Footnote 11: Professor Rankine's Five Principles:
1. To cut the joints and arrange the fastenings so as to weaken the pieces of timber they connect as little as possible.
2. To place each abutting surface in a joint as nearly as possible perpendicular to the pressure which it has to transmit.
3. To proportion the area of each surface to the pressure which it has to bear so that the timber may be safe against injury under the heavi
4. To proportion the fastenings so that they may be of equal strength with the pieces which they connect.
5. To place the fastenings in each piece of timber so that there shall be sufficient resistance to the giving way of the joint by the fastenings shearing or crushing their way thru the timber.
In laying out a series of measurements, it is important, when possible, that the rule be laid down once for all, and the additions be made on that, rather than that the rule should be moved along for each new member of the series.
In scoring around a board with knife and try-square, the head of the try-square should be held against the working face in scoring both edges, and against the working edge in scoring both faces, and not passed from one surface to another in succession.
In the laying out of a halved joint, Fig. 265, the gaging is all done from what will be one of the flush surfaces of the joined pieces. Then, if the gaged line should be slightly more or less than half the thickness of the pieces the closeness of the joint would not be affected.
2. When possible, in laying out a joint, use the method of superposition. Fig. 302. By this is meant the method by which the lay-out of one member is obtained directly from the other by laying (superposing) the latter on the former and marking or scribing the needed dimensions directly, instead of by measurement. It has the advantages of simplicity, speed, and greater probability of fit.
Familiar illustrations are in the making of halved joints, Fig. 265, dovetail joints, and scarfed or spliced joints, Fig. 264
3. Work systematically. In case the same process is to be repeated on a number of parts, complete this process in all before taking up another process. This is the principle of the division of labor applied to the individual workman.
In laying out duplicate or multiple parts, the proper cross measurements should be carefully laid out on one piece and then transferred with a try-square to the other parts laid accurately beside it. So when a number of like pieces are to be gaged, all the parts requiring the same setting should be gaged before the gage is reset for another gaging. This is a great saving of time and insures accuracy.
In making a number of like parts, if they are not too large much of the work can often be done in one piece before it is cut up. For example, to make a number of slats from a given piece of wood, the piece may first be brought to such dimensions that the length will be correct for the finished pieces and the thickness of the piece be equal to the width of the slats, Fig. 303. The face may then be gaged with a series of lines so that every other space will be equal to the required thickness of each slat, and the alternate spaces be just sufficient for the saw kerf and dressing. The slats may then be ripped apart and dressed to size.
Or a long strip may be planed to thickness and width and then be sawn up and finished to the proper lengths. For example, in a mitered picture-frame it may be convenient to plane up two pieces, each one long enough to make one long side and one short side.
In fitting up framed structures each part when fitted should be distinctly marked, so that there may be no confusion in assembling.
4. Where practicable secure the same conditions of grain in different elements of joined structures.
5. Where possible, allow for shrinkage without prejudice to construction.
The most obvious illustration of this principle is panel construction. In a panel, the frame, which is comparatively narrow, follows the principal dimensions, and hence does not seriously shrink or swell itself. But the panel, which is grooved into the frame can shrink or swell without harm to the general structure.
In a gained joint, as in a case of shelves, Fig. 266, the gain in the uprights does not extend quite to the front of the shelves, and there is a corresponding slight shoulder at the front end of the shelf, so that if the shelf and support shrink unevenly, no gap will be apparent.
A drawing-board, Fig. 280, is so made that it can shrink or swell without losing its flatness. Shingles when properly laid, can shrink or swell without the roof leaking.
6. Where feasible, undercut joined surfaces so as to give clearance on the inside and insure a tight appearance. But glued surfaces should be made to meet flat.
The shoulder of any tenon may be undercut so as to allow the edges of the tenoned piece to close up tight against the mortised piece.
In an end-lap halved joint, Fig. 265, the edges should meet all around; if they are to be glued together, they should not be undercut or they will not glue well.
In matched flooring, the underside of the boards is slightly narrower than the upper side so that the joint may close on the upper side without fail, Fig. 301. The ends of flooring boards are also slightly beveled so as to make a tight fit on the upper side.
7. Select the simplest form of joint and use the smallest number of abutments (bearing surfaces) possible, because the more complicated the joint or the greater the number of bearing surfaces, the less likelihood there is of a sound and inexpensive construction.
In a dovetail dado, Fig. 266, it is usually sufficient to make the dovetail on one side only.
Many very elaborately spliced joints have been devised, which have no practical advantage over the simple ones, Fig. 264.
A butt joint, Fig. 264, is stronger than a mitered joint, Fig. 268, in a box, for the latter is almost sure to shrink apart. Where appearance is important, a ledge and miter joint has the advantage of both, Fig. 268.
8. Keep a due proportion of strength between the fastenings (joints) and the pieces fastened: i. e., the construction should neither be frail on the one hand, because the pieces of wood are weakened by too much cutting, nor clumsy, on the other hand, because then the fastenings would be inordinately strong. In other words, the different parts should be equally strong.
In a scarf joint, Fig. 264 and, the angle should be oblique enough to give the greatest leverage.
In a tusk tenon, Fig. 267, No, the tenon is made but one-sixth the thickness of the timber, whereas the tusk is made much larger.
Where a mortise is to be cut in a timber bearing weight, it should be cut in the neutral axis, where the cutting of fibres will weaken it least.
In the mortise-and-tenon of a table-rail, Fig. 267, there should be a wide shoulder above the tenon of the rail so that the top of the leg above the mortise will not shear out. The mortise should be as near the outside of the leg as possible so that the inner corner of the leg may remain strong. The tenon should be strong enough to share the strain with the shoulders.
A dado joint, Fig. 266, should not be so deep as to weaken the supporting board.
A tenon should not be so large as to weaken the mortised piece.
Pins or other fastenings, Fig. 267, may weaken rather than strengthen a joint if they are so placed or are so large as to shear or crush their way thru the timber.
9. Place each abutting surface in a joint as nearly as possible perpendicular to the pressure which it has to transmit.
The thrust joint, Fig. 268, in a bridge truss, is exactly at right angles to the pressure.
It is on account of this principle that a spliced joint for compression, Fig. 264, is different from a spliced joint for tension; and that a housed braced joint, Fig. 269, is better than a plain braced joint.
A joint to resist vertical cross strain is stronger when scarfed vertically than horizontally.