Example.

A two-story-and-attic dwelling has brick walls 12 inches thick; the walls carry two tiers of beams of 20 feet span; is the wall strong enough? The brickwork is good and laid in cement mortar.

We will calculate the thickness required at first story beam level, Figure 88.

The load is, per running foot of wall:

Wall of Country House.

Wall

=

22.112

=

2464

lbs.

Wind

=

22. 15

=

330

lbs.

Second floor

=

10. 90

=

900

lbs.

Attic floor

=

10. 70

=

700

lbs.

Slate roof (incl wind and snow)

=

10. 50

=

500

lbs.

Total load

=

4894

lbs.

For the quality of brick described we should take from Table V:

(c/f) = 200 lbs.

The height between floors is 10 feet, or L=10, therefore, using formula (62) we have: w = d.(c/f)/0,0833+0,0475. l2/d2 = 12.200/0,0833+0,475. 10.10/12.12 = 5807 lbs.

bo that the wall is amply strong. If the wall were pierced to the extent of one-quarter with openings, the weight per running foot would be increased to 6525 lbs. Over 700 lbs. more than the safe load, still the wall, even then, would be safe enough, as Ave have allowed some 330 lbs. for wind, which would rarely, if ever, be so strong; and further, some 1200 lbs. for loads on floors, also a very ample allowance; and even if the two ever did exist together it would only run the compression (c/f) up to 225 lbs. per inch, and for a temporary stress this can be safely allowed.

The writer would state here, that the only fault he finds with formulae (59), (60), (62) and (63), is that their results are apt to give an excess of strength; still it is better to be in fault on the safe side and be sure.

Example.

The brick walls of a warehouse are 115 feet high, the 8 stories are each 14 feet high from floor to floor, or 12 feet in the clear. The load on floors per square foot, including the fire-proof construction, will average 300 lbs. What size should the walls be? The span of beams is 26 feet on an average. (See Fig. 89, page 142.)

According to the New York Building Law, the required thicknesses would be: first story, 32"; second, third, and fourth stories, 28"; fifth and sixth stories, 24"; seventh and eighth stories, 20".

At the seventh story level we have a load, as follows, for each running foot of wall:

Walls of City Warehouse.

Wall

=

30.1 2/3.112

=

5600

Wind

=

3.0.30

=

900

Roof

=

13.120

=

1560

Eighth floor

=

13.300

=

3900

Total

=

11960 lbs., or 6 tons.

The safe load on a 20" wall 12 feet high, from formula (63) is: w = 1 2/3.200/14+0,552. 12.12/1 2/3.1 2/3 = 333/14+0,552.51,84 = 7,84 tons, or

15622 lbs.

If one-quarter of the wall were used up for openings, slots, flues, etc., the load on the balance would be 8 tons per running foot, which is still safe, according to our formula.

At the fifth-story level the load would be:

Load above seventh floor

-

11960

Wall

28.2.112

=

6272

Wind

28.30

-

840

Sixth and seventh floors

2.13.300

=

7800

Total tons.

=

26872 lbs. or 13 1/2

The safe load on a 24" wall, 12 feet high, from formula (G3) is:

W = 2.200/14+0,552. 12.12/2.2 = 400/14+0,552.36 = 11,809 tons, or 23618 lbs.

This is about 10 per cent less than the load, and can be passed as safe, but if there were many flues, openings, etc., in wall, it should be thickened.

At the second-story level the load would be:

Load above fifth floor

=

26872

Wall

=

42. 2 1/3.112

=

10976

Wind

=

42. 30

=

1260

Third, fourth and fifth floors

=

3.13.300

-

11700

Total 25 tons.

==

50808,

or

The safe-load on a 28" wall, 12 feet high, from formula (63) is:

W = 2 1/3.200/14+0,552. 12.12/2 1/3. 2 1/. = 467/14+0,552.26.45 = 16,33 tons, or 32660 lbs.

Or, the wall would be dangerously weak at the second-floor level.

At the first-floor level the load would be:

Load above second floor

=

50808

Wall

=

14. 2 2/3.112

=

4181

Wind

=

14.30

=

420

Second floor

=

13.300

=

3900

Total

=

59309, or 29 1/2 tons

The safe-load on a 32" wall, 12 feet high, from formula (63) is:

W = 2 2/3.200/14+0,552. 12.12/2 2/3. 2 2/3 = 533/14+0,552.2025 = 21,169 tons,

or 42338 lbs.

The wall would, therefore, be weak at this point, too.

Now while the conditions we have assumed, an eight-story warehouse with all floors heavily loaded, would be very unusual, it answers to show how impossible it is to cover every case by a law, not based on the conditions of load, etc. In reality the arrangements of walls, as required by the law, are foolish. Unnecessary weight is piled on top of the wall by making the top 20" thick, which wall has nothing to do but to carry the roof. (If the span of beams were increased to 31 feet or more the law compels this top wall to be 24" thick, if 41 feet, it would have to be 28" thick, an evident waste of material.) It would be much better to make the top walls lighter, and add to the bottom; in this case, the writer would suggest that the eighth story be 12"; the seventh story 16"; the sixth story, 20"; the fifth story, 24"; the fourth story, 28"; the third story, 32"; the second story, 36", and the first story 40", see Figure 90. (Page 142.)

This would represent but 4 2/3 cubic feet of additional brickwork for every running foot of wall; or, if we make the first-story wall 36" too, as hereafter suggested, the amount of material would be exactly the same as required by the law, and yet the wall would be much better proportioned and stronger as a whole. For we should find (for L = 12 feet),

Actual load at eighth-floor level,

3832

Safe load on a 12" wall from Formula (62)

4298

Actual load at seventh-floor level,

10243

Safe load on a 16" wall from Formula (62)

9135

Actual load at sixth-floor level,

17176

Safe load on a 20" wall from Formula (62)

15729

Actual load at fifth-floor level,

24632

Safe load on a 24" wall from Formula (62)

23750

Actual load at fourth-floor level,

32611

Safe load on a 28" wall from Formula (62)

32825

Actual load at third-floor level,

41112

Safe load on a 32" wall from Formula (62)

42638

Actual load at second-floor level,

50136

Safe load on a 36" wall from Formula (62)

52902

Actual load at first-floor level,

59683

Safe load on a 40" wall from Formula (62)

63492

The first-story wall could safely be made 36" if the brickwork is good, and there are not many flues, etc., in walls, for then we could use

(c/f) = 250, which would give a safe load on a 36" wall = 65127 lbs., or more than enough.

The above table shows how very closely the Formula (62) would agree with a practical and common-sense arrangement of exactly the same amount of material, as required by the law.

Walls And Piers 100170

Fig. 91.

Now, if the upper floor were laden with barrels, there might be some danger of these thrusting out the wall. We will suppose an extreme case, four layers of flour barrels packed against the wall, leaving a 5-foot aisle in the centre. We should have 20 barrels in each row ( Fig. 91), weighing in all 20.19C = 3920 lbs. These could not well be placed closer than 3 feet from end to end, or, say, 1307 lbs., per running foot of wall; of this amount only one-half will thrust against wall, or, say, 650 pounds. The radius of the barrel is about 20". If Figure 92 represents three of the barrels, and we make A B = to, = 1/2 the load of the flour barrels, per running foot of walls, it is evident that D B will represent the horizontal thrust on wall, per running foot. As D B is the radius, and as we know that A D = 2 D B or = 2 radii, we can easily find A B, for: