The framing shown for this building is more especially designed for concrete floor arches. In cases where terra cotta arches are used, a somewhat different arrangement of columns would probably be made.
In the framing of floors and roofs, it is not always advisable to use the exact sizes and weights of beams that are theoretically required ; there are often a number of practical considerations affecting the determination. As previously stated, standard sizes and weights should be used wherever practicable, as ordinarily these sizes are much more readily obtainable than others. If the general framing consists of standard sizes, and a few beams are so loaded as to require special sizes and weights, some change should if possible be made to avoid this, as to insist on the furnishing of a few beams of odd weights might cause serious delay in the delivery. In certain cases where it is of special advantage to make nearly all the beams of special weights, arrangements might be made for the delivery, provided the tonnage is large.
Beams, as far as possible, should be of the same size through out a given floor, since for a level ceiling different depths of beam would require furring, or extra filling, or special arches, Where girders of short span carry the ends of heavy beams or girders, it is sometimes necessary to use an uneconomical section in order to get a sufficient connection. For instance, a 10-inch beam might be strong enough to carry a 15-inch beam ; but the connection could not be made to a 10-inch beam, and therefore a larger sized beam or channel should be used. In general the girder should be of the same depth as the beam, or nearly so, unless the beam rests on top of the girder or is hung below it.
In some cases also — generally where small beams are used the standard end connections are not sufficient, and it may be necessary to use larger sizes.
Other special conditions of framing are likely to arise, affect ing the determination of sizes, so that the designer, in laying out the framing, should keep in mind the feasibility of making proper connections for framing the different parts.
When very heavy loads are carried by beams of short span, it is necessary to use a section that will have sufficient web area to prevent buckling. In such cases, the sizes of beams may be deter mined by this condition rather than by the bending moment caused by the loads. The tendency to cripple is greatest at the ends, and in order to determine the allowable fiber strain, a modification of the column formula as given below is applicable. The total shear should be considered to be carried by the web, and the combination of horizontal and vertical shear is equivalent to tension and compres sion forces acting at an angle of 45° with the axis of beam. The unsupported length in the formula, therefore, is the length between fillets on a line making 45° with the axis of beam.
Tie Rods. Tie rods should be spaced at distances not greater than twenty times the width of flange of floor beams.
The size of tie rods is generally inch diameter. An approxi mate determination of the required size can be made by use of the following formula giving the thrust from floor arches: W = load per square foot on arch, L = span of arch in feet, R = rise (in inches) of segmental arch, or effective depth of flat arch.* The spacing of the tie rods being known, the total strain on the rods is the thrust, as above, multiplied by the spacing. Divid ing this by the safe fiber strain of 15,000 lbs. per square inch, gives the net area of rods, or the area at the root of threads, and thus determines the diameter of the required rod.
The spacing of tie rods is generally determined by providing one or more lines dividing into equal spacing the length of beams between connections or walls. The number of lines is determined by the necessity of keeping the thrust within the capacity of a cer tain size rod, or by the limit of twenty times the flange width.