In arranging the beams upon the floor plan of a building, the first point to consider is the maximum load that will probably be placed upon the floor. The weight of the material comprising the floor - that is, the floor beams, girders, arches, flooring, timbers for nailing the flooring upon, the filling between timbers, partitions, and plastering on the ceiling and on partitions - is usually called the "dead load"

For the weight of a cubic foot of any of the materials likely to be used, refer to Table of Weight of Various Substances, and chapter on "Hollow Burnt Clay".

The weight of persons, or of stores of any kind, which may be placed upon the floor is called the " live load".

This load for dwellings or offices may be assumed at 75 pounds per square foot of floor surface; for places of public assembly, 120 pounds; for stores, factories, or for any manufacturing or commercial purpose, from 150 pounds upwards; for warehouses, 200 to 250 pounds; and for heavy machinery, 250 to 400 pounds.

## 27. Method Of Determining Rolled Iron Beams By Diagram

Having determined the load per square foot to be sustained, by referring to the following diagram showing the proper distances in feet between centres of beams for different spans and different uniform loads per square foot, proper rolled iron beams of 12,000 pounds strain may be found.

### Example 1

At what distance between centres must 9-inch heavy beams be set when the span is 15 feet and the entire load is 200 pounds per square foot? Ans. Follow the horizontal line from 15, on scale of distances between supports, to where it intersects the curve for 9-inch heavy beams, thence follow on line at right angles to scale of 200 pounds, and find the distance - 4 feet.

### Example 2

A floor of 30 feet span is to carry 300 pounds per square foot on beams 2 feet apart: what size beam should be used? Ans. The horizontal line for 30 feet and the vertical line from 2 feet on 300 pounds scale intersect near curves of 15-inch light and I2 1/4-inch heavy beams, either of which may be used.

* Diagram arranged by A. Faber du Faur, M.E.

### Example 3

What weight per square foot will a 12 1/4-inch heavy beam carry, at 25 feet span and 3 feet between centres? Arts. Follow up from intersection of the horizontal line for 25 feet span and the curve for 121/4-inch heavy beam, and 250 pounds to the square foot is found to be the nearest to 3 feet span. The beam will carry a little more.

## 28. Beams

Beams deeper than those drawn on the diagram are principally used for girders. For the strength and dimensions of most of the numerous sizes rolled, and for steel beams, etc., see the following tables of coefficients.

## 29. To Determine Coefficient For Beams

The following formula for uniform weights gives coefficient for 12,000 pounds strain:

1/8WL = 12,000 I/e, where W= weight in pounds uniformly distributed; L = length in inches; I = moment of inertia ; e = distance of extreme lamina from neutral axis (half the depth of I beam); C = coefficient.

WL = 96,000I/e; or if L be given in feet as is usual, then

WL = 8000 I/e-=C.

### Example

The moment of inertia of a 15-inch beam 50 pounds per foot = 522.6. Distance of extreme lamina, 7".5.

Coefficient = 8000 X ( 522.6/7.5) = 557,500.

## 30. Properties Of Wrought-Iron I Beams

 Depth of Beam. Weight per ft. Area ofSection. Thickness ofWeb. Width of Flange. Moment ofInertia, axis perpendicular to web at centre. Coefficient,12,000 lbs.strain. inches. lbs. inches. inches. inches. 20 90.7 27.2 .69 6.75 1650.3 1,320,000 20 66.7 20.0 .50 6.00 1238.0 990,000 15 80.0 24.0 .76 6.08 813.7 868,000 15 66.7 20.02 .50 6.00 707.0 748,000 15 60.0 18.0 .57 5.45 625.5 667,200 15 50.0 15.0 •49 5. 05 522.6 557.500 * 12 1/4 H. 56.7 16.77 .60 5-50 391.2 5II,000 12 56.5 17.0 .78 5.16 348.5 464,800 12 42.0 12.6 .51 4.63 274.8 366,400 12 1/4 L. 41.7 12.33 •47 4.79 288.0 377,000 10 1/2 H 45.0 13.36 •47 5.00 233.7 356,000 10 1/2 40.0 12.0 •55 4.80 201.7 307,200 101/2 L. 35.0 10.44 .38 4.50 185.6 283,000 10 1/2 31.5 9 5 .41 4.53 165.0 251,200 10 1/2 Ex. L. 30.0 8.90 .31 4.50 164.0 250,000 10 42.0 12.6 .50 4.75 198.8 3l8,100 10 36.0 10.8 •44 4.50 170.6 273,000 10 30.0 9.0 •37 4.31 145.8 233,300 9 38.5 11.6 .46 4.71 150.1 266,900 9 28.5 9.6 .40 4.16 110.3 196,000 9 23.5 7.1 •34 3.96 92.3 164.000 8 34.0 10.2 .50 4.50 102.0 203,900 8 27.0 8.1 .41 4.09 82.5 165,100 8 21.5 6.5 •33 3.71 66.2 132,300 7 22.0 6.6 .38 3.82 51.9 118.500 7 18.0 5.4 .26 3.52 44.2 101,100 6 16.0 4.8 •25 3.44 29.0 77,400 6 13.5 4.1 .24 3.24 24.4 65.100 5 12.0 3.6 .28 2.96 14.4 46,000 5 10.0 3.0 •23 2.85 12.5 40,000 4 7.0 2.1 .18 2.50 5.7 22,800 4 6.0 1.8 .18 2.18 4.6 18,300 3 9.0 2.7 .40 2.58 3.5 l8,900 3 5.5 1.7 .16 2.22 2.5 13,400

To find the safe load in pounds equally distributed, divide the coefficient by the span in feet. To find the safe load in pounds, weight in centre of span, divide the coefficient by the span in feet, and take one half the quotient.

## 31. Deflection

To find the deflections of beams for the above distributed loads, divide the square of the span in feet by 70 times the depth of beam in inches.

* Letters designate Heavy and Light sections.

## 32. Coefficients For Steel Beams

If L be given in feet, as Before for iron beams, but using 16,000 pounds strain, then

WL= 10,666 I/e = C.

### Example

The moment of inertia of a 9-inch beam 27 pounds per yard is 110.6. Distance of extreme lamina, 4.5.

Coefficient = 10,666 X (110.6/4.5) = 262,200.

## 33. Properties Of Steel I Beams

 Depth of Beam. Weight per ft. Area ofSection. Thickness ofWeb. Width of Flange. Moment ofInertia, axis perpendicular to web at centre. Coefficient,16,ooo lbs.strain. inches. lbs. inches. inches. inches. 24 100 30.0 •75 7.20 2322.3 2,064,000 24 80 23.2 .50 6.95 2059.3 1,830,500 20 80 23.5 .60 7.00 1449.2 1.545.600 20 64 18.8 .50 6.25 1146.0 1,222,400 15 75 22.1 •67 6.31 757.7 1,077,300 15 60 I7.6 •54 6.04 644.0 916,300 15 50 14.7 •45 5.75 529.7 753,300 15 41 I2.0 .40 5.50 424.1 603,200 12 40 11.7 •39 5.50 281.3 500,100 12 32 9.4 •35 5.25 222.3 395,200 10 32 9.7 •37 5.00 161.3 344,000 10 25.5 7.5 •32 4.75 123.7 263,800 9 27 7.9 • 31 4.75 110.6 262,200 9 21 6.2 •27 4.50 84.3 199,900 8 22 6.5 •27 4.50 71.9 191,600 8 18 5.3 25 4.25 57.8 154,000 7 20 5.9 •27 4.25 49.7 151,400 7 15.5 4.6 •23 4.00 38.6 117,600 6 16 4.7 .26 3.63 28.6 101,800 6 13 3.8 •23 3.50 23.5 83,500 5 13 3.8 .26 3.13 15.7 67,000 5 10 3.0 .22 3.00 12.4 52,900 4 10 2.9 .24 2.75 7.7 41,200 4 7.5 2.0 .20 2.63 5.9 31,400

To find the safe load in pounds equally distributed, divide the coefficient by the span in feet. To find the safe load in pounds, with weight in centre of span, divide the coefficient by the span in feet, and take one half the quotient.