268 PRACTICAL STRUCTURAL DESIGN 



Each load is assumed to be concentrated at the center of gravity 

 of each strip and the projection y is assumed to be the length of 

 a cantilever beam. The moment across the beam on the lines 

 bi, ch, dg, and ef, can be readily ascertained and the shears can 

 also be found on these lines. In this example we are assuming a 

 reinforced concrete beam. The thickness of the footing on each 

 line can be found in the usual way for the design of a concrete 

 beam, or slab, both for bending stress and for shear. The steel 

 may be proportioned and the logical method for arranging the 

 steel would be to have it in four layers, two normal to the sides 

 of the slab and two diagonal, as indicated by the dotted lines in 

 the lower part of Fig. 173. 

 Another method, used by the author, is to take the expres- 



Wy 



sion M = -j^> used for wall footings, and assume that the foot- 

 ing being square and there being eight projections instead of two, 



Wv 

 the expression should be M = -~> and use this moment to design 



a reinforced concrete beam having a width equal to the column 

 base on top of the footing. The beams are considered as being 

 so arranged that two are normal to the sides of the footing and 

 two are diagonal. They are designed as reinforced concrete beams 

 and as merged so that while each layer of steel carries the tension 

 for the beam it represents, the concrete is stressed in compression 

 from all directions, which makes it safe and increases its resist- 

 ance to shear. 



Reinforced concrete footings may be stepped or sloped on top. 

 If sloped the forms must be well anchored down, for the con- 

 crete will have a tendency to cause them to float. The author 

 obtained the best results with concrete footings by stepping them. 

 The steps are formed by frames of boards. The first step is cast 

 to the proper level and the frame for the next step placed on it, 

 when it becomes firm enough to carry the weight of the next step 

 without bulging up around the edges of the form. If the con- 

 crete is mixed to the proper consistency there will never be any 

 trouble with this bulging and the steps can be poured quickly. 

 The proper consistency for concrete is that of a soft tooth paste. 

 It should never be thin enough to pour into a form. For rein- 

 forced concrete it should be thin enough to flow very sluggishly 

 so it will surround the reinforcement, but it should never be so 



