This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.
Inserting the value of A from formula (61) we have: or the radius of flue will be 4 feet (diameter 8 feet).
Now making the walls at top of chimney 8" thick and adopting the rule of an outside batter of about 1/4" to the foot, or say 4" every 15 feet, we get a section as shown in Figure 87.
Let us examine the strength of the chimney at the five levels A, B, C, D and E.
The thickness of the base of each part is marked on the right-hand section, and the average thickness of the section of the part on the left-hand side.
Take the part above A; the average area is (22/7.52 - flue area) or, 78 - 50 = 28 square feet.
This multiplied by the height of the part and the weight of one cubic foot of brickwork (112 lbs.) gives the weight of the whole, or actual load.
W1 = 28.30.112 = 94080 lbs., or 47 tons.
The area of the base at A would be:
A=(22/7.5 1/32 - flue area ), or A = 89 - 50 =
39 square feet.
The height of the part is L = 30.
P2= 5 1/32+42/4 = 11,11
Inserting these values in Formula (GO) the safe load at A would be:
W= 39.200/14+0,0046. 30.30/11,11
= 440 tons, or about nine times the actual load. Now, in examining the joint B we must remember to take the whole load of brickwork to the top as well as whole length L to top (or 60 feet). The load on B we find is: W1 = 13l tons, while the safe load is: w = 63.200/14+0,046. 60/13 = 472 tons
Similarly, we should find on C the load:
W1 = 259 tons, while the safe load is: w = 89.200/14+0,046. 90.90/15.11 = 461 tons.
On D we should find the load:
W1 = 432 tons, while the safe load is:
W= 119.200/14+0,046. 120.120/17,44 = 448 tons.
Below D the wall is considerably over three feet thick, and is solid, therefore we can use ( c/f) = 300, provided good Portland cement is used and best brick, which should, of course, be the case at the base of such a high chimney. We should have then the load on E:
W1= 657 tons, while the safe load is:
W = 151.300/14+0,046. 150.150/20 = 690 tons.
The chimney is, therefore, more than amply safe at all points, the bottom being left too strong to provide for the entrance of flue, which will, of course, weaken it considerably. We might thin the upper parts, but the bricks saved would not amount to very much and the offsets would make very ugly spots, and be bad places for water to lodge. If the chimney had been square it would have been much stronger, though it would have taken considerably more material to build it.
It is generally best to build the flue of a chimney plumb from top to bottom, and, of course, of same area throughout. Sometimes the flue is gradually enlarged towards the top for some five to ten feet in height, which is not objectionable, and the writer has obtained good results thereby; some writers, though, claim the flue should be diminished at the top, which, however, the writer has never cared to try. Galvanized iron bands should be placed around the chimney at intervals, particularly around the top part, which is exposed very much to the disintegrating effects of the weather and the acids contained in the smoke. No smoke flue should ever be pargetted (plastered) inside, as the acids in the smoke will eat up the lime, crack the plaster, and cause it to fall. The crevices will fill with soot and be liable to catch fire. The mortar-joints of flues should be of cement, or, better yet, of fire-clay, and should be carefully struck, to avoid being eaten out by the acids.
Where walls are long, without buttresses or cross-walls, such as gable-walls, side-walls of building etc., we can take a slice of the wall, one running foot in length, and consider it as forced to yield (bulge) inwardly or outwardly, so that for ρ2 we should use:
=d2/12; where d the thickness of wall in inches. The area or a would then be, in square inches, a = 12.d. Inserting these values in formula (50) we have for
Calculation of Walls.-Bulging.
w =d.(c/f)/0,0833+0,0,475. L2/d2 (62)
Where w = the safe load, in lbs., on each running foot of wall (d" thick).
Where d = the thickness, in inches, of the wall at any point of its height.
Where L= the height, in feet, from said point to top of wall.
Where (c/f) = the safe resistance to crushing, in lbs., per square inch, as given in Table V. (See page 135.)
If it is preferred to use tons and feet, we insert in formula (GO): for A = D, where D the thickness of wall, in feet, and we have:
P2 = D2/12; therefore
W = D.(c/f)/14+0,0552. L2/D2 (63)
Where W = the safe load, in tons, of 2000 lbs., on each running foot of wall (D feet thick). Where D = the thickness of wall, in feet, at any point of its height. Where L = the height, in feet, from said point to the top of wall. Where (c/f) = the safe resistance to crushing of the material, in lbs., per square inch, as found in Table V. (See page 135.)
Where a wall is thoroughly anchored to each tier of floor beams, so that it cannot possibly bulge, except between floor-beams, use the height of story (that is, height between anchored beams in feet) in place of L and calculate d or D for the bottom of wall at each story.
The load on a wall consists of the wall itself, from the point at which the thickness is being calculated to the top, plus the weight of one foot in width by half the span of all the floors, roofs, partitions, etc. Where there are openings in a wall, add to pier the proportionate weight which would come over opening; that is, if we find the load per running foot on a wall to be 20000 lbs., and the wall consists of four-foot piers and three-foot openings alternating, the piers will, of course, carry not only 20000 lbs. per running foot, but the C0000 lbs. coining over each opening additional, and as there are four feet of pier we must add to each foot 00000/4 = 15000 lbs.; we therefore calculate the pier part of Avail to carry 35000 lbs. per running foot. The actual load on the wall must not exceed the safe load as found by the formula (62) or (63).