The location and position of the main interior columns having thus been fixed, the next thing is to locate any columns whose position is dependent on special features.

In this case, the corridor arrangement along the side E F at the end near D E makes it necessary to place this column out of the line of the others. On this account and to avoid excessive loads on the girder framing into this column, an extra column is put in the partition between toilet and vent at this end.

In the exterior walls, columns of course have to be placed at each corner and also at the angles in the side A B C D. The other exterior columns naturally are placed at the intersections of office partitions with exterior walls, because here the piers in the walls will be the widest. The distance from the ashlar line to the center of wall columns will vary in accordance with the architectural details Where should never be less than four inches of masonry outside of the extreme corner of column, and, if possible, there should be more.

Typical Floor Framing, Fig 44.

Typical Floor Framing, Fig 44.

The Steel Frame Continued 050072

Better protection is given the steel if the web is parallel with the face of the wall. Where the spandrel beams and lintels are very eccentric, however, this position results in an uneconomical section, since the weakest axis of the column is thus exposed to the greatest bending. Some designers, however, prefer to sacrifice economy in this regard to more efficient protection of the metal.

The columns thus having been placed according to the arrangement of the typical floor plan, the next step is to see if any changes are necessary to suit the conditions of the floors that differ from this plan, namely, the basement and the first floor. From a glance at the plan of the first floor, it will be seen that two of the columns come down in the main entrance in such position as to obstruct the passageway. It would be possible to change the position of these columns and make them conform to the first floor partitions. The results in the floors above, however, would not be so good, and therefore additional columns will be provided, supporting girders at the second-floor level to carry the columns above. A similar provision must be made for the wall column over the entrance.

The position of the columns thus having been determined, the girders follow by joining the centers of columns. The spacing of the beams will be determined largely by the system of floor arch to be used, except that, unless entirely impossible, a beam should come at each column in order to give lateral stiffness to the frame. If a terra cotta arch is to be used, the spacing should not be much over six feet at the maximum, and an arrangement such as shown would result. If a system of concrete arches is to be adopted, in which spans of eight or nine feet can be safely used, the beams between the two lines of girders on each side of the corridors may be omitted.

Certain other points should be noted in regard to this framing plan, as follows:

Columns should not be put at the front of elevators, as they cannot be fireproofed without interfering with the clear space of shaft.

Beams, if possible, should always be framed at right angles to girders, as oblique connections are expensive.

Beams should not frame off center of column if a little change in either column or beam can obviate it.

Columns on adjacent and parallel lines should, as far as possible, be opposite each other; that is, a beam framed to the center of one column should also meet the center of the next line of columns.

Spacing and 6pans of beams should be such as to develop their full strength.

Fig. 45 shows the wall sections and the resulting spandrel sections and wall girders. Not all the points that arise in such a framing can here be brought out; but from the foregoing the general method of treatment of such problems should be clear.

In buildings of a different character, many different and often more complex conditions will arise. The student, however, must always bear in mind that it is the duty of the designer to grasp fully the architect's details, and so to arrange his framing as to conform in all respects thereto, unless such details can themselves be changed more readily and to better advantage. It is essential for the designer to see not only what has already been determined, but what details will result when certain features are fully worked out; and in all his work the economy of design and framing, and the efficiency of the framework, should be kept constantly in mind.

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 throughout 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.

The Steel Frame Continued 050073

Fig. 45.

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, affecting 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 determined 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 compression 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 3/4 inch diameter. An approximate determination of the required size can be made by use of the following formula giving the thrust from floor arches:

T= 3 W L2 / 2R where T = thrust in pounds per linear foot of arch,

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. Dividing 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 certain size rod, or by the limit of twenty times the flange width.