Stairs with Curved Turns.
Sufficient examples of stairs having angles of greater or less degree at the turn or change of direction, to enable the student to build any stair of this class, have now been given. There are, however, other types of stairs in common use, whose turns are curved, and in which newels are employed only at the foot, and sometimes at the finish of the flight. These curved turns may be any part of a circle, according to the requirements of the case, but turns of a quarter-circle or half-circle are the more common. The string forming the curve is called a cylinder, or part of a cylinder, as the case may be. The radius of this circle or cylinder may be any length, according to the space assigned for the stair. The opening around which the stair winds is called the well-hole.
Fig. 56. Stair Serving for
Two Flights, with Mid-Floor
Landing.
[Fig. 56] shows a portion of a stairway having a well-hole with a 7-inch radius. This stair is rather peculiar, as it shows a quarter-space landing, and a quarter-space having three winders. The reason for this is the fact that the landing is on a level with the floor of another room, into which a door opens from the landing. This is a problem very often met with in practical work, where the main stair is often made to do the work of two flights because of one floor being so much lower than another.
A curved stair, sometimes called a geometrical stair, is shown in [Fig. 57], containing seven winders in the cylinder or well-hole, the first and last aligning with the diameter.
In [Fig. 58] is shown another example of this kind of stair, containing nine winders in the well-hole, with a circular wall-string. It is not often that stairs are built in this fashion, as most stairs having a circular well-hole finish against the wall in a manner similar to that shown in [Fig. 57].
Fig. 57. Geometrical Stair with
Seven Winders.
Sometimes, however, the workman will be confronted with a plan such as shown in [Fig. 58]; and he should know how to lay out the wall-string. In the elevation, [Fig. 58], the string is shown to be straight, similar to the string of a common straight flight. This results from having an equal width in the winders along the wall-string, and, as we have of necessity an equal width in the risers, the development of the string is merely a straight piece of board, as in an ordinary straight flight. In laying out the string, all we have to do is to make a common pitch-board, and, with it as a templet, mark the lines of the treads and risers on a straight piece of board, as shown at 1, 2, 3, 4, etc.
If you can manage to bend the string without kerfing (grooving), it will be all the better; if not, the kerfs (grooves) must be parallel to the rise. You can set out with a straight edge, full size, on a rough platform, just as shown in the diagram; and when the string is bent and set in place, the risers and winders will have their correct positions.
To bend these strings or otherwise prepare them for fastening against the wall, perhaps the easiest way is to saw the string with a fine saw, across the face, making parallel grooves. This method of bending is called kerfing, above referred to. The kerfs or grooves must be cut parallel to the lines of the risers, so as to be vertical when the string is in place. This method, however—handy though it may be—is not a good one, inasmuch as the saw groove will show more or less in the finished work.
Fig. 58. Plan of Circular Stair and Layout of Wall String for Same.
Another method is to build up or stave the string. There are several ways of doing this. In one, comparatively narrow pieces are cut to the required curve or to portions of it, and are fastened together, edge to edge, with glue and screws, until the necessary width is obtained ([see Fig. 59]). The heading joints may be either butted or beveled, the latter being stronger, and should be cross-tongued.
[Fig. 60] shows a method that may be followed when a wide string is required, or a piece curved in the direction of its width is needed for any purpose. The pieces are stepped over each other to suit the desired curve; and though shown square-edged in the figure, they are usually cut beveled, as then, by reversing them, two may be cut out of a batten.
 |  |
Fig. 59. | Fig. 60. |
Methods of Building Up Strings. | |
Panels and quick sweeps for similar purposes are obtained in the manner shown in [Fig. 61], by joining up narrow boards edge to edge at a suitable bevel to give the desired curve. The internal curve is frequently worked approximately, before gluing up. The numerous joints incidental to these methods limit their uses to painted or unimportant work.
Fig. 61. Building Up
a Curved Panel
or Quick Sweep.
In [Fig. 62] is shown a wreath-piece or curved portion of the outside string rising around the cylinder at the half-space. This is formed by reducing a short piece of string to a veneer between the springings; bending it upon a cylinder made to fit the plan; then, when it is secured in position, filling up the back of the veneer with staves glued across it; and, finally, gluing a piece of canvas over the whole. The appearance of the wreath-piece after it has been built up and removed from the cylinder is indicated in [Fig. 63]. The canvas back has been omitted to show the staving; and the counter-wedge key used for connecting the wreath-piece with the string is shown. The wreath-piece is, at this stage, ready for marking the outlines of the steps.
[Fig. 62] also shows the drum or shape around which strings may be bent, whether the strings are formed of veneers, staved, or kerfed. Another drum or shape is shown in [Fig. 64]. In this, a portion of a cylinder is formed in the manner clearly indicated; and the string, being set out on a veneer board sufficiently thin to bend easily, is laid down round the curve, such a number of pieces of like thickness being then added as will make the required thickness of the string. In working this method, glue is introduced between the veneers, which are then quickly strained down to the curved piece with hand screws. A string of almost any length can be formed in this way, by gluing a few feet at a time, and when that dries, removing the cylindrical curve and gluing down more, until the whole is completed. Several other methods will suggest themselves to the workman, of building up good, solid, circular strings.
Fig. 62. Wreath-Piece
Bent around Cylinder.
Fig. 63. Completed Wreath-Piece
Removed from Cylinder.
Fig. 64. Another Drum or Shape
for Building Curved Strings.
Fig. 65. Laying Out
Treads and Risers
around a Drum.
One method of laying out the treads and risers around a cylinder or drum, is shown in [Fig. 65]. The line D shows the curve of the rail. The lines showing treads and risers may be marked off on the cylinder, or they may be marked off after the veneer is bent around the drum or cylinder.
There are various methods of making inside cylinders or wells, and of fastening same to strings. One method is shown in [Fig. 66]. This gives a strong joint when properly made. It will be noticed that the cylinder is notched out on the back; the two blocks shown at the back of the offsets are wedges driven in to secure the cylinder in place, and to drive it up tight to the strings. [Fig. 67] shows an 8-inch well-hole with cylinder complete; also the method of trimming and finishing same. The cylinder, too, is shown in such a manner that its construction will be readily understood.
Stairs having a cylindrical or circular opening always require a weight support underneath them. This support, which is generally made of rough lumber, is called the carriage, because it is supposed to carry any reasonable load that may be placed upon the stairway. [Fig. 68] shows the under side of a half-space stair having a carriage beneath it. The timbers marked S are of rough stuff, and may be 2-inch by 6-inch or of greater dimensions. If they are cut to fit the risers and treads, they will require to be at least 2-inch by 8-inch.
In preparing the rough carriage for the winders, it will be best to let the back edge of the tread project beyond the back of the riser so that it forms a ledge as shown under C in [Fig. 69]. Then fix the cross-carriage pieces under the winders, with the back edge about flush with the backs of risers, securing one end to the well with screws, and the other to the wall string or the wall. Now cut short pieces, marked O O ([Fig. 68]), and fix them tightly in between the cross-carriage and the back of the riser as at B B in the section, [Fig. 69]. These carriages should be of 3-inch by 2-inch material. Now get a piece of wood, 1-inch by 3-inch, and cut pieces C C to fit tightly between the top back edge of the winders (or the ledge) and the pieces marked B B in section. This method makes a very sound and strong job of the winders; and if the stuff is roughly planed, and blocks are glued on each side of the short cross-pieces O O O, it is next to impossible for the winders ever to spring or squeak. When the weight is carried in this manner, the plasterer will have very little trouble in lathing so that a graceful soffit will be made under the stairs.
Fig. 66. One Method of Making an Inside Well.
Fig. 67. Construction and Trimming of 8-Inch Well-Hole.
The manner of placing the main stringers of the carriage S S, is shown at A, [Fig. 69]. [Fig. 68] shows a complete half-space stair; one-half of this, finished as shown, will answer well for a quarter-space stair.
Fig. 68. Under Side of Half-Space Stair, with
Carriages and Cross-Carriages.
Another method of forming a carriage for a stair is shown in [Fig. 70]. This is a peculiar but very handsome stair, inasmuch as the first and the last four steps are parallel, but the remainder balance or dance. The treads are numbered in this illustration; and the plan of the handrail is shown extending from the scroll at the bottom of the stairs to the landing on the second story. The trimmer T at the top of the stairs is also shown; and the rough strings or carriages, R S, R S, R S, are represented by dotted lines.
This plan represents a stair with a curtail step, and a scroll handrail resting over the curve of the curtail step. This type of stair is not now much in vogue in this country, though it is adopted occasionally in some of the larger cities. The use of heavy newel posts instead of curtail steps, is the prevailing style at present.
In laying out geometrical stairs, the steps are arranged on principles already described. The well-hole in the center is first laid down and the steps arranged around it. In circular stairs with an open well-hole, the handrail being on the inner side, the width of tread for the steps should be set off at about 18 inches from the handrail, this giving an approximately uniform rate of progress for anyone ascending or descending the stairway. In stairs with the rail on the outside, as sometimes occurs, it will be sufficient if the treads have the proper width at the middle point of their length.
Where a flight of stairs will likely be subject to great stress and wear, the carriages should be made much heavier than indicated in the foregoing figures; and there may be cases when it will be necessary to use iron bolts in the sides of the rough strings in order to give them greater strength. This necessity, however, will arise only in the case of stairs built in public buildings, churches, halls, factories, warehouses, or other buildings of a similar kind. Sometimes, even in house stairs it may be wise to strengthen the treads and risers by spiking pieces of board to the rough string, ends up, fitting them snugly against the under side of the tread and the back of the riser. The method of doing this is shown in [Fig. 71], in which the letter O shows the pieces nailed to the string.
Fig. 69. Method of Reinforcing Stair.
Fig. 70. Plan Showing One Method of Constructing
Carriage and Trimming Winding Stair.
Types of Stairs in Common Use.
In order to make the student familiar with types of stairs in general use at the present day, plans of a few of those most likely to be met with will now be given.
[Fig. 72] is a plan of a straight stair, with an ordinary cylinder at the top provided for a return rail on the landing. It also shows a stretch-out stringer at the starting.
[Fig. 73] is a plan of a stair with a landing and return steps.
[Fig. 74] is a plan of a stair with an acute angular landing and cylinder.
[Fig. 75] illustrates the same kind of stair as [Fig. 74], the angle, however, being obtuse.
[Fig. 76] exhibits a stair having a half-turn with two risers on landings.
[Fig. 77] is a plan of a quarter-space stair with four winders.
[Fig. 78] shows a stair similar to [Fig. 77], but with six winders.
Fig. 71. Reinforcing Treads and Risers by Blocks Nailed to String.
Fig. 72. Plan of Straight Stair with Cylinder at Top for Return Rail.
Fig. 73. Plan of Stair with
Landing and Return Steps.
[Fig. 79] shows a stair having five dancing winders.
[Fig. 80] is a plan of a half-space stair having five dancing winders and a quarter-space landing.
[Fig. 81] shows a half-space stair with dancing winders all around the cylinder.
[Fig. 82] shows a geometrical stair having winders all around the cylinder.
[Fig. 83] shows the plan and elevation of stairs which turn around a central post. This kind of stair is frequently used in large stores and in clubhouses and other similar places, and has a very graceful appearance. It is not very difficult to build if properly planned.
The only form of stair not shown which the student may be called upon to build, would very likely be one having an elliptical plan; but, as this form is so seldom used—being found, in fact, only in public buildings or great mansions—it rarely falls to the lot of the ordinary workman to be called upon to design or construct a stairway of this type.
Fig. 74. Plan of Stair with Acute-Angle Landing and Cylinder.
Fig. 75. Plan of Stair with Obtuse-Angle Landing and Cylinder.
Fig. 76. Half-Turn Stair with Two Risers on Landings.
Fig. 77. Quarter-Space Stair with Four Winders.
Fig. 78. Quarter-Space Stair with Six Winders.
Fig. 79. Stair with Five Dancing Winders.
Fig. 80. Half-Space Stair with Five Dancing Winders
and Quarter-Space Landing
Fig. 81. Half-Space Stair with Dancing Winders
all around Cylinder.
GEOMETRICAL STAIRWAYS AND
HAND-RAILING
The term geometrical is applied to stairways having any kind of curve for a plan.
The rails over the steps are made continuous from one story to another. The resulting winding or twisting pieces are called wreaths.
Wreaths.
Fig. 82.
Geometrical
Stair with
Winders all
Around
Cylinder.
Fig. 83. Plan and
Elevation of
Stairs Turning
around a
Central Post.
The construction of wreaths is based on a few geometrical problems—namely, the projection of straight and curved lines into an oblique plane; and the finding of the angle of inclination of the plane into which the lines and curves are projected. This angle is called the bevel, and by its use the wreath is made to twist.
In [Fig. 84] is shown an obtuse-angle plan; in [Fig. 85], an acute-angle plan; and in [Fig. 86], a semicircle enclosed within straight lines.
Projection. A knowledge of how to project the lines and curves in each of these plans into an oblique plane, and to find the angle of inclination of the plane, will enable the student to construct any and all kinds of wreaths.
The straight lines a, b, c, d in the plan, [Fig. 86], are known as tangents; and the curve, the central line of the plan wreath.
The straight line across from n to n is the diameter; and the perpendicular line from it to the lines c and b is the radius.
A tangent line may be defined as a line touching a curve without cutting it, and is made use of in handrailing to square the joints of the wreaths.
Tangent System.
The tangent system of handrailing takes its name from the use made of the tangents for this purpose.
In [Fig. 86], it is shown that the joints connecting the central line of rail with the plan rails w of the straight flights, are placed right at the springing; that is, they are in line with the diameter of the semicircle, and square to the side tangents a and d.
The center joint of the crown tangents is shown to be square to tangents b and c. When these lines are projected into an oblique plane, the joints of the wreaths can be made to butt square by applying the bevel to them.
All handrail wreaths are assumed to rest on an oblique plane while ascending around a well-hole, either in connecting two flights or in connecting one flight to a landing, as the case may be.
In the simplest cases of construction, the wreath rests on an inclined plane that inclines in one direction only, to either side of the well-hole; while in other cases it rests on a plane that inclines to two sides.
Fig. 84. Obtuse-Angle Plan.
[Fig. 87] illustrates what is meant by a plane inclining in one direction. It will be noticed that the lower part of the figure is a reproduction of the quadrant enclosed by the tangents a and b in [Fig. 86]. The quadrant, [Fig. 87], represents a central line of a wreath that is to ascend from the joint on the plan tangent a the height of h above the tangent b.
Fig. 85. Acute-Angle Plan.
Fig. 86. Semicircular Plan.
In [Fig. 88], a view of [Fig. 87] is given in which the tangents a and b are shown in plan, and also the quadrant representing the plan central line of a wreath. The curved line extending from a to h in this figure represents the development of the central line of the plan wreath, and, as shown, it rests on an oblique plane inclining to one side only—namely, to the side of the plan tangent a. The joints are made square to the developed tangents a and m of the inclined plane; it is for this purpose only that tangents are made use of in wreath construction. They are shown in the figure to consist of two lines, a and m, which are two adjoining sides of a developed section (in this case, of a square prism), the section being the assumed inclined plane whereon the wreath rests in its ascent from a to h. The joint at h, if made square to the tangent m, will be a true, square butt-joint; so also will be the joint at a, if made square to the tangent a.
In practical work it will be required to find the correct geometrical angle between the two developed tangents a and m; and here, again, it may be observed that the finding of the correct angle between the two developed tangents is the essential purpose of every tangent system of handrailing.
Fig. 87. Illustrating Plane Inclined
in One Direction Only.
Fig. 88. Plan Line of Rail Projected into
Oblique Plane Inclined to One Side Only.
In [Fig. 89] is shown the geometrical solution—the one necessary to find the angle between the tangents as required on the face-mould to square the joints of the wreath. The figure is shown to be similar to [Fig. 87], except that it has an additional portion marked “Section.” This section is the true shape of the oblique plane whereon the wreath ascends, a view of which is given in [Fig. 88]. It will be observed that one side of it is the developed tangent m; another side, the developed tangent a″ (= a). The angle between the two as here presented is the one required on the face-mould to square the joints.
In this example, [Fig. 89], owing to the plane being oblique in one direction only, the shape of the section is found by merely drawing the tangent a″ at right angles to the tangent m, making it equal in length to the level tangent a in the plan. By drawing lines parallel to a″ and m respectively, the form of the section will be found, its outlines being the projections of the plan lines; and the angle between the two tangents, as already said, is the angle required on the face-mould to square the joints of the wreath.
The solution here presented will enable the student to find the correct direction of the tangents as required on the face-mould to square joints, in all cases of practical work where one tangent of a wreath is level and the other tangent is inclined, a condition usually met with in level-landing stairways.
[Fig. 90] exhibits a condition of tangents where the two are equally inclined. The plan here also is taken from [Fig. 86]. The inclination of the tangents is made equal to the inclination of tangent b in [Fig.86], as shown at m in [Figs. 87], [88], and [89].
Fig. 89. Finding Angle between Tangents.
In [Fig. 91], a view of [Fig. 90] is given, showing clearly the inclination of the tangents c″ and d″ over and above the plan tangents c and d. The central line of the wreath is shown extending along the sectional plane, over and above its plan lines, from one joint to the other, and, at the joints, made square to the inclined tangents c″ and d″. It is evident from the view here given, that the condition necessary to square the joint at each end would be to find the true angle between the tangents c″ and d″, which would give the correct direction to each tangent.
In [Fig. 92] is shown how to find this angle correctly as required on the face-mould to square the joints. In this figure is shown the same plan as in Figs. [90] and [91], and the same inclination to the tangents as in [Fig. 90], so that, except for the portion marked “Section,” it would be similar to [Fig. 90].
To find the correct angle for the tangents of the face-mould, draw the line m from d, square to the inclined line of the tangents c′ d″; revolve the bottom inclined tangent c′ to cut line m in n, where the joint is shown fixed; and from this point draw the line c″ to w. The intersection of this line with the upper tangent d″ forms the correct angle as required on the face-mould. By drawing the joints square to these two lines, they will butt square with the rail that is to connect with them, or to the joint of another wreath that may belong to the cylinder or well-hole.
Fig. 90. Two Tangents Equally Inclined.
Fig. 91. Plan Lines Projected into Oblique Plane
Inclined to Two Sides.
Fig. 92. Finding Angle between Tangents.
[Fig. 93] is another view of these tangents in position placed over and above the plan tangents of the well-hole. It will be observed that this figure is made up of [Figs. 88] and [91] combined. [Fig. 88], as here presented, is shown to connect with a level-landing rail at a. The joint having been made square to the level tangent, a will butt square to a square end of the level rail. The joint at h is shown to connect the two wreaths and is made square to the inclined tangent m of the lower wreath, and also square to the inclined tangent c″ of the upper wreath; the two tangents, aligning, guarantee a square butt-joint. The upper joint is made square to the tangent d″, which is here shown to align with the rail of the connecting flight; the joint will consequently butt square to the end of the rail of the flight above.
The view given in this diagram is that of a wreath starting from a level landing, and winding around a well-hole, connecting the landing with a flight of stairs leading to a second story. It is presented to elucidate the use made of tangents to square the joints in wreath construction. The wreath is shown to be in two sections, one extending from the level-landing rail at a to a joint in the center of the well-hole at h, this section having one level tangent a and one inclined tangent m; the other section is shown to extend from h to n, where it is butt-jointed to the rail of the flight above.
Fig. 93. Laying Out Line of Wreath to Start from
Level-Landing Rail. Wind around Well-Hole, and
Connect at Landing with Flight to Upper Story.
This figure clearly shows that the joint at a of the bottom wreath—owing to the tangent a being level and therefore aligning with the level rail of the landing—will be a true butt-joint; and that the joint at h, which connects the two wreaths, will also be a true butt-joint, owing to it being made square to the tangent m of the bottom wreath and to the tangent c″ of the upper wreath, both tangents having the same inclination; also the joint at n will butt square to the rail of the flight above, owing to it being made square to the tangent d″, which is shown to have the same inclination as the rail of the flight adjoining.
As previously stated, the use made of tangents is to square the joints of the wreaths; and in this diagram it is clearly shown that the way they can be made of use is by giving each tangent its true direction. How to find the true direction, or the angle between the tangents a and m shown in this diagram, was demonstrated in [Fig. 89]; and how to find the direction of the tangents c″ and d″ was shown in [Fig. 92].
Fig. 94. Tangents Unfolded to Find Their Inclination.
[Fig. 94] is presented to help further toward an understanding of the tangents. In this diagram they are unfolded; that is, they are stretched out for the purpose of finding the inclination of each one over and above the plan tangents. The side plan tangent a is shown stretched out to the floor line, and its elevation a′ is a level line. The side plan tangent d is also stretched out to the floor line, as shown by the arc n′ m′. By this process the plan tangents are now in one straight line on the floor line, as shown from w to m′. Upon each one, erect a perpendicular line as shown, and from m′ measure to n, the height the wreath is to ascend around the well-hole. In practice, the number of risers in the well-hole will determine this height.
Fig. 95. Well-Hole Connecting Two Flights, with Two Wreath-Pieces,
Each Containing Portions of Unequal Pitch.
Now, from point n, draw a few treads and risers as shown; and along the nosing of the steps, draw the pitch-line; continue this line over the tangents d″, c″, and m, down to where it connects with the bottom level tangent, as shown. This gives the pitch or inclination to the tangents over and above the well-hole. The same line is shown in [Fig. 93], folded around the well-hole, from n, where it connects with the flight at the upper end of the well-hole, to a, where it connects with the level-landing rail at the bottom of the well-hole. It will be observed that the upper portion, from joint n to joint h, over the tangents c″ and d″, coincides with the pitch-line of the same tangents as presented in [Fig. 92], where they are used to find the true angle between the tangents as it is required on the face-mould to square the joints of the wreath at h.
In [Fig. 89] the same pitch is shown given to tangent m as in [Fig. 94]; and in both figures the pitch is shown to be the same as that over and above the upper connecting tangents c″ and d″, which is a necessary condition where a joint, as shown at h in [Figs. 93] and [94], is to connect two pieces of wreath as in this example.
In [Fig. 94] are shown the two face-moulds for the wreaths, placed upon the pitch-line of the tangents over the well-hole. The angles between the tangents of the face-moulds have been found in this figure by the same method as in [Figs. 89] and [92], which, if compared with the present figure, will be found to correspond, excepting only the curves of the face-moulds in [Fig. 94].
The foregoing explanation of the tangents will give the student a fairly good idea of the use made of tangents in wreath construction. The treatment, however, would not be complete if left off at this point, as it shows how to handle tangents under only two conditions—namely, first, when one tangent inclines and the other is level, as at a and m; second, when both tangents incline, as shown at c″ and d″.
Fig. 96. Finding Angle between Tangents
for Bottom Wreath of [Fig. 95].
Fig. 97. Finding Angle between Tangents
for Upper Wreath of [Fig. 95].
In [Fig. 95] is shown a well-hole connecting two flights, where two portions of unequal pitch occur in both pieces of wreath. The first piece over the tangents a and b is shown to extend from the square end of the straight rail of the bottom flight, to the joint in the center of the well-hole, the bottom tangent a″ in this wreath inclining more than the upper tangent b″. The other piece of wreath is shown to connect with the bottom one at the joint h″ in the center of the well-hole, and to extend over tangents c″ and d″ to connect with the rail of the upper flight. The relative inclination of the two tangents in this wreath, is the reverse of that of the two tangents of the lower wreath. In the lower piece, the bottom tangent a″, as previously stated, inclines considerably more than does the upper tangent b″; while in the upper piece, the bottom tangent c″ inclines considerably less than the upper tangent d″.
The question may arise: What causes this? Is it for variation in the inclination of the tangents over the well-hole? It is simply owing to the tangents being used in handrailing to square the joints.
The inclination of the bottom tangent a″ of the bottom wreath is clearly shown in the diagram to be determined by the inclination of the bottom flight. The joint at a″ is made square to both the straight rail of the flight and to the bottom tangent of the wreath; the rail and tangent, therefore, must be equally inclined, otherwise the joint will not be a true butt-joint. The same remarks apply to the joint at 5, where the upper wreath is shown jointed to the straight rail of the upper flight. In this case, tangent d″ must be fixed to incline conformably to the inclination of the upper rail; otherwise the joint at 5 will not be a true butt-joint.
Fig. 98. Diagram of Tangents and Face-Mould
for Stair with Well-Hole at Upper Landing.
The same principle is applied in determining the pitch or inclination over the crown tangents b″ and c″. Owing to the necessity of jointing the two wreaths, as shown at h, these two tangents must have the same inclination, and therefore must be fixed, as shown from 2 to 4, over the crown of the well-hole.
The tangents as here presented are those of the elevation, not of the face-mould. Tangent a″ is the elevation of the side plan tangent a; tangents b″ and c″ are shown to be the elevations of the plan tangents b and c; so, also, is the tangent d″ the elevation of the side plan tangent d.
Fig. 99. Drawing
Mould when
One Tangent
Is Level and
One Inclined
over Right-
Angled Plan.
If this diagram were folded, as [Fig. 94] was shown to be in [Fig. 93], the tangents of the elevation—namely, a″, b″, c″, d″—would stand over and above the plan tangents a, b, c, d of the well-hole. In practical work, this diagram must be drawn full size. It gives the correct length to each tangent as required on the face-mould, and furnishes also the data for the layout of the mould.
[Fig. 96] shows how to find the angle between the tangents of the face-mould for the bottom wreath, which, as shown in [Fig. 95], is to span over the first plan quadrant a b. The elevation tangents a″ and b″, as shown, will be the tangents of the mould. To find the angle between the tangents, draw the line a h in [Fig. 96]; and from a, measure to 2 the length of the bottom tangent a″ in [Fig. 95]; the length from 2 to h, [Fig. 96], will equal the length of the upper tangent b″, [Fig. 95].
From 2 to 1, measure a distance equal to 2-1 in [Fig. 95], the latter being found by dropping a perpendicular from w to meet the tangent b″ extended. Upon 1, erect a perpendicular line; and placing the dividers on 2, extend to a; turn over to the perpendicular at a″; connect this point with 2, and the line will be the bottom tangent as required on the face-mould. The upper tangent will be the line 2-h, and the angle between the two lines is shown at 2. Make the joint at h square to 2-h, and at a″ square to a″-2.
Fig. 100. Plan of Curved Steps and Stringer at Bottom of Stair.
The mould as it appears in [Fig. 96] is complete, except the curve, which is comparatively a small matter to put on, as will be shown further on. The main thing is to find the angle between the tangents, which is shown at 2, to give them the direction to square the joints.
In [Fig. 97] is shown how to find the angle between the tangents c″ and d″ shown in [Fig. 95], as required on the face-mould. On the line h-5, make h-4 equal to the length of the bottom tangent of the wreath, as shown at h″-4 in [Fig. 95]; and 4-5 equal to the length of the upper tangent d″. Measure from 4 the distance shown at 4-6 in [Fig. 95], and place it from 4 to 6 as shown in [Fig. 97]; upon 6 erect a perpendicular line. Now place the dividers on 4; extend to h; turn over to cut the perpendicular in h″; connect this point with 4, and the angle shown at 4 will be the angle required to square the joints of the wreath as shown at h″ and 5, where the joint at 5 is shown drawn square to the line 4-5, and the joint at h″ square to the line 4 h″.
[Fig. 98] is a diagram of tangents and face-mould for a stairway having a well-hole at the top landing. The tangents in this example will be two equally inclined tangents for the bottom wreath; and for the top wreath, one inclined and one level, the latter aligning with the level rail of the landing.
Fig. 101. Finding Angle between Tangents
for Squaring Joints of Ramped Wreath.
The face-mould, as here presented, will further help toward an understanding of the layout of face-moulds as shown in Figs. [96] and [97]. It will be observed that the pitch of the bottom rail is continued from a″ to b″, a condition caused by the necessity of jointing the wreath to the end of the straight rail at a″, the joint being made square to both the straight rail and the bottom tangent a″. From b″ a line is drawn to d″, which is a fixed point determined by the number of risers in the well-hole. From point d″, the level tangent d″ 5 is drawn in line with the level rail of the landing; thus the pitch-line of the tangents over the well-hole is found, and, as was shown in the explanation of [Fig. 95], the tangents as here presented will be those required on the face-mould to square the joints of the wreath.
In [Fig. 98] the tangents of the face-mould for the bottom wreath are shown to be a″ and b″. To place tangent a″ in position on the face-mould, it is revolved, as shown by the arc, to m, cutting a line previously drawn from w square to the tangent b″ extended. Then, by connecting m to b″, the bottom tangent is placed in position on the face-mould. The joint at m is to be made square to it; and the joint at c, the other end of the mould, is to be made square to the tangent b″.
Fig. 102. Bottom Steps with Obtuse-Angle Plan.
Fig. 103. Developing Face-Mould, Obtuse-Angle Plan.
The upper piece of wreath in this example is shown to have tangent c″ inclining, the inclination being the same as that of the upper tangent b″ of the bottom wreath, so that the joint at c″, when made square to both tangents, will butt square when put together. The tangent d″ is shown to be level, so that the joint at 5, when squared with it, will butt square with the square end of the level-landing rail. The level tangent is shown revolved to its position on the face-mould, as from 5 to 2. In this last position, it will be observed that its angle with the inclined tangent c″ is a right angle; and it should be remembered that in every similar case where one tangent inclines and one is level over a square-angle plan tangent, the angle between the two tangents will be a right angle on the face-mould. A knowledge of this principle will enable the student to draw the mould for this wreath, as shown in [Fig. 99], by merely drawing two lines perpendicular to each other, as d″ 5 and d″ c″, equal respectively to the level tangent d″ 5 and the inclined tangent c″ in [Fig. 98]. The joint at 5 is to be made square to d″ 5; and that at c″, to d″ c″. Comparing this figure with the face-mould as shown for the upper wreath in [Fig. 98], it will be observed that both are alike.
In practical work the stair-builder is often called upon to deal with cases in which the conditions of tangents differ from all the examples thus far given. An instance of this sort is shown in [Fig. 100], in which the angles between the tangents on the plan are acute. In all the preceding examples, the tangents on the plan were at right angles; that is, they were square to one another.
Fig. 104. Cutting Wreath from Plank.
Fig. 105. Wreath Twisted, Ready to be Moulded.
[Fig. 100] is a plan of a few curved steps placed at the bottom of a stairway with a curved stringer, which is struck from a center o. The plan tangents a and b are shown to form an acute angle with each other. The rail above a plan of this design is usually ramped at the bottom end, where it intersects the newel post, and, when so treated, the bottom tangent a will have to be level.
Fig. 106. Twisted Wreath Raised to Position,
with Sides Plumb.
In [Fig. 101] is shown how to find the angle between the tangents on the face-mould that gives them the correct direction for squaring the joints of the wreath when it is determined to have it ramped. This figure must be drawn full size. Usually an ordinary drawing-board will answer the purpose. Upon the board, reproduce the plan of the tangents and curve of the center line of rail as shown in [Fig. 100]. Measure the height of 5 risers, as shown in [Fig. 101], from the floor line to 5; and draw the pitch of the flight adjoining the wreath, from 5 to the floor line. From the newel, draw the dotted line to w, square to the floor line; from w, draw the line w m, square to the pitch-line b″. Now take the length of the bottom level tangent on a trammel, or on dividers if large enough, and extend it from n to m, cutting the line drawn previously from w, at m. Connect m to n as shown by the line a″. The intersection of this line with b″ determines the angle between the two tangents a″ and b″ of the face-mould, which gives them the correct direction as required on the face-mould for squaring the joints. The joint at m is made square to tangent a″; and the joint at 5, to tangent b″.
Fig. 107. Finding Bevel,
Bottom Tangent Inclined,
Top One Level.
Fig. 108. Application of Bevels in Fitting Wreath to Rail.
In [Fig. 102] is presented an example of a few steps at the bottom of a stairway in which the tangents of the plan form an obtuse angle with each other. The curve of the central line of the rail in this case will be less than a quadrant, and, as shown, is struck from the center o, the curve covering the three first steps from the newel to the springing.
In [Fig. 103] is shown how to develop the tangents of the face-mould. Reproduce the tangents and curve of the plan in full size. Fix point 3 at a height equal to 3 risers from the floor line; at this point place the pitch-board of the flight to determine the pitch over the curve as shown from 3 through b″ to the floor line. From the newel, draw a line to w, square to the floor line; and from w, square to the pitch-line b″, draw the line w m; connect m to n. This last line is the development of the bottom plan tangent a; and the line b″ is the development of the plan tangent b; and the angle between the two lines a″ and b″ will give each line its true direction as required on the face-mould for squaring the joints of the wreath, as shown at m to connect square with the newel, and at 3 to connect square to the rail of the connecting flight.
Fig. 109. Face-Mould and Bevel for Wreath, Bottom Tangent Level,
Top One Inclined.
The wreath in this example follows the nosing line of the steps without being ramped as it was in the examples shown in [Figs. 100] and [101]. In those figures the bottom tangent a was level, while in [Fig. 103] it inclines equal to the pitch of the upper tangent b″ and of the flight adjoining. In other words, the method shown in [Fig. 101] is applied to a construction in which the wreath is ramped; while in [Fig. 103] the method is applicable to a wreath following the nosing line all along the curve to the newel.
The stair-builder is supposed to know how to construct a wreath under both conditions, as the conditions are usually determined by the Architect.
Fig. 110. Finding Bevels for Wreath with Two Equally
Inclined Tangents.
The foregoing examples cover all conditions of tangents that are likely to turn up in practice, and, if clearly understood, will enable the student to lay out the face-moulds for all kinds of curves.
Bevels to Square the Wreaths.
The next process in the construction of a wreath that the handrailer will be called upon to perform, is to find the bevels that will, by being applied to each end of it, give the correct angle to square or twist it when winding around the well-hole from one flight to another flight, or from a flight to a landing, as the case may be.
Fig. 111. Application of Bevels to Wreath Ascending
on Plane Inclined Equally in Two Directions.
Fig. 112. Finding Bevel Where Upper Tangent Inclines More Than Lower One.
The wreath is first cut from the plank square to its surface as shown in [Fig. 104]. After the application of the bevels, it is twisted, as shown in [Fig. 105], ready to be moulded; and when in position, ascending from one end of the curve to the other end, over the inclined plane of the section around the well-hole, its sides will be plumb, as shown in [Fig. 106] at b. In this figure, as also in [Fig. 105], the wreath a lies in a horizontal position in which its sides appear to be out of plumb as much as the bevels are out of plumb. In the upper part of the figure, the wreath b is shown placed in its position upon the plane of the section, where its sides are seen to be plumb. It is evident, as shown in the relative position of the wreath in this figure, that, if the bevel is the correct angle of the plane of the section whereon the wreath b rests in its ascent over the well-hole, the wreath will in that case have its sides plumb all along when in position. It is for this purpose that the bevels are needed.
Fig. 113. Finding Bevel Where Upper Tangent Inclines Less Than Lower One.
A method of finding the bevels for all wreaths (which is considered rather difficult) will now be explained:
First Case. In [Fig. 107] is shown a case where the bottom tangent of a wreath is inclining, and the top one level, similar to the top wreath shown in [Fig. 98]. It has already been noted that the plane of the section for this kind of wreath inclines to one side only; therefore one bevel only will be required to square it, which is shown at d, [Fig. 107]. A view of this plane is given in [Fig. 108]; and the bevel d, as there shown, indicates the angle of the inclination, which also is the bevel required to square the end d of the wreath. The bevel is shown applied to the end of the landing rail in exactly the same manner in which it is to be applied to the end of the wreath. The true bevel for this wreath is found at the upper angle of the pitch-board. At the end a, as already stated, no bevel is required, owing to the plane inclining in one direction only. [Fig. 109] shows a face-mould and bevel for a wreath with the bottom tangent level and the top tangent inclining, such as the piece at the bottom connecting with the landing rail in [Fig. 94].
Fig. 114. Finding Bevel Where Tangents Incline
Equally over Obtuse-Angle Plan.
Fig. 115. Same Plan as in Fig. 114,
but with Bottom Tangent Level.
Second Case. It may be required to find the bevels for a wreath having two equally inclined tangents. An example of this kind also is shown in [Fig. 94], where both the tangents c″ and d″ of the upper wreath incline equally. Two bevels are required in this case, because the plane of the section is inclined in two directions; but, owing to the inclinations being alike, it follows that the two will be the same. They are to be applied to both ends of the wreath, and, as shown in [Fig. 105], in the same direction—namely, toward the inside of the wreath for the bottom end, and toward the outside for the upper end.
Fig. 116. Finding Bevels
for Wreath of Fig. 115.
In [Fig. 110] the method of finding the bevels is shown. A line is drawn from w to c″, square to the pitch of the tangents, and turned over to the ground line at h, which point is connected to a as shown. The bevel is at h. To show that equal tangents have equal bevels, the line m is drawn, having the same inclination as the bottom tangent c″, but in another direction. Place the dividers on o′, and turn to touch the lines d″ and m, as shown by the semicircle. The line from o′ to n is equal to the side plan tangent w a, and both the bevels here shown are equal to the one already found. They represent the angle of inclination of the plane whereon the wreath ascends, a view of which is given in [Fig. 111], where the plane is shown to incline equally in two directions. At both ends is shown a section of a rail; and the bevels are applied to show how, by means of them, the wreath is squared or twisted when winding around the well-hole and ascending upon the plane of the section. The view given in this figure will enable the student to understand the nature of the bevels found in [Fig. 110] for a wreath having two equally inclined tangents; also for all other wreaths of equally inclined tangents, in that every wreath in such case is assumed to rest upon an inclined plane in its ascent over the well-hole, the bevel in every case being the angle of the inclined plane.
Fig. 117. Upper Tangent Inclined. Lower
Tangent Level, Over Acute-Angle Plan.
Third Case. In this example, two unequal tangents are given, the upper tangent inclining more than the bottom one. The method shown in [Fig. 110] to find the bevels for a wreath with two equal tangents, is applicable to all conditions of variation in the inclination of the tangents. In [Fig. 112] is shown a case where the upper tangent d″ inclines more than the bottom one c″. The method in all cases is to continue the line of the upper tangent d″, [Fig. 112], to the ground line as shown at n; from n, draw a line to a, which will be the horizontal trace of the plane. Now, from o, draw a line parallel to a n, as shown from o to d, upon d, erect a perpendicular line to cut the tangent d″, as shown, at m; and draw the line m u o″. Make u o″ equal to the length of the plan tangent as shown by the arc from o. Put one leg of the dividers on u; extend to touch the upper tangent d″, and turn over to 1; connect 1 to o″; the bevel at 1 is to be applied to tangent d″. Again place the dividers on u; extend to the line h, and turn over to 2 as shown; connect 2 to o″, and the bevel shown at 2 will be the one to apply to the bottom tangent c″. It will be observed that the line h represents the bottom tangent. It is the same length and has the same inclination. An example of this kind of wreath was shown in [Fig. 95], where the upper tangent d″ is shown to incline more than the bottom tangent c″ in the top piece extending from h″ to 5. Bevel 1, found in [Fig. 112], is the real bevel for the end 5; and bevel 2, for the end h″ of the wreath shown from h″ to 5 in [Fig. 95].
Fig. 118. Finding Bevels
for Wreath of Plan, [Fig. 117].
Fourth Case. In [Fig. 113] is shown how to find the bevels for a wreath when the upper tangent inclines less than the bottom tangent. This example is the reverse of the preceding one; it is the condition of tangents found in the bottom piece of wreath shown in [Fig. 95]. To find the bevel, continue the upper tangent b″ to the ground line, as shown at n; connect n to a, which will be the horizontal trace of the plane. From o, draw a line parallel to n a, as shown from o to d; upon d, erect a perpendicular line to cut the continued portion of the upper tangent b″ in m; from m, draw the line m u o″ across as shown. Now place the dividers on u; extend to touch the upper tangent, and turn over to 1, connect 1 to o″; the bevel at 1 will be the one to apply to the tangent b″ at h, where the two wreaths are shown connected in [Fig. 95]. Again place the dividers on u; extend to touch the line c; turn over to 2; connect 2 to o″; the bevel at 2 is to be applied to the bottom tangent a″ at the joint where it is shown to connect with the rail of the flight.
Fifth Case. In this case we have two equally inclined tangents over an obtuse-angle plan. In [Fig. 102] is shown a plan of this kind; and in [Fig. 103], the development of the face-mould.
In [Fig. 114] is shown how to find the bevel. From a, draw a line to a′, square to the ground line. Place the dividers on a′; extend to touch the pitch of tangents, and turn over as shown to m; connect m to a. The bevel at m will be the only one required for this wreath, but it will have to be applied to both ends, owing to the two tangents being inclined.
Sixth Case. In this case we have one tangent inclining and one tangent level, over an acute-angle plan.
Fig. 119. Laying Out Curves on Face-Mould with Pins and String.
In [Fig. 115] is shown the same plan as in [Fig. 114]; but in this case the bottom tangent a″ is to be a level tangent. Probably this condition is the most commonly met with in wreath construction at the present time. A small curve is considered to add to the appearance of the stair and rail; and consequently it has become almost a “fad” to have a little curve or stretch-out at the bottom of the stairway, and in most cases the rail is ramped to intersect the newel at right angles instead of at the pitch of the flight. In such a case, the bottom tangent a″ will have to be a level tangent, as shown at a″ in [Fig. 115], the pitch of the flight being over the plan tangent b only.
To find the bevels when tangent b″ inclines and tangent a″ is level, make a c in [Fig. 116] equal to a c in [Fig. 115]. This line will be the base of the two bevels. Upon a, erect the line a w m at right angles to a c; make a w equal to o w in [Fig. 115]; connect w and c; the bevel at w will be the one to apply to tangent b″ at n where the wreath is joined to the rail of the flight. Again, make a m in [Fig. 116] equal the distance shown in [Fig. 115] between w and m, which is the full height over which tangent b″ is inclined; connect m to c in [Fig. 116], and at m is the bevel to be applied to the level tangent a″.
Fig. 120. Simple Method of Drawing Curves on Face-Mould.
Fig. 121. Tangents, Bevels, Mould-Curves, etc., from Bottom Wreath
of [Fig. 95], In which Upper Tangent Inclines Less than Lower One.
Seventh Case. In this case, illustrated in [Fig. 117], the upper tangent b″ is shown to incline, and the bottom tangent a″ to be level, over an acute-angle plan. The plan here is the same as that in [Fig. 100], where a curve is shown to stretch out from the line of the straight stringer at the bottom of a flight to a newel, and is large enough to contain five treads, which are gracefully rounded to cut the curve of the central line of rail in 1, 2, 3, 4. This curve also may be used to connect a landing rail to a flight, either at top or bottom, when the plan is acute-angled, as will be shown further on.
Fig. 122. Developed Section of Plane Inclining Unequally
in Two Directions.
Fig. 123. Arranging Risers around Well-Hole on Level Landing Stair,
with Radius of Central Line of Rail One-Half Width of Tread.
To find the bevels—for there will be two bevels necessary for this wreath, owing to one tangent b″ being inclined and the other tangent a″ being level—make a c, [Fig. 118], equal to a c in [Fig. 117], which is a line drawn square to the ground line from the newel and shown in all preceding figures to have been used for the base of a triangle containing the bevel. Make a w in [Fig. 118] equal to w o in [Fig. 117], which is a line drawn square to the inclined tangent b″ from w; connect w and c in [Fig. 118]. The bevel shown at w will be the one to be applied to the joint 5 on tangent b″, [Fig. 117]. Again, make a m in [Fig. 118] equal to the distance shown in [Fig. 117] between the line representing the level tangent and the line m′ 5, which is the height that tangent b″ is shown to rise; connect m to c in [Fig. 118]; the bevel shown at m is to be applied to the end that intersects with the newel as shown at m in [Fig. 117].
The wreath is shown developed in [Fig. 101] for this case; so that, with [Fig. 100] for plan, [Fig. 101] for the development of the wreath, and [Figs. 117] and [118] for finding the bevels, the method of handling any similar case in practical work can be found.
How to Put the Curves on the Face-Mould.
It has been shown how to find the angle between the tangents of the face-mould, and that the angle is for the purpose of squaring the joints at the ends of the wreath. In [Fig. 119] is shown how to lay out the curves by means of pins and a string—a very common practice among stair-builders. In this example the face-mould has equal tangents as shown at c″ and d″. The angle between the two tangents is shown at m as it will be required on the face-mould. In this figure a line is drawn from m parallel to the line drawn from h, which is marked in the diagram as “Directing Ordinate of Section.” The line drawn from m will contain the minor axes; and a line drawn through the corner of the section at 3 will contain the major axes of the ellipses that will constitute the curves of the mould.
Fig. 124. Arrangement of Risers Around Well-Hole
with Radius Larger Than One-Half Width of Tread.
Fig. 125. Arrangement of Risers around Well-Hole,
with Risers Spaced Full Width of Tread.
Fig. 126. Plan of Stair
Shown in [Fig. 123].
Fig. 127. Plan of Stair
Shown in [Fig. 124].
Fig. 128. Plan of Stair
Shown in [Fig. 125].
Fig. 129. Drawing Face-Mould
for Wreath from Pitch-Board.
The major is to be drawn square to the minor, as shown. Place, from point 3, the circle shown on the minor, at the same distance as the circle in the plan is fixed from the point o. The diameter of this circle indicates the width of the curve at this point The width at each end is determined by the bevels. The distance a b, as shown upon the long edge of the bevel, is equal to ½ the width of the mould, and is the hypotenuse of a right-angled triangle whose base is ½ the width of the rail. By placing this dimension on each side of n, as shown at b and b, and on each side of h″ on the other end of the mould, as shown also at b and b, we obtain the points b 2 b on the inside of the curve, and the points b 1 b on the outside. It will now be necessary to find the elliptical curves that will contain these points; and before this can be done, the exact length of the minor and major axes respectively must be determined. The length of the minor axis for the inside curve will be the distance shown from 3 to 2; and its length for the outside will be the distance shown from 3 to 1.
To find the length of the major axis for the inside, take the length of half the minor for the inside on the dividers: place one leg on b, extend to cut the major in z, continue to the minor as shown at k. The distance from b to k will be the length of the semi-major axis for the inside curve.
Fig. 130. Development of Face-Mould for Wreath
Connecting Rail of Flight with Level-Landing Rail.
To draw the curve, the points or foci where the pins are to be fixed must be found on the major axis. To find these points, take the length of b k (which is, as previously found, the exact length of the semi-major for the inside curve) on the dividers; fix one leg at 2, and describe the arc Y, cutting the major where the pins are shown fixed, at o and o. Now take a piece of string long enough to form a loop around the two and extending, when tight, to 2, where the pencil is placed; and, keeping the string tight, sweep the curve from b to b.
Fig. 131. Arranging Risers in Quarter-Turn between Two Flights.
The same method, for finding the major and foci for the outside curve, is shown in the diagram. The line drawn from b on the outside of the joint at n, to w, is the semi-major for the outside curve; and the points where the outside pins are shown on the major will be the foci.
Fig. 132. Arrangement of Risers around Quarter-Turn
Giving Tangents Equal Pitch with Connecting Flight.
Fig. 133. Finding Bevel for
Wreath of Plan, Fig. 132.
To draw the curves of the mould according to this method, which is a scientific one, may seem a complicated problem; but once it is understood, it becomes very simple. A simpler way to draw them, however, is shown in [Fig. 120].
The width on the minor and at each end will have to be determined by the method just explained in connection with [Fig. 119]. In [Fig. 120], the points b at the ends, and the points in which the circumference of the circle cuts the minor axis, will be points contained in the curves, as already explained. Now take a flexible lath; bend it to touch b, z, and b for the inside curve, and b, w, and b for the outside curve. This method is handy where the curve is comparatively flat, as in the example here shown; but where the mould has a sharp curvature, as in case of the one shown in [Fig. 101], the method shown in [Fig. 119] must be adhered to.
Fig. 134. Well-Hole with Riser in Center. Tangents
of Face-Mould, and Central Line of Rail, Developed.
With a clear knowledge of the above two methods, the student will be able to put curves on any mould.
The mould shown in these two diagrams, [Figs. 119] and [120], is for the upper wreath, extending from h to n in [Fig. 94]. A practical handrailer would draw only what is shown in [Fig. 120]. He would take the lengths of tangents from [Fig. 94], and place them as shown at h m and m n. By comparing [Fig. 120] with the tangents of the upper wreath in [Fig. 94], it will be easy for the student to understand the remaining lines shown in [Fig. 120]. The bevels are shown applied to the mould in [Fig. 105], to give it the twist. In [Fig. 106], is shown how, after the rail is twisted and placed in position over and above the quadrant c d in [Fig. 94], its sides will be plumb.
Fig. 135. Arrangement of Risers in
in Stair with Obtuse-Angle Plan.
Fig. 136. Arrangement of Risers in Obtuse-Angle
Plan, Giving Equal Pitch over Tangents and Flights.
Face-Mould Developed.
In [Fig. 121] are shown the tangents taken from the bottom wreath in [Fig. 95]. It was shown how to develop the section and find the angle for the tangents in the face-mould, in [Fig. 113]. The method shown in [Fig. 119] for putting on the curves, would be the most suitable.
Fig. 137. Arrangement of Risers in Flight with Curve at Landing.
[Fig. 121] is presented more for the purposes of study than as a method of construction. It contains all the lines made use of to find the developed section of a plane inclining unequally in two different directions, as shown in [Fig. 122].
Fig. 138. Development of
Face-Moulds for Plan,
[Fig. 137].
Arrangement of Risers in and around Well-Hole.
An important matter in wreath construction is to have a knowledge of how to arrange the risers in and around a well-hole. A great deal of labor and material is saved through it; also a far better appearance to the finished rail may be secured.
In level-landing stairways, the easiest example is the one shown in [Fig. 123], in which the radius of the central line of rail is made equal to one-half the width of a tread. In the diagram the radius is shown to be 5 inches, and the treads 10 inches. The risers are placed in the springing, as at a and a. The elevation of the tangents by this arrangement will be, as shown, one level and one inclined, for each piece of wreath. When in this position, there is no trouble in finding the angle of the tangent as required on the face-mould, owing to that angle, as in every such case, being a right angle, as shown at w; also no special bevel will have to be found, because the upper bevel of the pitch-board contains the angle required.
The same results are obtained in the example shown in [Fig. 124], in which the radius of the well-hole is larger than half the width of a tread, by placing the riser a at a distance from c equal to half the width of a tread, instead of at the springing as in the preceding example.
In [Fig. 125] is shown a case where the risers are placed at a distance from c equal to a full tread, the effect in respect to the tangents of the face-mould and bevel being the same as in the two preceding examples. In [Fig. 126] is shown the plan of [Fig. 123]; in [Fig. 127], the plan of [Fig. 124]; and in [Fig. 128], the plan of [Fig. 125]. For the wreaths shown in all these figures, there will be no necessity of springing the plank, which is a term used in handrailing to denote the twisting of the wreath; and no other bevel than the one at the upper end of the pitch-board will be required. This type of wreath, also, is the one that is required at the top of a landing when the rail of the flight intersects with a level-landing rail.
In [Fig. 129] is shown a very simple method of drawing the face-mould for this wreath from the pitch-board. Make a c equal to the radius of the plan central line of rail as shown at the curve in [Fig. 130]. From where line c c″ cuts the long side of the pitch-board, the line c″ a″ is drawn at right angles to the long edge, and is made equal to the length of the plan tangent a c, [Fig. 130]. The curve is drawn by means of pins and string or a trammel.
In [Fig. 131] is shown a quarter-turn between two flights. The correct method of placing the risers in and around the curve, is to put the last one in the first flight and the first one in the second flight one-half a step from the intersection of the crown tangents. By this arrangement, as shown in [Fig. 132], the pitch-line of the tangents will equal the pitch of the connecting flight, thus securing the second easiest condition of tangents for the face-mould—namely, as shown, two equal tangents. For this wreath, only one bevel will be needed, and it is made up of the radius of the plan central line of the rail o c, [Fig. 131], for base, and the line 1-2, [Fig. 132], for altitude, as shown in [Fig. 133].
The bevel shown in this figure has been previously explained in [Figs. 105] and [106]. It is to be applied to both ends of the wreath.
The example shown in [Fig. 134] is of a well-hole having a riser in the center. If the radius of the plan central line of rail is made equal to one-half a tread, the pitch of tangents will be the same as of the flights adjoining, thus securing two equal tangents for the two sections of wreath. In this figure the tangents of the face-mould are developed, and also the central line of the rail, as shown over and above each quadrant and upon the pitch-line of tangents.
The same method may be employed in stairways having obtuse-angle and acute-angle plans, as shown in [Fig. 135], in which two flights are placed at an obtuse angle to each other. If the risers shown at a and a are placed one-half a tread from c, this will produce in the elevation a pitch-line over the tangents equal to that over the flights adjoining, as shown in [Fig. 136], in which also is shown the face-mould for the wreath that will span over the curve from one flight to another.
In [Fig. 137] is shown a flight having the same curve at a landing. The same arrangement is adhered to respecting the placing of the risers, as shown at a and a. In [Fig. 138] is shown how to develop the face-moulds.
FINISHED ROOF TRUSS IN FIRST PRESBYTERIAN CHURCH, SYRACUSE, N. Y.
Tracy & Swartwout, Architects; Ballantyne & Evans, Associated.
Reproduced by courtesy of “The Architectural Review.”