It is not that the writer advocates a wide stem in the T-beam, in order to dispense with the aid of the slab.  What he desires to point out is that a full analysis of a T-beam shows that such a width is needed in the stem.

Regarding the elastic theory, Mr. Mensch, in his discussion, shows that he does not understand the writer’s meaning in pointing out the objections to the elastic theory applied to arches.  The moment of inertia of the abutment will, of course, be many times that of the arch ring; but of what use is this large moment of inertia when the abutment suddenly stops at its foundation?  The abutment cannot be anchored for bending into the rock; it is simply a block of concrete resting on a support.  The great bending moment at the end of the arch, which is found by the elastic theory (on paper), has merely to overturn this block of concrete, and it is aided very materially in this by the thrust of the arch.  The deformation of the abutment, due to deficiency in its moment of inertia, is a theoretical trifle which might very aptly be minutely considered by the elastic arch theorist.  He appears to have settled all fears on that score among his votaries.  The settlement of the abutment both vertically and horizontally, a thing of tremendously more magnitude and importance, he has totally ignored.

Most soils are more or less compressible.  The resultant thrust on an arch abutment is usually in a direction cutting about the edge of the middle third.  The effect of this force is to tend to cause more settlement of the abutment at the outer, than at the inner, edge, or, in other words, it would cause the abutment to rotate.  In addition to this the same force tends to spread the abutments apart.  Both these efforts put an initial bending moment in the arch ring at the springing; a moment not calculated, and impossible to calculate.

Messrs. Taylor and Thompson, in their book, give much space to the elastic theory of the reinforced concrete arch.  Little of that space, however, is taken up with the abutment, and the case they give has abutments in solid rock with a slope about normal to the thrust of the arch ring.  They recommend that the thrust be made to strike as near the middle of the base of the abutment as possible.

Malverd A. Howe, M. Am.  Soc.  C. E., in a recent issue of Engineering News, shows how to find the stresses and moments in an elastic arch; but he does not say anything about how to take care of the large bending moments which he finds at the springing.

Specialists in arch construction state that when the centering is struck, every arch increases in span by settlement.  Is this one fact not enough to make the elastic theory a nullity, for that theory assumes immovable abutments?