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Practical Stair Building and Handrailing / By the square section and falling line system. cover

Practical Stair Building and Handrailing / By the square section and falling line system.

Chapter 5: PLATE I. ELEMENTARY PROBLEMS.
By W. H. Wood
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About This Book

A practical trade manual that presents step-by-step methods for laying out, cutting, and assembling stairs and handrails. It begins with elementary geometric problems and stretch-outs used to form curves and easings, then explains how to transfer site dimensions onto rods, set out risers, goings, strings, newels, landings and winders, and apply the steel square for accurate profiles. Plates and worked examples illustrate full-size layouts, recommendations for rise-and-run proportions, and a tested square-section and falling-line approach to handrailing, with detailed workshop techniques for cutting, fitting and joining components.

PLATE 1.

PLATE I.
ELEMENTARY PROBLEMS.

Fig. 1. Draw a straight line, equal in length to the semicircle A B C. With A and C as centres, and for radius A C, strike the two arcs to intersect each other in S. Join S A and S C extended, to cut the line through B in D and E. Then, D E is the length of the required line, and if this was bent around the semicircle it would reach from A to C. This line throughout this work is termed the stretch-out of the semicircle.

Fig. 2. Given the length D E, find the radius to strike a semi-*circle equal in length to it. Draw a line from E at 60°, and from B at 45° to D E, to cross each other at C. Draw from B square to D E, and from C parallel to D E to meet in O; then O B will be the required radius.

Figs. 3, 4 and 5 show how to bisect any given angle. Let A B C be the given angle. With B as centre, strike the arc D D to any radius. With D D as centres, and for radius more than half the distance D D, describe arcs intersecting in E. Then, a line from B to E will bisect the angle.

Figs. 6, 7 and 8 show how to ease any given angle, that is to form a curve that will connect the two straight lines, from any two given points, on those lines. Let A B and B C be the two lines forming the given angle, and it is required to connect those lines from A to C. Divide A B and B C into any number of equal parts, connect those parts, and the curve will be formed if A B and B C has been divided into a sufficient number of parts.

Fig. 9 shows a semi-ellipse, A B being the semi-major axis, and B D the semi-minor axis. Let A B and D B, Fig. 10, equal A B and D B, Fig. 9. To strike the curve, move this rod around, keeping D on the major axis, and A on the minor axis, and mark off points at the end of the rod all round.

Fig. 11. Given a semi-ellipse, draw a normal tangent. Determine the foci of the ellipse F F. With D as centre, and for radius A B strike arcs of circles at F F. At any point on the curve, say at S, draw lines to F F and bisect the angle. Now draw through S, square to this line that bisects the angle for the required normal tangent.