For fair brick in' lime and cement (mixed) mortar, we should use:

(c/f) = 50

And for the best brickwork in cement mortar, we should use: (c/f) = 200

If, however, a wall (or pier) is over 3 feet thick, and laid in good cement mortar, with the best hard-burned brick, and there are not many flues, etc., in the wall, we can safely use:

(c/f)=250

If the wall (or pier) is over 3 feet thick, and there are no flues or openings, and the best brick and foreign Portland cements are used, it would be perfectly safe to use:

(c/f) = 300.

Example.

A tower 16 feet square outside, carries a steeple weigh-ing, including wind-pressure, some 15 tons. The belfry' openings, on each side, are central and virtually equal to openings 8 feet wide by 18 feel high each. There are 8 feel of solid wall over openings. What should be the thickness of belfry piers? The masonry is ordinary rubble-work. •

In the first place we will try Formula (60) giving strength of whole tower at base of belfry piers. The load will be: 4.(26.16 - 18.8 - 26.1 2/3) = 892 superficial feet of masonry 20" thick and weighing 250 lbs. per superficial foot = 223000 lbs. (see Figures

Tower

Walls.

Fig. 84

Fig. 85.

84 and 85): add to this spire and we have at foot of belfry piers: Actual load = 253000 lbs. or = 126 tons.

Now P2 (the square of the radius of gyration) would be P2 = I/A; the area A = 1G2 - (12 2/32 + 4.8.1 2/3) =43; the moment of inertia I

= 1/12. (164 - 12 2/34 - 3 1/3.83 - 8.163+ 8.12 2/33) =1799.

Therefore P2= 1799/43 = 41,8. Now for rubble-work, Table V, (c/f ) = 100; and, from Formula (60), the safe load would be: w= 43.100/14 +0,046, 26.25/41,8 = 4300/14,77

= 291 tons; or more than strong enough.

Now let us examine the strength of each pier by itself, Figure 86. In the first place we must find the distance y of the neutral axis M-N from say the line A B. This from

Piers at opening.

Fig. 86.

Table I, Section No. 20 is:

48.202 /2+20.28. (20+28/2)/48.20+20.28 = 18."8; or,say, y = 19".

Now i = 20.293 +28.13+ 48.193 = 272347 (in inches) and a = 20.48 + 20.28 = 1520 square inches, therefore = i/a = 179

(in inches).

The length of each pier is 18 feet, or L=18.

Therefore, from Formula (59) we have the safe load:

W = 1520.100/1+0,475 18.18/179 = 81940 pounds, or say the safe load on each pier would be 41 tons.

The actual load we know is 126/4 = 31 1/2 tons, or the pier is more than safe.

Now let us see how far down it would be safe to carry the 20" walls. We use formula (60) and have from Section Number 4, of Table 1:

P2 = 162+12 2/32/12 = 34 2/3 (in feet).

Thickness of walls.

The area would be

A = 162 - 12 2/32 = 96 square feet. The load for each additional foot under belfry would be then:

96.150 = 14400 lbs., or 7,2 tons. The whole load from top down for each additional foot would be, in tons:

W1 = 126 + (L - 26).7,2 = 7,2.L - 61 While the safe load from Formula (60) would be: w= 96.100/14 + 0,046. L2/34 2/3____

Now trying this for a point 50 feet below spire, we should have the actual load:

W1 = 7,2.50 - 61 = 299 tons, and the safe load:

W = 96.100/14+0,046. 50.50/34 2/3 = 554 tons, or, we can go still lower with the 20" work. For 70 feet below spire, we should have actual load:

W1= 7,2.70 - 61 = 443 to while the safe load: w = 96.100/14x0,046. 70.70/34 2/3 = 468 tons, or, 70 feet would be about the limit of the 20" work.

If we now thicken the walls to 24", we should have

A=112 square feet.

P2 from Section 4, Table I, = 33 1/2 (in feet). The weight per foot would be 112.150 = 16800 lbs. (or 8,4 tons) additional for every foot in height of 24" work. Therefore the actual load would be,

443 + (L - 70).8,4 or

W1 = L.S,4 - 145. Now, for L= 80 feet, we should have the actual load:

W1 = 527 tons, while the safe load would be:

W = 112.100/14+0,046. 80.80/33 1/3 = 491 tons.

This, though a little less than the actual load, might be passed. Rubble stone work, however, should not be built to such height, good brickwork in cement would be better, as it can be built lighter; for (c/f)= 200, would give larger results, and brickwork weighs less, besides; then, too, we have the additional advantage of saving considerable weight on the foundations.

Thickening the walls of a tower or chimney on the inside does not strengthen them nearly so much as the same material applied to the outside would, either by offsetting the wall outside, or by building piers and buttresses.

It is mainly for this reason, and also to keep the flue uniform, that chimneys have their outside dimensions increased towards the bottom.

Example.

A circular brick chimney is to be built 150 feel high, the flue entering about 6 feet from the base; the horsepower of boilers is 1980 HP. What size should the chimney bet The formula for size of flue is:

Calculation of chimneys.

(61)

Where A = the area of flue, in square feet. Where L = the length of vertical flue in fee Where HP=the total horse-power of boiler;

A circular flue will always give a better draught than any other form, and the nearer the flue is to the circle the better will its shape be.

In our case the flue is circular, so that we will have

Size of flue.

A=22/7. R2 (see Table I, Sec. No. 7) or