Journal of Structural Engineering

An analysis of stress states in a hyperbolic cooling tower supported on columns caused by thermal field is presented. Numerical calculations of the magnitudes of thermal stresses are based on experimental measurements of the temperature field. Particular emphasis is given to the problem of the thermal stresses occurring in a region close to the base of the tower. It seems that the results obtained might be useful in engineering design processes.

Nondestructive ultrasonic testing is a more accurate alternative for assessing the strength of timber piles than the conventional practice of visual inspection. However, because the ultrasonic method is relatively new, there is a need to develop guidelines that can be used to define the spacing between test points required for a desired level of accuracy in testing. Analyses of data obtained from timber piles covering a range of compressive strengths were used to develop spacing guidelines. The data base consisted of nine treated southern yellow pine timber piles from four bridges in Maryland. Semivariogram modeling was used as the statistical procedure for characterizing the stochastic properties of the ultrasonic wave velocity measurements. Kriging is used to estimate the expected wave velocity for points between measured values. The results provide a relationship between the relative accuracy and the relative spacing of point measurements. Confidence intervals can be applied to assess the expected error variation between point measurements. The methodology presented in the paper can also be utilized in the nondestructive evaluation of other structural components.

Once the sizes of the cross sections of members of continuous beams or grids are assumed, it is possible to perform by computer—for any loading—the structural analysis and the design checks for serviceability and ultimate strength. A computer program that performs these tasks is described. The program is particularly suitable for bridge design. With the prestressing jacking force and cable profiles specified as data, the loss due to friction and anchorage set is automatically calculated. The effects of creep and shrinkage of concrete and relaxation of prestressed steel are accounted for from the requirements of equilibrium and compatibility of strain in concrete and steel. The instantaneous and time‐dependent displacements, the stresses, and crack width when cracking occurs are calculated. The output also includes the cross‐sectional areas of the longitudinal non‐prestressed reinforcement and the number of stirrups necessary to resist the factored bending and twisting moments and shearing forces. For segmental construction or other multi‐stage construction methods, the program gives the stresses and deformations in each construction stage and after a long period. The reinforced concrete structures considered can have any amount of prestressing, varying from zero (allowing cracking), to full prestressing (eliminating cracks).

The paper presents an approximate elastic solution to the statical problem of a thin concrete shell foundation. The soil‐structure interaction follows the Winkler concept of soil with random subgrade modulus. The randomness of the soil subgrade modulus renders the problem stochastically nonlinear. The method of statical solution is based on the finite difference procedure in the variational formulation and, to account for the probabilistic nature of the problem, is combined with the method of realizations in one approach, and with the perturbation method (small random parameter method) in the other case. The shell foundation that is dealt with in this paper consists of four hyperbolic‐paraboloid (in short hypar or HP) shells and a set of straight ribs. For the illustrative problem, the results consist of the estimates for the expectations and standard deviations of the discrete values of the structural displacement and internal force fields.

The problem of optimal design of active structures has been shown to be one of simultaneous structural and control design optimization. The basic equations represent, in general, a large system of coupled nonlinear differential equations. The purpose of this paper is to present a numerical design procedure which optimizes the structural and controller parameters simultaneously. Two examples illustrating the nature of the optimization problem and the numerical procedure involved are presented.

It is well established, as a result of many field tests, that slab‐ongirder bridges are usually stiffer in flexure than is predicted by normal deflection analysis. An example is given in the paper to support this contention. Restraint to horizontal movement at girder supports is identified by field tests on actual bridges as the main reason for this enhanced stiffness. Simple expressions are derived in the paper, by use of which the beneficial effect of girder support restraint can be taken into account in the evaluation of the load‐carrying capacity of single‐span existing bridges. These simple expressions relate to girder deflections and moments, and to the stresses in the bottom flanges of the girders, all of which reduce differently as a consequence of bearing restraint. It is shown that girder restraint can reduce live load moments in existing single‐span slab‐on‐girder bridges by up to 20%

An analytical iterative method for the static analysis of continuous cable‐stayed bridges is presented. The towers can have any degree of flexibility and the interaction with their supporting media (caissons or piles) is considered. The system is divided into two substructures: the tower and the girder plus the cables. The continuous girder is solved by means of the method of three‐moment equations, while the deflections are calculated from Fourier series. It was found that a small number of iteration cycles and Fourier coefficients are sufficient for convergence and a few simultaneous equations are required for solving the entire system. Therefore, large bridge systems with a large number of cables can be analyzed under different loading conditions using the PC computers. A comparison between the numerical results of the present method and those obtained from the nonlinear stiffness method shows the advantages of the present method and also shows that nonlinearity effects are not important for such types of bridges.

The design of highway sign support structures is governed by the AASHTO Specifications which limit the dead load deflection of the beam to $d^2/400\text{,}$ where d is the depth of the traffic sign in feet. In many cases, the more slender monotube sign support structures, which have become more popular in recent years, can not satisfy this deflection criterion. The results of a parametric study of monotube highway sign support structures are presented in this paper. Structures with various column and beam stiffnesses, spans, area and location of traffic signs were analyzed for static and dynamic (wind) loads. Vortex shedding is a prime consideration for such structures; this was accounted for in the dynamic analysis. It was found that stress levels are well below the allowable values, although the deflections exceeded the AASHTO criterion by significant margins. It was also concluded that for typical structures, resonance was not a likely occurrence. Recommendations are made for the analysis and design procedures.

This paper shows that the closed form expression for the elastic out‐of‐plane buckling of doubly symmetric beam‐columns under uniform moment can be expressed in form similar to that of beams by introducing a beam‐column parameter, $\eta ={\mathrm{4r}}_o^2/h^2$ in which $r_o$ is the radius of gyration about the centroid and h is the distance between flange centroids. The closed form solution is equally applicable to tie‐beams. For beam‐columns/tie‐beams under other loading conditions, accurate solutions are determined using the Rayleigh‐Ritz energy approach. Approximate formulas to predict the out‐of‐plane buckling capacities of the beam‐columns/tie‐beams under moment gradient, uniformly distributed load, and central concentrated load are presented. The proposed moment modification factor formulas furnish reasonably accurate predictions of the buckling capacities of beam‐columns/tie beams and may thus be adopted by code rules.

The results of a comprehensive study of the seismic response of curved steel box girder bridges are presented. Multiple‐span bridges with up to five spans are analyzed. The bridge is modeled using 3‐D space frame elements and El Centro earthquake accelerogram is used as a dynamic input to calculate the maximum responses at the bridge deck and columns. Different elements of the bridge model and the seismic loading are examined, and a comparison between the response history and the response spectrum methods for analyzing curved bridges, using El Centro earthquake accelerogram, shows that the latter technique fails when vibration modes with relatively high frequencies are considered. The simultaneous application of the earthquake loadings in the three global directions is also discussed. Parametric studies are performed and the effect of the span length, radius of curvature, bridge weight, and column geometry are presented.

Increased local deformation of pin plates with large pin-to-hole clearances is discussed. Test data are used to develop a curve quantifying this increase. A simple design approach is suggested by which existing code allowable stresses can be adjusted to account for the increased deformation problem.

This study investigated the tensile strength of Douglas-fir loaded at an angle to the grain. Strength was determined for grain angles of 15, 30, 45 and 60 degrees in the radial-longitudinal plane. Strength was found to drop dramatically from a grain orientation of zero to 15 degrees. Hankinson's formula, the Tsai-Hill failure theory and the recently developed hyperbolic formula were compared to the experimental data to determine which theory gave the best prediction. Hankinson's formula with s = 1.5 and n = 2, and the Tsai-Hill theory overstated strength at 15 degrees and did not provide a good prediction of the data at the remaining grain angles. The hyperbolic formula was found to give an accurate prediction of the data at all grain angles tested.

The differential equation for elastic deformation of a cylindrical shell is formulated and solved. The particular solution is for grain pressure given by Jannsen's formula and includes frictional force of grain on the wall and the weight of the wall itself. If the bottom edge of the silo is restrained from radial displacement, localized circumferential compression, shear and bending moment develop.