A Rudimentary Treatise on the Principles of Construction in the Carpentry and Joinery of Roofs (Paperback)

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. 1859 Excerpt: ...a square yard of covering is given, a steeper roof requires stronger rafters, and that when the scantling of the timbers is also given3 the relative strength of a rafter is inversely as its length. But there is now another circumstance to be taken into the account, viz., For modem examples of largely spanned constructed Iron Roofs, see Atlas to these vols., 124 in the series. the support which one rafter leg gives to the other. The best form of a rafter will therefore be that in which the relative strength of the legs, and their mutual support, give the greatest product. Describe on the width AC, Fig. 13, the semicircle ACF, and bisect it by the radius YD. Produce the rafter AB to the circumference in E, join EC, and draw the perpendicular EG. Now AB: AD:: AC: AE, andAE =-, andAE is inversely as AB, and may therefore represent its strength in relation to the weight actually lying on it. Also the support which CB gives to AB is as CE, because CE is perpendicular to AB. Therefore the form which renders AE x EC a maximum seems to be that which has the greatest strength. But AC: AE = EC: EG, and EG = ACEC, and is therefore proportional to AE.EC. Now EG is a maximum when B is in F, and a square pitch is in this respect the strongest. But it is very doubtful whether this construction is deduced from just principles. There is another strain to which the leg AB is exposed, which is not taken into the account. This arises from the curvature which it unavoidably acquires by the transverse pressure of its load. In this state it is pressed in its own direction by the abutment and load of the other leg. The relation between this strain and the resistance of the piece is not very distinctly known. Euler has given a dissertation on this subject (which is of great importance