Art. XXIII.—On Skew Arches.

By W. Arthur, C.E.

pelled engineers to avail themselves of the principle, and now skew arches are to be met with on nearly every line of railway in Great Britain.

Bridges in Otago.

In a colony like this, bridges as a rule have hitherto been constructed of timber. This is owing to the rapidity and cheapness with which such works can be carried out, and the circumstances of a young colony seem to justify such economy. But I question whether there is in this any real economy in the long run. For even where the workmanship is of the best and the quality of the material unexceptionable, timber bridges require constant repairing, and cannot at most be expected to last more than fifteen or twenty years. Iron bridges are no doubt very convenient in railway works and for great spans, but even they are not equal in durability to good stone arches. This fact has caused the Parisians to substitute arches of masonry in their main thoroughfares, for the iron bridges previously erected there. English engineers are coming round also to admit, that stone after all, has many advantages over iron in permanent structures. Most of the bridges recently built in Otago by the Provincial Government are a great improvement on timber pile bridges, as the piers and abutments have been built in masonry, the superstructures only being in timber. The only stone arches however, of any importance, which Otago at present possesses, are those on the Main North Road from Dunedin to Oamaru, five in number, and two or three on the road from Palmerston to the interior; the greatest span of any one of these being sixty feet. There are no skew arches in Otago and I am not aware of the existence of one in any part of New Zealand at present.

On bridges in Otago there was spent by the Provincial Government, during last year alone, no less than £34,751, so the kind of material which is best for their construction is a consideration worthy of the attention of all good colonists.

Skew Arches.

I will now proceed to describe the principles and construction of skew arches in masonry, illustrated by drawings, and a small model of an actual segmental arch, built seven years ago. These drawings are No. 1, and No. 2, appended to this paper: No. 1 shewing half elevation, plan and section; and No. 2, the development, on a flat surface, of the intrados and extrados, which is the more important and necessary drawing for the guidance of the builder.

Definition.

A skew arch in masonry may be defined as being an arch whose abutments are equal, parallel, but not directly opposite each other, and whose courses, from face to face, are not parallel but inclined to abutments, and are spiral surfaces. The angle of skew, θ on Drawing No. 1, is the angle

Section on Square and Skeus.

A B. In the same way draw face line C D, and then the heading joints of skewbacks, and face quoins at right angles to coursing joints. The other heading joints of soffit may be left to the builder to arrange, care being taken that a good bond is maintained throughout. This is the usual method of designing the development of the intrados, and, taken in connection with plan and development of extrados on same drawing, it is very convenient, so far as showing the relation of the different parts. But it is reversed from its normal position, or turned upside down: this will be referred to again.

Face Joints.

The elevation on skew or elevation of face, must have the face joints, or rather their chords, drawn from a centre lower than the axis of the cylinder and from which point they radiate. This property in skew arches was discovered by Mr. Buck, and is known as the focal eccentricity, or the difference between centre of cylinder and centre from which chords of face-joints radiate. The formula for calculating this is 60 = Rad. × tan. θ × tan. ø; and a geometrical method is given by diagram in “Masonry and Stone-cutting,” by Dobson.

Extrados.

The development of the extrados should next be drawn. This is done similarly to that of the intrados, but with this difference, that the coursing spirals are not at right angles to the heading spirals. The reason of this is that the length of the coursing spirals, measured or projected on the axis of the cylinder is the same for intrados and extrados, but the length of the heading spirals is greater in the extrados than the intrados. Another consequence is that the angle of extrados G A′ H or θ, is greater than the angle of intrados β. The figure A′ B′ C′ D′, Drawing No. 2, represents a development of the extrados.

Elevation, etc.

The more essential designs having now been completed, from these the elevation, plan and cross section, shewn in Drawing No. 1, are drawn. In the elevation, the only matters further to be noted are that the back of the arch-stones should be stopped, and the courses of spandril walls built to correspond, thus securing greater stability than if these precautions were neglected. The plan shews the peculiar serrated appearance which the springers or skewbacks present, owing to the obliquity of the courses; and it will also be perceived that the boss stones at the obtuse and acute angles, are greater and less respectively than the other skewbacks, for the same reason.

Bathlin Burn Bridge.

The remaining peculiarities of skew arches, and the rules which are

necessary to be observed in construction, may perhaps be more conveniently laid before you if, during the rest of this paper, I adhere as nearly as possible to a description of the methods actually adopted in the Bathlin Bridge. Drawing No. 1 shows the ordinary designs that were used, and the principles above explained and represented by Drawing No. 2, were carried out in a modified form.

Skewbacks or Springers.

First, the skewbacks were cut to sizes, and templets taken from impost line A C (as d e f templet for soffit), and built into position, the face of quoins being cut to lie in perpendicular plane; the stones dressed to thickness of arch-ring, and the extrados left rough and quarry-faced—templet, ã g h, not being used. When skewbacks were fixed, centreing and laggings were erected carefully. The intrados was drawn on paper on a scale of two feet to an inch, but instead of being turned upside down, as in drawing No. 2, it was designed in its normal position; an elevation on skew and section on square, on same scale, and a full-sized drawing of twisting rules, as sketched in No. 2, were made; but no development of extrados was drawn, it was found sufficient to calculate angle of extrados ø. In using the normal development of intrados for this arch, it was found to secure much convenience to the builder, who was thus saved the awkwardness of always treating the arch-stones as inverted. A large wooden platform was constructed adjoining site of bridge, and on it a full-size drawing was made of development of intrados in its natural position, and the sizes and joints of all the stones arranged on it. On the laggings the coursing spirals were laid down or marked off from the development on the platform.

Angle of Twist.

The angle of twist (ø—β) having been found by calculation, the winding strip and parallel rule were drawn full size, and from these the actual rules were cut, which the builder used in dressing the beds of the arch-stones to the proper twist. The divergent portion of winding strip shown is that applicable to stones of three feet in length, applied at right angles to cours-ing spirals. These twisting rules may be used either as rules or templets.

Face angle of Quoins.

The next thing in importance, requiring great care, was the working the faces of the quoins to the proper angle with the soffit. From the springing to the keystone the faces of quoins make different angles with the coursing joints. On the side next the acute angle these angles are acute, and on the side next the obtuse angle they are obtuse; and the angles equi-distant from keystone are complements of one another. The angle in each case was

measured on the laggings between a perpendicular plane in line of face and the coursing spiral at the particular point. A convenient method to find this angle is with a board, one edge of which is dressed to the curve of the soffit in the direction of spiral courses, applied at a point marked at the centre, or any convenient point, of this curved edge to the face-line on laggings, and resting on laggings in the true position of a coursing spiral. A plumb-line run then carefully along the upper edge of board till the weight points exactly on the face line, will give a point on that edge, which joined by a pencil line with centre-point on curved edge below, will represent the actual angle and its complement at the particular course where the measurement is taken. From this board the templets may be made.

Fig. 2.

The obliquity of the arch causes a curious result in the length of the top and bottom of quoins. That is, on the acute side of arch the soffit of the quoins is longer than the top or extrados, while on the obtuse side the soffit of the quoins is shorter than the extrados.

Working of Arch Stones.

In the operation of dressing or working the arch stones, such as the quoins, a plain surface is first prepared approximating in size and direction a coursing joint or bed, and on this the curve of the arch soffit, in the same direction, is drafted. The twisting rules are next applied, and the plane surface is worked off to the proper twist, right handed or left, as the case may be. Then the soffit is worked to the arch square—(a rule made by joining a straight-edge at right angles to a rule having the curve of the arch) —the heading joint is dressed at right angles to soffit, and the face to a rule or templet forming the correct angle of the face. There are also the necessary dimensions of quoins to be taken from diagram on platform and from drawings as required.

Though not all mathematically accurate, these rules as I have now given them, for the building of a skew arch, are those commonly followed in practice, and give sufficiently good results to justify their use.

Skew Arches of other forms.

In the above description of the design and construction of a skew arch, it will be observed that a segmental arch only has been treated of. There are other forms of skew arches rendered sometimes unavoidable by the peculiar circumstances of the case, such as an elliptical skew arch, and a skew arch the plan of which is on a curve.