Determination of Loads, The first step in the calculatior of a beam or girder is to determine the exact amount of load to be carried, and its distribution. Loads may be uniformly distributed or concentrated, or both in combination. The case of a simple floor or roof beam usually involves only the calculation of the area carried and the load per square foot. The load per square foot is made up of two parts - namely, dead load, or the weight of the construction; and live load, the superimposed load. The latter is generally specified by law, as noted previously under "Building Laws and Specifications."

The calculation of the dead load has to be made in detail to fit each case. In the case of a floor beam this would consist of the arch between the beams, the steel beams and girders, the filling on top of the arch, the wood or other top flooring, the ceiling, and the partitions. These weights cannot be accurately determined until the spacing and size of beams are fixed; so their features have to be assumed at first. The process in general is illustrated by the following case:

Assume a terra cotta arch 8 inches deep, beams spaced about 5 feet center to center, 3 inches of filling and screeds on top of the arch, a 7/8-inch hemlock under floor, and a l 1/8-inch oak top floor. The weights then are as follows:

8-in. arch

30

lbs.

Steel = 18/5 = 3.6, or say

=

4

,,

Filling = 3 x 5

=

15

,,

7/8-in. floor = 7/8 x 2, say

=

2

,,

1 1/8 -in. top = 1.125 X 3.67, say

=

4

,,

Ceiling (no furring)

=

7

,,

Partition = 32 x 10/5

=

64

,,

Total Dead Load

126

lbs.

The calculation of the dead weight per square foot of partitions is made up of the weight of blocks, if of terra cotta, and of the plastering on both sides. If the structure is of wire lath, the weight is that of the framing and plastering. These weights per square foot have already been given in the chapter on Fire-proofing.

Only the height of the story is used, as the partition stops at the ceiling. In the above case it is assumed that the partition may go anywhere, and therefore, in some cases, may come directly over a beam, thus being entirely carried by it. If the partitions are in general located so as to come between beams, and no provision is desired for other possible locations, the above partition load might be reduced one-half, as a partition would then be carried by two beams. Or if the partitions came only over girders, the load might be omitted entirely in the calculation of the beams.

In the above total dead load, it should be noted that the allowance for steel does not include the weight of girders. This of course should not be included for the beams. In the calculation of the girders the weight of the girder itself should be added.

The calculation of dead load cannot be absolutely exact, any more than can the determination of the exact amount of live load that will have to be carried. It should always, however, be worked out in detail as above, so that as close an approximation as possible shall be made.

Tables XIV and XVI, of Part I, and Table XVII, Part II, give the weights of different materials and forms of construction, for use in determination of dead loads under different conditions.

The floor arch is assumed to carry all its load vertically to the beams, and the load therefore is the product of the area and the load carried per square foot. This neglect of thrust from the arch is on the safe side as regards the determination of amount of load on the beam.

Distribution of Loads. The load on a girder is generally concentrated at one or more points, and involves the calculation of the reactions from the beams. Girders therefore, as a general thing, are not calculated until after the beams. A girder may also have a uniform load from one side, or from a partition or wall,

Table XVII. Weights Of Various Substances And Materials Of Construction

SUBSTANCE.

AVERAGE WEIGHT IN POUNDS PER CUBIC FOOT.

Aluminum

162

Ash

38

to

47

Asphaltum

62

to

112

Brass (cast)

490

to

525

Brick

100

to

150

Brickwork

100

to

140

Cement, Portland

80

to

110

Cement, Rosendale

55

to

65

Cherry

42

Chestnut

41

Clay, Potter's, dry

112

to

143

Clay, in dry lumps

65

Coal - Anthracite

52

to

60

Coal - Bituminous

47

to

52

Coke

23

to

32

Concrete-Stone and Portland cement

140

Concrete - Cinders and Portland cement

96

Copper, cast

542

Copper, rolled

555

Cypress

64

Earth - Common loam, dry and loose

72

to

80

Earth - Common loam, dry and rammed

90

to

100

Earth - Common loam, soft-flowing mud

110

to

120

Elm

35

Gneiss, common

168

Gneiss, in loose piles

96

Gold, cast pure or 24 karat

1,204

Gold, pure-hammered

1,217

Granite

160

to

178

Gravel

90

to

130

Hemlock

25

SUBSTANCE.

AVERAGE WEIGHT IN POUNDS PER CUBIC FOOT.

Hickory

53

Iron,cast

450

Iron, wrought

480

Lead, commercial

710

Limestone

153

to

178

Lime, quick

95

Mahogany

35

to

53

Marble

158

to

180

Masonry, granite or limestone, dressed

165

Masonry, granite or limestone, rubble

154

Masonry, granite or limestone, dry rubble

138

Masonry, sandstone 1/8 less than above

Mortar, hardened

87

to

112

Oak, live

60

Oak, white

47

Oak, red

32

to

45

Pine, white

25

Pine, yellow Northern

34

Pine, yellow Southern

45

Poplar

29

Platinum

1,342

Quartz

165

Sand

90

to

130

Snow, freshly fallen

5

to

12

Snow, moist compacted

15

to

50

Slate

175

Spruce

25

Steel

490

Sycamore

37

Tar

62

Terra Cotta

106

Terra Cotta masonry

112

Tin, cast

459

Note. Where weights of wood are given above they are for perfectly dry wood. Green timbers weigh from one-fifth to one-half more than dry, ordinary building timbers, one-sixth more than dry.

thus bringing sometimes very unsymmetrical loading. Openings also affect the distribution of loading on a beam or girder.

Stairs should be figured as fully loaded with the assumed live load and the dead weight of their own construction, and as being supported by the girder on which they rest. In the case of very heavy live loads, as in warehouses, the customary live load in office buildings could be used in determining the load for stairs.

If the framing plan is drawn accurately to scale, the position of concentrated loads can be determined by scaling. In the case of short girders with heavy loads, however, a slight error in determining the position of loads would appreciably affect the result; hence it is necessary to exercise caution in scaling the position, to avoid any chance of great variation from true measurement.

Beams and girders carrying elevator machinery should have the loads and their position determined with special care. To this end the layout of the company installing the machinery should always be used in final calculation. This layout gives the loads at the different points; and therefore the exact position on the supporting beams, and the reaction on the girders, can be determined. As elevators are liable to cause a shock in sudden starting and stopping, it is customary to multiply the total load by two to allow for this shock.

In the calculation of the girder the laws of some cities allow a reduction amounting to a certain percentage of the live load, on the assumption that the whole area adjacent to a girder is not likely to be loaded to its maximum at the same time. This, however, should not be done in warehouses, nor where on the other hand the assumed loads are very light; and in any case it should be done with discretion.

Lintels. The size and character of lintel beams depends (1) on load to be carried, (2) on arrangement of openings over beams. (3) on practical considerations of construction.