Fig. 335. Crane-head and femur. (After Culmann and H. Meyer.)
nothing more nor less than a diagram of the lines of stress, or directions of compression and tension, in the loaded structure: in short, that nature was strengthening the bone in precisely the manner and direction in which strength was needed. In the accompanying diagram of a crane-head, by Culmann, we recognise a slight modification (caused entirely by the curved shape of the structure) of the still simpler lines of tension and compression which we have already seen in our end-supported beam as represented in Fig. [332]. In the shaft of the crane, the concave {683} or inner side, overhung by the loaded head, is the “compression-member”; the outer side is the “tension-member”; and the pressure-lines, starting from the loaded surface, gather themselves together, always in the direction of the resultant pressure, till they form a close bundle running down the compressed side of the shaft: while the tension-lines, running upwards along the opposite side of the shaft, spread out through the head, orthogonally to, and linking together, the system of compression-lines. The head of the femur (Fig. [335]) is a little more complicated in form and a little less symmetrical than Culmann’s diagrammatic crane, from which it chiefly differs in the fact that the load is divided into two parts, that namely which is borne by the head of the bone, and that smaller portion which rests upon the great trochanter; but this merely amounts to saying that a notch has been cut out of the curved upper surface of the structure, and we have no difficulty in seeing that the anatomical arrangement of the trabeculae follows precisely the mechanical distribution of compressive and tensile stress or, in other words, accords perfectly with the theoretical stress-diagram of the crane. The lines of stress are bundled close together along the sides of the shaft, and lost or concealed there in the substance of the solid wall of bone; but in and near the head of the bone, a peripheral shell of bone does not suffice to contain them, and they spread out through the central mass in the actual concrete form of bony trabeculae[622]. {684}
Mutatis mutandis, the same phenomenon may be traced in any other bone which carries weight and is liable to flexure; and in the os calcis and the tibia, and more or less in all the bones of the lower limb, the arrangement is found to be very simple and clear.
Fig. 336. Diagram of stress-lines in the human foot. (From Sir D. MacAlister, after H. Meyer.)
Thus, in the os calcis, the weight resting on the head of the bone has to be transmitted partly through the backward-projecting heel to the ground, and partly forwards through its articulation with the cuboid bone, to the arch of the foot. We thus have, very much as in a triangular roof-tree, two compression-members, sloping apart from one another; and these have to be bound together by a “tie” or tension-member, corresponding to the third, horizontal member of the truss.
So far, dealing wholly with the stresses and strains due to tension and compression, we have altogether omitted to speak of a third very important factor in the engineer’s calculations, namely what is known as “shearing stress.” A shearing force is one which produces “angular distortion” in a figure, or (what comes to the same thing) which tends to cause its particles to {685} slide over one another. A shearing stress is a somewhat complicated thing, and we must try to illustrate it (however imperfectly) in the simplest possible way. If we build up a pillar, for instance, of a pile of flat horizontal slates, or of a pack of cards, a vertical load placed upon it will produce compression, but will have no tendency to cause one card to slide, or shear, upon another; and in like manner, if we make up a cable of parallel wires and, letting it hang vertically, load it evenly with a weight, again the tensile stress produced has no tendency to cause one wire to slip or shear upon another. But the case would have
Fig. 337. Trabecular structure of the os calcis. (From MacAlister.)