Deflection of Girders

I AM well aware that this subject is not strictly in the line of mining engineering, yet as it is a subject with which mining engineers at times have something to do, I have thought, perhaps, it might not be wholly out of place to communicate to the Institute something of the method used in determining deflection, and of its final issue. Having felt a need of some simple formula for determining the deflection of girders of uniform cross-section under any load, I have been led through the counsel of Mr. Frederick J. Slade, to whom I am indebted for many suggestions, to undertake a labor of which I shall in this paper give only some of the most important features. The results arrived at agree with those obtainable from the received formula; of Weisbach, Rankine, and others, but the expressions given by these authors, and by all others that I have at hand, are of such a form that they are not easily applied by those whose higher mathematics have become rusty from disuse, and they require, moreover, too much labor in their application to be of practical value. The general formula that I have adopted is similar to that given by Rankine, and is deflection = [mWl3 -El], in which l is the span, W the total load, E the modulus of elasticity, I the moment of inertia of the uniform cross-section of the girder, and m a factor depending for its value on the mode of distribution of the load. The problem then is to find the value of this factor m in the formula, and for some distributions of the load it leads to a number of mathematical difficulties. In this place I shall consider first the girder to be loaded symmet-