The size of floor-beams can be ascertained by the preceding rules for the stiffness of materials. These rules give the required dimensions for the various kinds of material in common use. The rules may be somewhat abridged for ordinary use, if some of the quantities represented in the formula be made constant within certain limits. For example, if the load per foot superficial upon the floor be fixed, and the deflection, then these, together with the constant represented by F, may be reduced to one constant. For dwellings, the load per foot may be taken at 70 pounds, the weight proper to be allowed for a crowd of people on their feet. (Transverse Strains, Art. 114.) To this add 20 for the weight of the material of which the floor is composed, and the sum, 90, is the value of f, or the weight per foot superficial for dwellings. Then c f l - U(Art. 130). The rate of deflection allowable for this load may be fixed at 0.03 inch per foot of the length, or δ = 0.03 l. Substituting these values in equation (35.), we obtain -

bd3 = cfll3 = 90 cl3 =1875 cl3/F,

1.6 Fx.03l 1.6x.03F

or -

bd3=1875/F cl3, (43.)

Putting j to represent 1875/F, we have-

bd3=jcl3. (44.)

Now, by reducing 1875/F, for the six woods in common use, the value of j for each is found as follows:

 Georgia Pine................................................................................... j = 0.32 Locust............................................................................................. j = 0.37 White Oak............................ j = 0.6 Spruce................................................................................................. j = 0.54 White Pine........................... j = 0.65 Hemlock.......................................................................................... j = 0.67

Equation (44.) is a rule for the floor-beams of dwellings; it may be used also to obtain the dimensions of beams for stores for all ordinary business. for it will require from 3 to 5 times the weight used in this rule, or from 200 to 400 (average 300) pounds to increase the deflection to the limit of elasticity in beams of the usual depths and lengths. For light stores, therefore, loaded, say, to 150 pounds per foot, the beams would be safe, but the deflection would be increased to 0.06 per foot. When so great a deflection as this. would not be objectionable to the eye, then this rule (44.) will serve for the beams of light stores. But for first-class stores, taking the rate of deflection at .04 per foot, and fixing the weight per superficial foot at 275 pounds, including the weight of the material of which the floor is constructed, and letting k represent the constant, then -

bd2=kcl3 (45.)

and for -

 Georgia Pine.................................................................................... k = 0.73 Locust............................................................................................... k = 0.85 White Oak........................... k = 1.38 Spruce............................... k = 1.48 White Pine.......................... k = 1.23 Hemlock............................. k = 1.53