REENFORCED CONCRETE 



159 



2. A standard mixture for reenforced floors, beams, and columns, 

 for arches, for reenforced engine or machine foundations subject to 

 vibrations, and for tanks, sewers, conduits, and other water-tight 

 work. Proportions 1:2:4; that is, one barrel (4 bags) of packed 

 Portland cement to two barrels (7.6 cu. ft.) of loose sand to four 

 barrels (15.2 cu. ft.) of loose gravel or broken stone. 



3. A medium mixture for ordinary machine foundations, re- 

 taining walls, abutments, piers, thin foundation walls, building 

 walls, ordinary floors, sidewalks, and sewers with heavy walls. Pro- 

 portions 1 : 2i : 5 ; that is, one barrel (4 bags) of packed Portland 

 cement to two and one half barrels (9.5 cu. ft.) of loose sand to 

 five barrels (19 cu. ft.) of loose gravel or broken stone. 



4. A lean mixture for unimportant work in masses, for heavy 

 walls, for large foundations supporting a stationary load, and for 

 backing for stone masonry. Proportions 1:3:6; that is, one barrel 

 (4 bags) of packed Portland cement to three barrels (11.4 cu. ft.) of 

 loose sand to six barrels (22.8 cu. ft.) of loose gravel or broken stone. 



95. Design of reenforced concrete beams. Since concrete is a mate- 

 rial which does not conform to Hooke's law and moreover does 

 not obey the same elastic law for tension as for compression, the 

 exact analysis of stress in a plain or reenforced concrete beam would 

 be much more complicated than that obtained under the assump- 

 tions of the common theory of flexure. The physical properties of 

 concrete, however, depend so largely on the quality of material and 

 workmanship, that for practical purposes the conditions do not war- 

 rant a rigorous analysis. The following simple formulas, although 

 based on approximate assumptions, give results which agree closely 

 with experiment and practice. 



Consider first a plain concrete beam, that is, one without reen- 

 forcement. The elastic law for tension is in this case (see Fig. 108) 



and for compression *- = E c . 



c 



To simplify the solution, however, assume the straight-line law of 

 distribution of stress ; that is, assume m 1 = m z = 1. Note, however, 



