Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
degree of approximation. The magnitude of such an approximation
may be illustrated by an example in which the moment Mo 0 is assumed
to be 0.300P. The resultant moment M0x is found from Equation
(228) to be
Ma% = 0.300P - 0.029P = 0.271P
whereas an assumption that the edges are "50 per cent fixed" gives a
moment
approx. MA = 0.300P - 0.035P = 0.265P.
In this example the error in the resultant moment M"0 is only about
2 per cent.
VIII. DISCUSSION
40. Concluding Remarks.-This bulletin presents the formal solutions
of a number of problems involving continuous slabs which support
concentrated loads. The bulletin is intended primarily as a
source of reference from which material may be drawn for application
to such related problems as are selected for further study. No attempt
has been made here to develop a design procedure. Solutions
have been determined which, it is believed, are capable of furnishing
a better understanding of the behavior of bridge slabs and their
supporting beams.
Mathematical solutions, such as those contained herein, are
subject to certain limitations. These limitations are a direct result
of the assumptions made in the analysis. While it is recognized that
such assumptions as homogeneity and perfect elasticity of material
cannot be realized in an actual slab, the results obtained on the basis
of these assumptions may be used as a fairly reliable measure of the
behavior of the slab.
Formulas are given for the bending moments in the supporting
beams as well as in the slabs. The magnitudes of the errors which
may arise from the assumption that the supporting beams exert only
vertical forces upon the slab are yet to be determined.
In a given problem a solution in the form of an infinite series is a
suitable tool for analysis provided that the labor involved in its use
can be justified. It is possible in some cases to observe the variables
which enter a given problem and to select the form of solution which
will be simplest to use. In general, a solution may be made to consist
of two parts, a basic solution and a correction." The basic solution
may be chosen in a variety of ways. The best choice is that one which