This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ...to include both tension and compression) is: Multiply the intensity of the radial pressure by the radius of the hoop, the product is the tension at any meridian section of the hoop. The correctness of this rule appears at once from consideration of fluid pressure in a tube, in which it is seen that the tensions at the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ...to include both tension and compression) is: Multiply the intensity of the radial pressure by the radius of the hoop, the product is the tension at any meridian section of the hoop. The correctness of this rule appears at once from consideration of fluid pressure in a tube, in which it is seen that the tensions at the two extremities of a diameter prevent the total pressure on that diameter from tearing the tube asunder. Now in the case before us t, y is the radial force distributed along a certain lune. The number of degrees of which the lune consists is at present undetermined: let it be determined on the supposition that it shall be such a number of degrees as to cause that the total radial force against it shall be equal to the hoop tension. Call the total radial force P and the hoop tension T, then the lune is to be Buch that P--T. Also let 6 be the number of degrees in the lune, then 90-=-$ is the number of lunesin a quarter of the dome, and 90 P-H0 is the radial force against a quarter of the dome, which last must be divided by n to obtain the hoop tension; because if p is the intensity of radial pressure, nrp is the total pressure against a quadrant and rp, as previously stated, is the hoop tension. The ratio of these is it, and by this we must divide the total radial pressure in every case to obtain hoop tension 360 3607T lit from which the scale of weight is easily found, thus; let W be the total weight of the dome and r its radius, then 2nr: W l: n, the weight per unit, or the hoop tension per unit of the distances ty or sx. Distances at or as, on the same scale, represent the thrust tangential to the dome in the direction of the meridian sections, and uniformly distributed over an arc of 57.3--: e.g. if we divide att measured as a force by 6 X Uj..
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