for the conversion factor multiple ${\alpha }_N$ were determined. The conversion factor multiple has the property that product of ${\alpha }_N\text{,}$ the exposure factor EX, the thermal factor T and the N‐year mean recurrence interval (MRI) ground load equals the N‐year (MRI) ground load equals the N‐year MRI roof load. The conversion factor multiples ${\alpha }_N$ for mean recurrence intervals of 25, 50 and 100 years are presented for 128 sites in the United States. The 50 year MRI multiples for all except four sites fell in the range $0.56⩽{\alpha }_{50}⩽0.66\text{.}$ These values were compared with roof snow loads provisions in the 1982 American National Standard. It was found that the use of the ANSI‐1982 ground loads, which have a MRI of about 50 years, in conjunction with the ANSI‐1982 coversion factor multiple of 0.70 results, on average, in a flat roof snow load with a MRI of about 80 years.

The dynamic response of multistory reinforced concrete coupled walls was evaluated from the perspective of linear models based on response spectra, modal analysis, and reduced effective stiffnesses. This study indicates that: (1) Linear models based on plausible reductions in stiffness and reasonable ductility demands in the structural components can provide an adequate basis for designing reinforced concrete structures; (2) the design of multistory reinforced concrete coupled walls must include the effects of concrete cracking, slip of the reinforcement, and ductility demands in the structural components. Special attention must be given to the redistribution of flexural moments and shear forces between the wall in tension and the wall in compression; (3) natural frequencies of reinforced concrete structures can be significantly reduced by cracking caused by shrinking of the concrete; and (4) to avoid catastrophic collapse in coupled wall systems, the structural system should be designed such that the coupling beams are the only members that suffer severe yield cycles, and their energy dissipation capacity is utilized before the walls are subjected to high or extreme ductility demands.

A yield line method is developed to analyze reinforced concrete slabs‐on‐grade to determine collapse loads. The particular cases discussed are: (1) A one‐way slab with a line load at mid‐span; (2) a slab with a central load; (3) a slab with a load at a free edge; and (4) a slab with a load at a free corner. For each case, an expression for the collapse load is given in terms of material and geometric parameters. Plots of collapse load magnitude vs. a load distribution parameter are presented for the proposed analysis method and compared to analyses found in previous literature.

The finite element solutions of deep beams are presented. Two types of deep beam elements are introduced. The first element simulates the exact analytical solution of the deep beam of rectangular cross section. The element stiffness matrix is developed by solving the plane stress elasticity equations with the selection of the proper boundary conditions. The second element simulates the approximate solution of the deep beam of arbitrary cross section as it assumes a cubic normal strain distribution along the beam cross section. The element stiffness matrix is derived by applying the principle of virtual displacements of the system. The two elements are found to yield similar results for beam aspect ratios which are greater than 1.0. The deep beam element solutions were compared to the conventional engineering theory of beam solutions for simple (cantilever) structures and complex (turbine generator pedestal) structures; the results of the two methods of solution were found to differ significantly.

The assessment of reliability for framed steel structures is approached by the determination of limit state surfaces in load space. Surfaces corresponding to initial yield, plastic hinge formation and mechanism formation or structural instability are found by an incremental loading procedure along proportional load paths from the point of expected values. A previously derived stiffness matrix for wide‐flange steel members subject to elasto‐plastic bending and derived from moment‐thrust‐curvature equations is utilized. The nonlinear frame response is based on a tangential stiffness matrix for which each cross section of a member may experience various degrees of partial plastic behavior. A recent model for the nonlinear behavior of connections reflecting moment and axial force coupling due to noncentroidal rotation is also incorporated. Turkstra's rule of load combination permits the inclusion of arbitrary point‐in‐time as well as lifetime maximum probability distributions of live and wind loads.

The Marine Parkway Bridge in New York, New York, spans Rockaway Inlet connecting the boroughs of Brooklyn and Queens. In 1970, the boom of a crane mounted on a barge crossing beneath the bridge struck the lower chords of the main vertical lift span causing severe damage. In addition, extensive member corrosion had occurred over the years necessitating replacement of some of the vertical truss members of the approach trusses. A detailed presentation of how these repairs were made is provided since little information is available in published literature on repair and replacement of major truss members under load. It is believed that documentation of the procedures utilized will be useful to other practicing engineers. The repairs to the lower chord members were accomplished by providing a temporary replacement member consisting of prestressed bars. The replacement of the vertical truss member was achieved by temporary replacement with hangers.

A method is developed to estimate the reliability of a seismically damaged structure that will be subjected to future earthquakes. Damage states are defined, and conditional as well as initial damage probability matrices are introduced, in such a manner that the definition of the damage is consistent with the kind of accuracy achieved when the extent of the structural damage is estimated through field inspections. The initial damage probability matrix indicates the probabilities that an undamaged structure will produce various degrees of damage, representative of the corresponding states of damage after it is subjected to an earthquake of a specified intensity. The conditional damage probability matrix is essentially a Markovian transition matrix and describes the transition probability with which a structure in a certain state of damage will reach another state after being subjected to an earthquake of given intensity. The validity of using such probability damage matrices is demonstrated analytically and further verified by a Monte Carlo simulation with the aid of a nonlinear dynamic structural analysis involving artificially generated earthquakes.

Results are presented from an investigation on stiffening wideflange steel beams for torsional loading. Four types of stiffeners, involving either plate elements or small sections of channels, were used for pin ended, fix ended and cantilevered beams subject to either concentrated or distributed torques. Both the quantity and the location of the stiffeners were varied. A finite element analysis was used to develop design recommendations on the type of stiffener, the size, and the placement.

The long‐term variation of bending moment distribution caused by creep in a continuous beam erected sequentially in span‐length sections with overhangs is analyzed. A linear aging creep law is assumed. The problem involves changes of the structural system from statically determinate to indeterminate, a gradual increase in the number of redundant moments, and age differences between various cross sections. A system of Volterra integral equations for the history of support bending moments is derived. By considering infinitely many equal spans, which is good enough whenever there are more than a few spans, one can take advantage of a periodicity condition for the construction cycle; this reduces the problem to a single equation which is of a novel type in creep theory—an integral‐difference equation involving time lags in the integrated unknown. The solution exhibits sudden jumps at times equal to multiples of the construction cycle. The jumps decay with time roughly in a geometric progression. Approximation of time integrals with finite sums yields a large system of simultaneous linear algebraic equations. These equations cannot be solved recurrently, step‐by‐step. By solving the large equation system with a computer, the effects of the duration of the construction cycle, of concrete age at assembly of span from segments, and of the overhang length are studied numerically.

A technique is presented for convenient implementation of mathematical programming in structural design developing what is termed a “generalized formulation.” It is shown that once a generalized formulation has been created for a particular structure, it can be used to design many similar structures without having to reformulate the problem. A simple plate girder example is used to introduce the concept of generalized formulations using the computer program IGGP, a program based on the Generalized Geometric Programming method. A generalized formulation is then developed for the design of a simply‐supported composite highyway bridge with steel stringers and concrete slab. An example solution is also presented.

A wood floor analysis methodology is described which utilizes a finite‐element mathematical model along with input parameters which can be obtained through nondestructive evaluation and the use of predictive techniques. The mathematical model is implemented through the computer program FEAFLO (Finite Element Analysis of FLOors). The comprehensive method was verified by comparing computed deflections under concentrated loads to measured results from 22 full‐sized experimental floor specimens built and tested in earlier studies. The analysis method predicts floor behavior far more closely and consistently than do other analysis methods which consider the stiffness of the loaded joist only. Consideration of both the component variability and the structural interaction in the floor were shown to be needed to accurately predict the response of wood floor systems. With the availability of this verified analysis method, along with results of studies under both concentrated and uniformly‐distributed loads, sufficient information now exists for the design profession to utilize a more rational analysis procedure for rectangular, simplysupported wood floor systems.

The concept of the envelope curve which was based primarily on plain concrete is extended to confined concrete subjected to cyclic loading. Spirally confined normal weight and light weight concrete specimens were subjected to stress and strain cycling loadings at low as well as high strain rates. Analytical expressions were developed to predict the envelope curve as well as the peak strength and the corresponding strain. All analytical expressions are functions of plain concrete strength $\left(f_c^{\prime }\right)$ and the confinement index $\left(f_r\right)$ which is a measure of the effective confinement.

The failure of the Imperial County Services Building in El Centro, California, during the Imperial Valley Earthquake on October 15, 1979 is examined. The event was exceptional insofar as a modern reinforced concrete building, designed to comply with a recent code, extensively instrumented and previously subjected to dynamic testing, was severely damaged. Available records of measured dynamic characteristics and traces of the motions induced by the earthquake in both the adjacent ground and the structure, enable critical analyses to be made of the failure modes. Building configuration and composition are summarized, together with the strong motion records obtained during the earthquake. A three‐dimensional mathematical model of the building is developed and the results of computer analyses are presented. Elastic analyses are used as a basis of justifying the model and both elastic and non‐linear three‐dimensional time history analyses are described. Good correlation between analytical results and field observations is established. In particular the combined effect of biaxial moment and axial load in causing ground floor column failure is demonstrated.

For rational design of concrete structures subjected to impact and impulsive loading, the constitutive properties of concrete over a wide range of strain rates are required. With this aim in mind, concrete and fiber reinforced concrete beams were tested in a drop‐weight, instrumented impact testing machine. During the impact event, loads, deflections and strains were monitored. The modulus of rupture at high strain rates obtained in impact loading was up‐to twice that observed at low strain rate (static loading). With increasing strain rate, the load‐deflection curves became less nonlinear. The energy absorbed by fiber reinforced concrete beams was as much as 100 times that for unreinforced beams. The influence of matrix mix proportions, relative humidity during curing and the type of fibers (steel, polypropylene and glass) on impact properties are presented. Cracking appears to be the major process responsible for the observed strain‐rate effects in concrete and fiber reinforced concrete.

An efficient numerical procedure for the material and geometric nonlinear analysis of reinforced and prestressed concrete slabs and panels including the time‐dependent effects due to load history, temperature history, creep, shrinkage and aging of the concrete and relaxation of prestress is developed. The procedure, based on the finite element method, is capable of predicting the response of these structures throughout their service load history as well as throughout elastic, cracking, inelastic and ultimate load ranges. An updated Lagrangian formulation is employed to take the effects of changing structural geometry on the response of planar structures into account. Slabs or panels having an arbitrary tendon layout with either pretensioned, or bonded or unbonded post‐tensioned tendons can be analyzed. Two numerical examples are presented to study the validity and applicability of the present method. The results obtained are compared with experimental and/or analytical results obtained by other investigators.