If a minimum quantity of lumber is to be used consistent with the deformation allowed, it follows that the dimensions and spacing of the supporting lumber must be actually com puted from the weight or pressure against the sheeting. For columns and for walls where a considerable height of wet concrete is to be placed at once, the pressure may be calculated as a liquid. Mr. W. J. Douglas assumes that the concrete is a liquid of half its own weight, or 75 pounds per cubic foot.
In ordinary walls, where the concrete is placed in layers, computation is not usually nec essary, since general experience has shown that maximum spacing for 1-inch boards is 2 feet, for plank is 4 feet, and for 2-inch plank is 5 feet. Studding generally varies from 3 by 4 inch to 4 by 6 inch, according to the character of the work and the distance between the horizontal braces or waling, 4 by 4 inch being the most useful size.
Floor forms are better based upon an allow able deflection than upon strength, in order to give sufficient stiffness to prevent partial rup ture of the concrete or sagging beams.
In calculating we must add to the weight of the concrete itself—that is, to the dead load—a construction live load which may be assumed as liable to come upon the concrete while setting. Definite units of stress must also be assumed in the lumber.
We would suggest the following basis for computation, these being values which have been adopted for use: (1) Weight of concrete, including reinforcement, 154 lbs. per cu. ft.
(2) Live load, 75 lbs. per sq. ft. upon slab, or 50 lbs. per sq. ft. in figuring beam and girder forms.
(3) For allowable compression in struts, use 600 to 1.200 lbs. per sq. in., varying with the ratio of the size of the strut to its length. (See table below.) If timber
beams are calculated for strength, use 750 lbs. per sq. in. extreme transverse fiber stress.
(4) Compute plank joists and timber beams by the following formula, allowing a maximum deflection of N inch : 3W1 384E1 (1) and, --- (2) 12 in which, d=Greatest deflection in inches; W=Total load on plank or timber ; 1=Distance between supports in inches; E=Modulus of elasticity of lumber used; I=Moment of inertia of cross-section of plank or joist; b=Breadth of lumber; h=Depth of lumber.
The formula is the ordinary formula for cal culating deflection except that the coefficient is taken as an approximate mean between for a beam with fixed ends, and for a beam with ends simply supported.
For spruce lumber and other woods com monly used in form construction, E may be as sumed as 1,300,000 lbs. per sq. in.
Formula (1) may be solved for I, from which the size of joist required may be readily estimated.
The weight of concrete per cubic foot is some what higher than is frequently used, but is none too much where a dense mixture and an ordinary percentage of steel is used. For very rot gh cal culation, however, it is frequently convenient to remember that 144 lbs. per cubic foot is equiva lent to the product of the dimensions of the beam in inches times a length of one foot.
The suggested live load is assumed to include the weight of men and barrows filled with con crete, and of structural material which may be piled upon the floor, not including, however, the weight of piles of cement or sand or stone, which should never be allowed upon a floor unless it is supported by concrete sufficiently strong to bear the weight, or by struts under all the floors below.
The units for stress in struts are somewhat higher than in timber construction, because the load is a temporary one. The extreme variation given is due to the fact that when a column or strut is longer than about sixteen times its smallest width there is a tendency to bend, which must be prevented either by bracing it both ways or by allowing a smaller load per square inch. For struts ordinarily used, the stresses given in Table I may be assumed for different heights.