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mental conflict between psychology and medicine; it arises among physicians, on the one hand, and psychologists who are masters of certain medical techniques and occupied with certain medical problems that medicine has not assimilated. Medicine should assume greater responsibility for them, when the conflict will disappear. Meanwhile the administrative duty of psychology is to develop progressively higher standards in training and accomplishment and, within those limits where reasonably accurate judgment is possible, means of attesting those who meet these standards. That this can and should be done on the psychometric level seems clear. On the level of the independent consultant, one must distinguish carefully between measures that further the services of psychology to society and those that seem primarily for the interest of a professional group. The latter policy would certainly be without value, and might be disastrous, to the standing of the profession as a whole.

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1. The subject of the strength of flat slabs has received considerable attention during the past ten years. In November, 1910, the floor of the Deere and Webber Building ‡ at Minneapolis was tested. This was the first field test of a reinforced-concrete building floor in which strain measurements in the reinforcement and in the concrete were taken at various places in the building. Since that time many other tests have been made and much study has been given to the analytical side of the problem.

While considerable work has been done on the correlation of the analytical and the experimental results, it does not seem that the possibilities of useful work in this direction have been exhausted. It is the purpose of this paper to present information which correlates the results of tests of a fairly large number of slab structures with the results of analysis, so that the report may aid in the formulation of building regulations for slabs.

The field of this report may be divided into three parts: (a) analysis of moments and stresses in slabs, (b) study of the relation between the observed and the computed steel stresses in reinforced-concrete beams, made for the purpose of assisting in the interpretation of slab tests, (c) a study of the test results for flat slabs with a view of comparing the moments of the observed steel stresses with the bending moments indicated by the analysis, and of estimating the factor of safety.

The mathematical analysis is the work of Mr. Westergaard. The analysis of the beam tests to show the relation between the computed and the observed stresses is the work of Mr. Slater.

2. ACKNOWLEDGMENT. The expense of the report has been borne jointly by the American Concrete Institute and the United States Bureau of Standards.

The Corrugated Bar Co., of Buffalo, N. Y., and A. R. Lord, of the Lord Engineering Company, of Chicago, have furnished the results of a number of tests which had not been published, or which had been published only in part.

Acknowledgment is made to M. C. Nichols, graduate student, and to J. P. Lawlor and K. H. Siecke, seniors in engineering, in the University of Illinois, for their assistance in working up the data of the tests.

Assistant Professor of Theoretical and Applied Mechanics, University of Illinois.
Engineer Physicist, U. S. Bureau of Standards.

A. R. Lord, Test of a Flat Slab Floor in a Reinforced-concrete Building, National Association of Cement Users, v. 6, 1910.

BY H. M. WESTERGAARD.

3. SCOPE OF THE ANALYSIS. A slab is sometimes analyzed by considering it as divided into strips, each carrying a certain portion of the total load. One may expect to obtain, by this method, an exact analysis of a structure consisting of strips which cross one another and carry the loads as assumed. This structure, however, is quite different from the slab. The degree of approximation obtained may be judged by the resemblance or lack of resemblance between the strip-structure and the actual slab. As the resemblance is not very close, the approximation, naturally, is not very satisfactory. The ordinary theory of beams, too, is approximate, not exact, when applied to actual beams. Assumptions are introduced in the beam theory: for example, the plane cross-sections remain plane after the bending, and the material is perfectly elastic. But the approximation in the beam theory is much closer than in the strip analysis of plates. The explanation is simple: the beam to which the beam theory applies exactly has a closer resemblance to actual beams than the strip-structure has to slabs. It is possible, however, to analyze slabs more exactly than can be done by the strip method. If an analysis of slabs is to compare in exactness with beam analysis, then it must be based on a structure which resembles actual slabs more closely than does the strip structure. It is hardly possible at present to cover by analysis the whole range of designs of reinforced-concrete slabs. It is expedient, therefore, to confine this investigation to a single type. The homogeneous slab of perfectly elastic material is selected; homogeneous slabs have a fairly close resemblance to other slabs, and exact methods exist by which they may be analyzed. The selection of a homogeneous elastic material agrees with common practice in the investigation of statically indeterminate structures. For example, the distribution of bending moments in a reinforced-concrete arch or frame is often determined by replacing the structure by one of homogeneous material. The plan is then to investigate distributions of moments in homogeneous slabs. These distributions may be used as a basis for the study of the experimental data.

Theoretical analysis is under the disadvantage that its processes are often rather more remote from the actual phenomena which are studied, than are the processes of direct physical tests. For this reason alone it would be out of the question to rely on the results of theoretical analysis only. There are, on the other hand, advantages of theoretical analysis which fully warrant its extensive use in conjunction with physical tests. One may appreciate these advantages by looking upon the theoretical analysis as being, in a sense, a test in which the testing apparatus consists of the principles of statics and geometry, expressed in equations, and in which the structure tested is the structure assumed in the analysis. The equations may be solved with any desired exactness, and the structure has dimensions

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