New York Paper - The Stresses in the Mine Roof (with Discussion)

The stresses in the simplest structures are often those we find most difficult to analyze. The most complex condition in mine stresses is found in simple tunnels where the roof, the sides, and the floor are a monolith. The functions of the parts are like the parts themselves not distinct and spccialized, and the problems to be solved are like those in a metal structure with riveted joints or a redundancy of bars. This difficulty explains perhaps why the condition has not been treated. But just because it cannot be discussed in its entirety is no reason why it should be treated as an action of parts with spccialized functions as a roof beam with supports and a foundation. The problern cannot be ignored on the ground that it is not of sufficient importance to warrant careful consideration, because conditions of complete monolithism, of which the tunnel is the type, are found materially unchanged in room-and-pillar and in longwall work. This unity between roof, sides, and floor, which to the coal miner is a difficult conception, really deserves a scientific appellation, and perhaps holoid (from holos, whole, and eidos, form) will serve the purpose as well as any other. In a simple tunnel the roof, the sides, and the floor form integral parts of one and the same structure, and the distortion of one cannot be conceived without a consequent strain in the others. Thus when the roof of the tunnel droops by reason of its weight, the upper parts of the sides are drawn in becausc they are integrally connected with the roof and must approach each other whenever, by the sagging of the roof, the distance between any two points in it is diminished. (See Fig. 1.) Thc sides in their turn operate on the floor of the holoid structure, producing a tensile stress. The writer has always been impressed with the value of soap as a means of illustrating the action of mine stresses. With that idea in mind' a cake of naphtha soap measuring 43/8 by 2¼ by 19i in. was taken and a tunnel was made through it 13/4 in. long, 21/2 in. wide and 1¼ in. high. (See Fig. 2.) A load was then placed at the mid-span of the tunnel. Eventually, the upper bar, or "roof," broke at the