Under the load of 300,000 pounds, I e should be 210 in 3, and two 20-inch 65-pound I-beams may be used.
The lower tier of beams carries two loads of 400,000 and 300,000 pounds respectively, acting downward upon its upper surface, each distributed over 2.5 feet as shown, and a load of 4000 pounds per square foot uniformly distributed over its lower surface. There are sections of maximum moment under each load and at some point between them. These sections are where the shear passes through zero. Let y=distance from end of beam to section. Under the heavier load, the shear is The greatest moment is 300,000 lb.-ft. or 3,600,000 lb.-in., and the required I'e is 3,600,000/16,000=225 Eleven 6-in. 12.25-pound I-beams, I/e = 21.8 each, flange 3.33 inches wide, clearance 8.4 inches may be used. Three or four additional beams may be introduced if thought desirable to reduce the clearance. If this is not done, light transverse reinforcement might be placed in the concrete covering the beams.
The moments might be somewhat decreased and the positive and negative moments made more nearly equal by making the foundation narrower upon the end carrying the smaller load and widening the other end. The same steel area would then be needed at both ends and the spaces between the beams would widen from one end to the other.
It may frequently be convenient to carry three or more piers or columns upon one grillage. In such a design, the line of action of the resultant of all the loads must pass through the center of area of the grillage. Two loads are usually carried upon one set of the upper tier of beams, which is arranged to give uniform loading to the tier below at right angles to it.
Timber grillages may be employed where the footing is so located as to be continually wet. They are also commonly used for tem porary footings which are to be removed in a comparatively short tine. These foundations are usually constructed by placing a layer of 2-inch planks on the bed to be occupied by the footing and across these one or more series of timbers in the same manner that the I-beams are used in the steel grillages. The timbers must be capable of carrying the bending moments due to transmitting the loads from the walls or piers to the soil upon which the footing rests.
On top of the grillage a floor, usually of 3-inch plank, is placed to carry the base of the masonry. All timber in such foundations must be kept below low water and the spaces between the timbers should be filled with sand or broken stone.
191. Reinforced Concrete Footings.—Reinforced concrete slabs are ordinarily used as footings for the distribution of loads in spread foundations. When used under walls, these consist of a cantilever projecting on each side of the wall; the determination of thickness and amount of reinforcement is made as for a simple cantilever. When used under columns or piers, the load may be transmitted to the slab through beams, or flat slabs with two-way or four-way reinforcement may be employed.
When beams are used, the moments may be computed by the methods used for I-beam grillages and reinforced concrete beams and slabs with one-way reinforcement designed to resist these moments in the usual manner. If the construction is monolithic, the maximum stresses occur in the sections where the slabs join the beams and in the beams where they join the base of the pier. The stresses in such foundations may be ac curately computed in so far as the loads are known, and they are not subject to the assump tions required in the flat-slab computations. Usually these footings are cheaper in cost of materials than flat-slab foot ings, but require more form work in construction.
In a flat-slab footing with two-way reinforcement, the maximum moment in the slab occurs in the sections through the face of the pier. In the footing shown in Fig. 107, it is assumed that the section through each face carries the moment between that face and the side of the footing. Thus, the moment of the upward pressures on the area A BCD is supposed to he borne by the section C—D. These moments are not uniformly distributed over the section, but must be greater in the portion between C and D than in its ends. From experiments made at the University of Illinois, Professor Talbot concludes that "For footings having projections of ordinary dimen sions, the critical section for the bending moment for one direction I Bulletin No. 67, Engineering Experiment Station, Univ. of I11.