Practical Geometry for the Architect, Engineer, Surveyor and Mechanic

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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. 1882 edition. Excerpt: ...instead of on a straight-line as in the cycloid; then the curve which a pencil on the circum N ference of the rolling circle will mark out is called ail epicycloid. This curve is used to form the outline of the teeth of two cogged wheels which roll upon the outside of each other. If the generating circle rolls on the inside of the circumference of another circle, then a point on its circumference marks out the hypocycloid, which is used to form the outline of the teeth of cogged wheels, one of which rolls on the inside of the other. APPENDIX A. DIAGRAMS OF STRAINS. 201. One of the most important applications of practical geometry to constructional purposes is the drawing of diagrams of strains, whereby the relative strain on each part of a frame can be seen at a glance, and we are thus enabled to determine the amount of strength necessary for the several parts of the structure. Suppose a beam AB (fig. 165) to be fixed Fig. 165. in a wall at one end A, and to be loaded with a weight W, uniformly distributed over its entire length. Measure the length A C to represent on any convenient scale the quantity WxAB. Through the points B and C draw (142) a parabola having its vertex at B; then the moment of strain produced on the beam at any point D will be represented by the ordinate D E of the curve, on the same scale as that used for A C. Let AB (fig. 166) be a beam supported at each end, and loaded uniformly Fig. 166. throughout with a load W. Then if D is the centre of the beam, and we measure D C vertical and representing on a scale the quantity WxAB, and we draw a parabola through A, C and B, having its vertex at C, we find that the moment of strain at any point E of the beam will be represented on the same scale by the ordinate E F. The strains...show more

Product details

• 12-17
• Paperback | 72 pages
• 189 x 246 x 4mm | 145g
• Miami Fl, United States
• English
• black & white illustrations
• 123663425X
• 9781236634252