material will result from proper design. We shall consider the chimney as a semi-beam uniformly loaded.

Let us take any section. Let D

=

diameter of the stack at that section, diameter at a certain height above D = H1. The overthrowing

in inch-lbs. We are assuming a wind pressure in this case of 50 lbs. per sq. ft. and a certain coefficient = 67.

This will give a very approximate result. If absolute accuracy is aimed at, it will be necessary to resort to the tedious process of finding the centre of gravity of each section and note its height above the base construct a new formula for finding M。

= M2 = 201H2H2(D+d)

inch-lbs., while the mean wind pressure on each section

= 33.5(D2h)

=

=

H

Then we

(424)

(425)

D1 being the mean outside diameter of that section and height of section.

Then having a series of values of Equation 425, we can plot the results as in fig. 804. We refer the reader to graphic statics. In construction no vertical joints should be over each other; the seams, however, are only subject to crippling stresses. Now on the top section of the chimney we have no strain, but the least practical size of plate we would use for the purpose would be in.; rivets would be -in. diameter at 2-in. pitch. We shall also probably be able to keep the same size of plate right down the shaft, but in order to do so we shall have to greatly increase the number of rivets in each joint, and that is the reason for the bell-mouth shape always adopted at the base, because even by double riveting it would be difficult to get the required number of rivets. The design is proceeded with as follows:

1. Determine the size and height of stack.

2. Draw the centre line and mark off each plate section. For economy's sake they should be made all the same height, and large plates used to avoid too many vertical seams.

3. Mark the centre lines of all horizontal seams.

4. Through the proper points draw the outlines of the shell, making each

succeeding diameter larger in the correct proportion. The increase should be uniform. We are at present neglecting the weight of the stack.

5. Consider the foundation bolts.

Let 1, 2, and 1, be three values of the vertical lap in inches, as shown by fig. 805.

from which we proceed to find the correct diameter of the bolts, and the number of bolts will be settled by the designer to avoid large dimensions. We may then design the footings as shown in figs. 806, 807, and 808. The latter two forms are usually made of cast-steel sections, there being as many sections as bolts. They require, however, careful design in accordance

FIG. 806.

..
FIG. 807.

FIG. 808.

with engineering principles. We must also find the required thickness of metal in that part of the footing to which the shell is riveted. In it we have shear and tension set up by the rivets, and also a bending moment from the foundation bolts to consider.

Now find the net area of rivet-holes in square inches = Ra

D being the outside

diameter of the seam in inches, and d2 = diameter of rivet holes in inches. Divide this into half the load, and we have the tension set up in the cast-steel ring which must be within safe limits. Again, let a single plate area of one seam.

=

D being the outside diameter.

a = πDt

Then

(428)

Let S unit stress on plate in lbs. per square inch for tension and compression; then the total strain on one seam in lbs.

T = Sa.

=

T and

(429) Equation

and if there were two rows of rivets, half would come on each row. (427) is apt, however, to give rather low values when the bending moment is

excessive, in which case it would be advisable to take the modulus of section into account. Now in a steel chimney of the type we are describing the resistance to collapse is provided mainly by the weight of the base, because we are not considering the weight of the metal nor the firebrick lining, so as to be well on the safe side.

But the least practical value of W should be 3W, which has to be provided by the base. Taking brickwork at 112 lbs. per ft.-cube, the effect of this has then to be transmitted through the foundation bolts.

Bolts have been already discussed in Equation 426. But for simplicity's sake, the formula 431, using the same units as the previous one, may be adopted,

B1 being the diameter of the base plate, whose weight is not included in W. P should not exceed 8000 lbs. per sq. in. in this case. The steel base plate sections need not be bolted at the joints. The anchor plates are important. They should not bear more than 10 tons per sq. ft. of area, and to avoid overcrowding of these plates the bolts often have to be made in two lengths. In fig. 807 will be seen two values, P and l Knowing them, the thickness of metal at the bolt-head is found by

This applies to the foundation plates.

Ꭲ

=

Pl
2

(431a)

Fig. 809 shows a design for a stack on the foregoing principles. steel chimneys there is a practical limit to size and height on economical grounds, and in large power-stations it is usual to see very often two similar stacks side by side. There is usually a light ladder running the whole height. The fire-brick lining is usually carried further than shown in fig. 809.

We have dealt with the draught in a boiler furnace, and it is very often the duty of an engineer to see what the actual draught is.

The commonest method of measuring the draught in a flue is by a water gauge. This consists of a U-tube 3 or 4 in. long, made of, say, in. glass tube and graduated in inches. Test holes should be made through the brickwork at the boiler side of the side flue damper, economiser inlet, and chimney base. A reading should also be taken over the boiler fires. To use this gauge, a piece of 3-in. gaspipe about 6 ft. long is required, and india-rubber tubing to connect this to the water gauge. When the pipe is inserted in the flue, there will be a difference noted in the levels in the limbs of the water gauge. This level represents in inches of water the pressure in the flue below atmosphere. The pressure thus obtained will not give the quantity of

FIG. 809.

Firebrick
Lining.

gases or the velocity of them, although it is approximately proportional to the velocity. A wheel anemometer or Pitot tube anemometer would be necessary for getting the exact quantity of air used, or flue gases. The draught varies considerably in different boiler plants, and will be as low as 0.20 in. in the side flue at some places, and as high as 100 in. in the side flue at others. In a welldesigned boiler plant with, say, 0-80 in. chimney draught, the following draughts would be obtained: chimney base, 0.80 in.; economiser inlet, 0.65 in.; boiler side flues, 0.55 in.; over fires, 0.30 in. This would be the case with, say, three boilers fixed and working. The lowest draught at which it is possible to keep up the steam pressure is the best, the draught being regulated at the chimney damper. By doing this the speed of the gases is reduced, and consequently more heat is taken out of them before going to waste up the chimney. Bad draughts are generally caused by insufficient area of flues. The worst place, of course, will be found by the water-gauge readings at the different points, and will be where the greatest difference occurs in the results. Narrow economisers obstruct the draught, as do sharp corners, right-angle bends in the flues, etc. Air leakages through the brickwork, round the boiler shells, and round the flue doors, etc., also have a bad effect on both the draught and the fuel economy. A steam jet under the bars reduces the quantity of air going into the fires, but assists the fire to burn bright and keeps the bars cool. The height of the bridge is important, but the best height can only be found by experiment. Any accumulation of flue dust of course reduces the flue areas, and this should be removed often. If there is more than one opening to the chimney, a vertical wall should be built between, to prevent baffling effects between the two currents. In conclusion, it is always advisable to keep a thick, even fire, both for economy in fuel and improvement in draught. The apparatus is shown in fig. 809A.

2.

To Flue

FIG. 809A.

CHAPTER XXXVI.

STEEL AND IRON CONSTRUCTION AND DESIGN.

We now come to deal with a very important and comprehensive branch of the engineer's profession, that of designing structures in iron and steel, and the erection of the same in accordance with scientific principles. We say steel and iron, but the use of wrought iron in constructional work has practically fallen into disuse, steel being universally used, principally because of the economy due to its superior strength. The use of cast iron is still in a small measure retained for pillars of small dimensions, but its use in beams may be stated to have ceased. We would advise the reader carefully to lay to heart what has been said in Chapter XIII. on the properties of iron and steel, and also the principles enumerated in Chapters VII., VIII., IX., and X.

The object of the present chapter is to point out to the reader how these principles are put into actual practice. We are generally concerned also with the heavier branches of constructional steel, leaving light work such as hayricks, fencing, barns, and sheds to the architect; but we do not confine ourselves entirely to very heavy work, but rather aim at treating the subject so far as it concerns the municipal engineer. To start with, we proceed to investigate the scientific principles underlying the use of rivets and riveted work in general; we shall then discuss the properties of bolts.

In up-to-date shops, nowadays, the members of structures which require holes in them for riveting are drilled in the same way as parts of machines, the process being greatly facilitated by the special high-speed tool-steels now on the market. The practice of punching the holes is now considered very second-rate workmanship, and should not be allowed on any high-class

contracts.

All holes should be drilled to templet. Then, when drilled, the two plates or bars to be joined should be bolted together and the rivet-holes reamered out in. larger than the actual rivet. No drifting should be allowed under any circumstances. The plates are then taken apart and any burrs cut off with a chisel. The holes must then have their outer edges gone over with a broad countersink. Riveting is done as far as possible in the shops, and should be done by a hydraulic riveter, which should always be provided with a special means of hydraulically closing the plates. That riveting work which is done on the job usually has to be done by hand, but on large bridge contracts the installation of a self-contained hydraulic riveter, electrically driven, may be deemed justifiable. The rivets so driven are called Field rivets, and must be specially considered in ways we shall describe. Such work wants rigid inspection. It is most essential that skilled labour be employed throughout the work.