Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
As in most analytical treatments of structural problems, simplifying
assumptions are made. For example, in addition to the usual
assumptions of the ordinary slab theory, it is assumed that the supporting
beams exert only vertical forces upon the slab. It is recognized
that this assumption is not fulfilled in an actual bridge since
bond and friction produce the effect of a T beam. There is consequently
a shifting of the neutral surface of the slab in the neighborhood
of the supports. Nevertheless, it is possible that a modified
stiffness of supporting beam may be used to account for most of the
T beam effect. The facts concerning such questions as this can probably
be obtained satisfactorily only by laboratory and field tests.
Certain problems involve the so-called infinitely long slab. For
practical purposes a solution for such a slab may be interpreted as
applying to a long rectangular slab in which the two short edges are
so remote from the portion considered that the boundary conditions
at these edges have a negligible effect. Similarly, a solution for the
so-called semi-infinite slab may be interpreted as applying to an
area near one end of a long rectangular slab. The boundary conditions
on three edges affect such a solution, but the fourth edge is
assumed to be sufficiently remote to have a negligible effect.
In the analysis of the infinitely long slab, simply supported on two
edges, material use has been made of Nadai's form of the potential
function* 0, proportional to the moment sum, through which the
bending and twisting moments, shears and reactions become expressible
in finite form. It will be shown in Chapters III and IV that this
function and its derivatives may be similarly utilized in a number of
problems involving long slabs supporting concentrated loads.
In Chapters V and VI rectangular slabs, simply supported on
two opposite edges and having either two or three longitudinal
stringers, are treated. The solutions obtained in these chapters are
combined in various ways in Chapter VII to give additional solutions
or to give more convenient forms of the previous ones.
2. Acknowledgment.-The investigation of reinforced concrete
bridge slabs is being conducted in the Engineering Experiment
Station with the co6peration of the United States Bureau of Public
Roads and the Illinois Division of Highways. The project is under
the administrative direction of DEAN M. L. ENGER, Director of the
Engineering Experiment Station, PROFESSOR W. C. HUNTINGTON,
Head of the Department of Civil Engineering and PROFESSOR
*A. Nadai, Die elastischen Platten, 1925, p. 87.