Secondary Stresses in Framed Structures

Date of Award


Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering


H.R. Thayer


The purpose of this paper is two-fold: First, to present an adequate treatment of secondary stresses, and second, to introduce-three new methods evolved by the writer.

During recent years when the importance of secondary stresses has exhibited itself a large amount of literature has been written on the subject for advancing the science of structural design* & critical study made of these papers will at once reveal that they are subject to one or more defects which greatly impair their practical value. In the first place, too much attention has been paid to the mathematical theories, which could be greatly shortened for the benefit of practical engineers. Secondly, the treatment of the subject is generally limited to a narrow field, in which only a few methods are applied to only a certain class of structure. Thirdly, the treatment of the four existing methods is entirely too individual, in that the methods are generally considered as being separate from each other^notwithstanding the fact that they are more or less equivalent. Lastly, but not the least, the effect of secondary stresses on the design is not adequately considered and sometimes sadly neglected.

With a view to avoid the above defects it has been the writer's endeavor that the subject be treated in an entirely different way——that it be more practical, more comprehensive, and more logical; so that it could be easily understood and appreciated by those for whom the secondary stress has the most direct bearing the practical engineers. The writer is aware that not all of these objects are attained in this paper, on account of limited amount of time, but it is believed that the- scope of the work and the arrangement of materials are sufficiently effective so as to produce the desired results,

The methods for computing secondary stresses have been greatly improved in recent years. Two objections, however, still stand in the ways First, the amount of time involved is often excessive-, and second, the lack of a checking device by which the correctness of the various steps of procedure may be ensured. While there are numerous other defects these two alone are generally sufficient to reduce their practical utility. Ever since the beginning of 1917, when the writer undertook the analysis of secondary stresses in a two hinged arch, the results of which have been published in the Transactions of American Society of Civil Engineers, Vol. 82, p. 1104, it always occurred to him that there must be some method which is not only shorter and less cumbersome than the current ones but which also admits of a unique check. For two a and half years he has worked on the subject almost incessantly, striving to find some new method that will accomplish both. At last, much to his satisfaction, the graphic method of deformation contour was obtained; which not only takes less time, furnishes unique check, but also gives remarkably accurate results. Along with this method, almost contemporaneously, two more methods were evolved— the graphic method of successive deduction and the analytic solution of the graphic methods. All of the three methods are described in detail in Part III, page '38, which,being treated more or less independently, could be read without reference to other parts of the paper. A perusal of Chapter 10, page 105, is hereby recommended. As these methods are new in their field it is hoped that their usefulness be actually tested by further investigators.

Besides the two purposed of the paper as heretofore mentioned the following points deserve special attention: (1) The method for the solution of simultaneous equations, p. 25. (2) The approximate methods in Chapters 2 and 3, pages 115-125. (3) The well digested principles of design in Chapters 1 to 6, pages 140-151.


Written under the name Thomas Eason Mao.