While the concrete and imbedded steel beams in a footing are undoubtedly much stronger than the simple beams, it is not customary to figure the beams in such cases by the theory applying to steel imbedded simply in the tension side of concrete. Footings of this character are employed sometimes and their design will be taken up later.

Cantilever Foundations. The case of cantilever construction supporting a party wall is illustrated in Fig. 155. Let P be the wall column load, a the distance in feet from wall column to the pin bearing forming the fulcrum, and b the distance in feet from fulcrum to column at opposite end of cantilever. Then the load on fulcrum is P (a+b)/b. The distance a should be taken so that the fulcrum can be at the center of the footing and still keep within the party lines. Sometimes this cannot be done, and then the footing has to be designed to take account of this eccentricity of bearing. The cantilever is designed by determining the maximum moment and shear. The maximum moment in the above case is at the fulcrum and is Pa in foot pounds. In case the girder is a riveted girder, as is often the case, other features must be considered in its design, as will be explained later.

Fig 155.

In case the cantilever is in the floor, as it sometimes is, as shown by Fig. 156, and in addition to the wall column, carries a floor load, then the position of maximum moment must be determined in a manner similar to that explained for combined footings. The connection of the cantilever at the interior column must be designed to resist this upward tendency and in case the reaction from the dead-wall load is greater than the dead load carried by this column the cantilever arm should be extended to the next column so as to decrease this reaction; or the column must be anchored and all connections designed to resist this upward reaction.

Fig. 156.

Fig. 156 shows also a steel concrete retaining wall to hold up the earth under an adjoining building which foots some distance above the new foundations.

Fig. 157 illustrates the case of a party wall foundation designed to carry a future wall column for the adjoining building and the column of the present building. The eccentricity of bearing is shown in this case, and this and the necessity of spreading in the direction of the wall rather than across it are the important features.

PLAN OF FOOTINGS AT CORNER UNDER CORNER COLUMN AND OLD WALL. Fig. 157.

The matter of design of foundations is one always requiring accurate knowledge of the special conditions incident to the problem and the nature of the soil, and is largely influenced by practical considerations and the judgment of the designer. It is not safe to lay down any fixed values to be followed in all cases. Foundations in soil which are at all questionable, should never be designed except by an expert, who is capable of judging the extent to which the ordinary methods of procedure must be modified.

Retaining Walls are walls built to resist the thrust of earth pressure. These walls may also be bearing walls for loads above. The pressure of earth tends to cause failure of the wall in the following ways:

(1). To slide on its base.

(2). To slide on some horizontal joint.

(3). To overturn bodily.

(4). To fail by buckling.

To resist the tendency to slide on its base, the dead weight of the wall, or of the wall and the load it carries, must be sufficient to resist the horizontal pressure without exceeding the coefficient of friction between the material of the wall and the surface upon which it rests.

To resist the second tendency the weight above any joint must be sufficient to resist the pressure above the joint without exceeding the coefficient of friction of masonry upon masonry.

The overturning moment of the earth pressure about the edge of rotation must be balanced by the moment of the weight of the wall and of the superimposed load about the same edge.

The fourth condition applies only to retaining walls supported at their tops and built generally of concrete and steel. A retaining wall so supported would have to resist tension in one side and, as a masonry joint is not intended to resist tension, such construction involves the use of steel. Such construction is becoming more common on account of the saving in space due to the thinness of the wall. In Fig. 156 is shown such a wall. The tensile strength is supplied by the beams running horizontally and the twisted vertical rods.

The resulting pressure due to the thrust of the earth and the weight of wall and superimposed load must fall within the base in order to give equilibrium, and within the middle third of the base to avoid tension on the masonry joints. Figs. 158-159 show types of retaining walls.

Fig. 158.

F,g 159.

Underpinning Shoring and Sheath Piling. Underpinning is the term given to the processes of carrying down old foundations or walls adjacent to new construction to the level of the new construction.

It very often happens that footings of new buildings will be twenty or thirty feet below the bottom of the footings of the walls of an adjacent old building. To leave the old footings at this higher level after the excavation of the new building is made, would necessitate making the wall heavy enough to act as a retaining wall, to resist the pressure on the soil back of it. It is generally more practicable, therefore, to hold up the old wall temporarily by timber braces, needles, wedges, etc., and build new work up under it from the level of the footings of the new buildings. This new foundation under the old wall is called underpinning, and the construction necessary to hold it in place, during the process of underpinning, is called shoring. This latter term applies to all bracing of old walls or adjacent construction during the construction of the new work, whether the wall is underpinned or not.

Where a mass of earth is to be held in place to enable new excavation to be made without disturbing it, heavy planks set edge to edge are driven down as the excavation proceeds, and braced at intervals by breast pieces or heavy timbers to keep the plank from bulging under the pressure of the earth. This construction is called sheath piling. The planks, generally, are pulled out after the wall, which is designed to permanently hold the earth in place, is built; sometimes, however, it is left in place.