STRENGTH OF TUBES.

Metal in the form of tubes resists all strain liable to occur in cycle work better than in any other form. In regard to strain of compression, we find, in “Wood’s Resistance of Materials,” the following summary:

“Experiments heretofore made do not indicate a specific law of resistance to buckling, but the following general facts appear to be established: The resistance of buckling is always less than that of crushing, and is nearly independent of the length. Cylindrical tubes are strongest, and next in order are square tubes, and then the rectangular. Rectangular tubes are not so strong as tubes of this form .”

There is, however, very little direct crushing strain on the tubes in a cycle; it is almost entirely a strain of flexure or bending; hence this is the only interesting feature pertaining to the subject in cycling work.

Since a tube is stronger than a solid bar, for same weight the intuitive idea is to make the tube as large as possible, and the mathematical demonstration which we append shows this to be correct, generally speaking.

Let R equal the strain per square inch of cross-section of the tube at the point farthest removed from the neutral axis at the instant of rupture.

Tube sections.

Suppose Fig. 1 to represent the half of the tube, and that you are trying to bend it down at the ends. The particles towards the top will be pulled apart, while those at the bottom are crowded together; somewhere between the top and bottom the particles are neither pulled apart nor crowded together. Were the tube solid, the line of these particles would be the neutral axis. In the tube an imaginary line through the centre of the hole does not vary much from said axis. Now the moment of rupture = ^Rπ_{4r_e}(r⁴_e − r⁴_i), where r_e and r_i ([Fig. 2]) are the exterior and interior radii; ^Rπ₄ is a constant, which we will call K, whence we can write moment of rupture = K(r_e² − r_i²) (r_e² + r_i²) ÷ r_e. Here the factor (r_e² − r_i²) is proportional to the area of the annular cross-section and is constant, while the other factor, (r_e² + r_i²) ÷ r_e or, r_e + ^r_i_{r_e} r_i, though less than 2r_e, gets nearer and nearer to 2r_e as r_e gets large and r_i approaches r_e.

Therefore we have, that in resistance to flexure the tube should be as large in diameter as practicable, which means that it must be as thin as possible. This result is only modified in practice by the necessity of guarding against dinging and also against imperfections in the steel. A surface crack will ruin a very thin tube which otherwise may be harmless in a thicker, but it is safe to say that it is best to use reasonably large thin tubes.

Oval tubes are of an advantage only when the direction of the strain is positively known and when it invariably occurs in that direction. Since the tube finds its greatest limit of general resistance in cylindrical form, to alter that form must necessarily weaken it more in one direction than it strengthens it in another.