relative economy of different beams having equal strength or capacity.

Table XX, which is reproduced with slight modifications, by courtesy of the Atlas Portland Cement Co., from their book on the utilization of "Concrete in Factory Construction," gives the proper dimensions for beams and slabs that will carry uniformly distributed floor or roof loads of 125, 50, and 30 pounds respectively, per square foot. These beams, if checked over, by the straight line formulas (10) and (11), of Chapter XVIII, will be found to average about seven-tenths per cent of steel, to have a fibre stress in the concrete of about 500 pounds per square inch, and in the steel of between 12,000 and 15,000 pounds per square inch.

TABLE XVII.-BEAM DEPTHS AND THEIR SQUARES.

Example, Involving Use of Tables.-Compute the cost of beams spaced 8 feet apart, and having a span of 12 feet which will support a 6-inch slab of concrete in addition to a floor load of 140 pounds per square foot.

Estimated weight of beam, Table XVIII, 12 x 24 ins. (288 × 12)

=

3,456 lbs. 13,440 + 6,912 + 3,456

=

23,808 lbs.

TABLE XVIII.

Weight of Heavy Reinforced Concrete Beams in Pounds per Lineal Foot, also Cost of the Concrete in Dollars per Lineal Foot at the Rate of $10.00 per Cubic Yard.

16

20

32

4

.041 .052

20

25

5

052 065

6

24

42

28

.072

8

32

10

122

+

16

Cost

24 28 36 40 48 56 64 72 Weight .062 .072 .083 093 103.124 .144 .165.185 Cost 30 35 40 45 50 60 70 80 90 Weight 077 .090.103.116.129.155.180 .206.232 Cost 30 36 48 54 60 72 84 96 108 Weight .062 .077.093 .108 .124 .139.155.185 .216 .247 .278 Cost 35 42 49 56 63 70 84 98 112 126 Weight .090.108 .126.144 .162.180.216 .252.288 .324 40 48 56 64 72 80 96 112 128 144 Weight .083 103 .124 144 165 185 .206.247 .288 .330 371 Cost 36 45 54 63 72 81 90 108 126 144 .093 .116.139.162 .185 .208.232.278 324 371 40 50 бо 70 80 90 100 120 140 160 .129.155.180 .206 .232 .257 309 .360 .412 .463 Cost 72 84 96 108 120 144 168 192 216 Weight .155.185 .216 .247 .278 .309.371

18

371

417

.834 Cost

20

Weight per lineal foot =

180

360 Weight

Breadth in inches multi

.463

TOTAL DEPTH IN INCHES.

24

26

28

30

.617.741 .864 .988 1.111 Cost

With 2 inches of concrete below the steel, the dimensions will be 12 x 24 ins.

From Table XVIII, the concrete will cost, at the rate of $10.00 per cu. yd.

.741 X 12 = $8.89

From formula (2) the steel area will be,

.22 X 12 X .007

1.85 sq. ins.

From Table XIX, this is equal to the area of 5-5/8 inch square bars, and from the same table the cost at the rate of 2 cents per pound will be

5 X 12 X .027 = $1.62

add 60 per cent for the cost of upper flange bars, stirrups, bent ends, and fabricating, and the total cost will be

The corresponding costs with different steel ratios will be found to be as follows:

.0055 lower flange steel dimensions 12 X 25 ins., steel 5-9/16 in. sq. bars, cost $11.37

5-5/8
5-3/4
5-13/16"

These are relative costs based on concrete at $10.00 per cu. yd., and steel at 2 cents per pound. With concrete at $15.00 per cu. yd., the beam with .007 steel would be the cheapest in cost.

Design of Stirrups. In a beam supporting a uniformly distributed load, stirrups are required when the total load, including the weight of the beam in pounds, divided by the sectional area in square inches, exceeds 60, or when

Stirrups are, however, desirable in all beams, as they add considerably to their strength and ability to withstand shocks. Stirrups may be either vertical or inclined. They are most efficient when inclined at an angle of 45 degrees toward the end of the girder.

Ransome's Rule.-Mr. E. L. Ransome's rule is to employ four stirrups at each end of the beam, the first at 1/4 of the depth from the end, the second at 1/2 the depth from the first, while the spacing

of the third is 3/4 of the depth and of the fourth, a distance equal to the depth. These stirrups are in general composed of 1/4 to 3/8 inch rods.

Stirrups should go through the beam into the floor slab, where they are bent to run parallel with the slab for about six inches. Stirrups should always be fastened to or looped around the bottom rods. In place of stirrups a sheet of expanded metal or other wire fabric may be placed in the web of the beam.

An improvement over the use of loose rods and stirrups consists in the unit system of reinforcement, where all of the members are assembled into one frame. These are illustrated in another chapter, and include the Kahn, Cummings, Unit, and Girder frames.

Design of Bond.-The steel bars may be considered safe against slipping when not called upon to sustain more than 50 pounds bond stress per square inch of surface area.

In a beam carrying a symmetrical or uniform load, this condition may be expressed by the following formula:

where W denotes the load on the beam in pounds.

W' denotes the weight of the beam itself.

(8)

n denotes the sum of the perimeters of the steel bars in inches. d denotes the depth to the plane of the steel in inches.

In the previous example, W + W'

=

23,808, d= 22 ins., and since

which is barely within the required limit of 50. With a greater bond stress, the number of bars would need to be increased.

Summary of Method of Procedure in Design of Beams and Slabs. The following is a brief summary of the different steps involved in the design of a beam or slab carrying a uniformly distributed load, as previously described in this chapter.