SLABS, CROSS-BEAMS, AND GIRDERS 157 



lever. Angles, such as those between the flange and the stem, are always 

 a source of weakness and it is good practice to bevel off the corners of 

 the forms, as shown. 



62. Beams with Steel in Top and Bottom. Compressive stresses 

 are generally carried by concrete more economically than by 

 steel. It is sometimes desirable, however, to place steel in the 

 compression as well as in the tension side of the beam. When a 

 rectangular beam is limited as to size, double-reinforcement is 

 sometimes the result, and in such cases the value of the steel 

 reinforcement on the compressive side needs to be known. 

 The effectiveness of steel in compression has sometimes been 

 questioned, but the results of tests indicate that the steel does 

 its share of the work. 



Double-reinforcement is more commonly met with at the sup- 

 ports of continuous T-beams. At such places the bending mo- 

 ment is negative, the flange is under tension and is reinforced, 

 and the lower part of the web is under compression. Also some 

 of the center span steel is carried horizontally into the support 

 and may be figured with the concrete to assist it in taking com- 

 pression provided, of course, that its length beyond the center of 

 support is sufficient to provide bond. A continuous beam at the 

 supports is consequently double-reinforced, and the case is simi- 

 lar to double-reinforcement at the center of a span with the 

 exception that the compressive and tensile stresses about the 

 neutral axis are inverted. 



A great deal of care is necessary in designing the supports 

 of continuous beams. Many concrete buildings have been built 

 with insufficient steel through the top of the supports to take the 

 tension and insufficient concrete, or concrete and steel, at the 

 bottom of beams at such points to take the compression. With 

 such designs, large cracks have occurred at the supports. 



The formulas which are used in the design of double-reinforced 

 rectangular beams are derived by means of the same fundamental 

 principles as already explained for beams with single reinforce- 

 ment. The derivation of these formulas will not be given since 

 the method followed is similar to that already outlined in Art. 33. 



In deriving the following formulas the compression in the con- 

 crete is assumed to follow the linear law and the tension in it is 

 neglected; the formulas then apply to working conditions only. 



