160 REINFORCED CONCRETE CONSTRUCTION 



forced rectangular beam at the center of span. It should be 

 noticed that the Joint Committee allows a higher compression 

 in the concrete at the supports than at the middle of the beam, 

 because of the fact that the negative moment decreases very 

 rapidly and only a short section is under maximum stress. Also, 

 a slight excess of stress at this point does not in any way en- 

 danger the structure but merely increases somewhat the positive 

 moment on the beam. A unit stress of 750 Ib. per square inch 

 is permitted. (See Art. 40.) 



There are three methods of reducing the compressive stress 

 in the concrete at the bottom of the beam over supports: (1) 

 by increasing the amount of compressive steel in the bottom 

 of the beam; (2) by increasing the area of compressive concrete, 

 which may or may not require a flat haunch depending upon 

 the width of the support; and (3) by increasing the areas of 

 both steel and concrete. In any case the increase must be 

 made by trial. If the plan is to deepen the beam appreciably, 

 thus forming a flat haunch, the new depth at the support must 

 be chosen arbitrarily and the formulas for double-reinforced 

 rectangular beams should be employed in order to determine if 

 the new fiber stresses are satisfactory. 



Under ordinary conditions the computations for a uniformly 

 loaded beam need be made only at one point that is, at the sup- 

 port since the point to end the slope can be approximately 

 figured by the following formula from Taylor and Thompson: 1 



_l M 2 -M l 

 in which ~5 M 2 



M 2 = negative bending moment at the support. 

 M l = moment of resistance of the inverted T-beam with- 

 out the haunch, governed by the concrete. 



x = length of haunch. 



/ = span of beam. 



The above formula is approximate (but sufficiently accurate 

 for this work) due to the fact that the point of zero bending 

 moment is considered to occur at a distance from the support 

 equal to one-fifth the span. By similar triangles (Fig. 77) 



5 



The bond stress along the horizontal rods at the top of a 

 continuous beam over supports may be found by the same 



1 From Taylor and Thompson's " Concrete, Plain and Reinforced," 2nd edition, page 430. 

 Copyright, 1905, 1909, by Frederick W. Taylor. 



